%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM859+1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:22:15 AM UTC 2025
% Result : Theorem 0.86s 1.04s
% Output : Proof 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : NUM859+1 : TPTP v9.0.0. Released v4.1.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 02:02:26 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.86/1.04 % SZS status Theorem
% 0.86/1.04 % SZS output start Proof
% 0.86/1.04 tff(model_max_type, type, (
% 0.86/1.04 model_max: ( $i * $i * $i ) > $o)).
% 0.86/1.04 tff(tptp_fun_Z_1_type, type, (
% 0.86/1.04 tptp_fun_Z_1: ( $i * $i * $i ) > $i)).
% 0.86/1.04 tff(tptp_fun_X_5_type, type, (
% 0.86/1.04 tptp_fun_X_5: $i)).
% 0.86/1.04 tff(max_type, type, (
% 0.86/1.04 max: ( $i * $i ) > $i)).
% 0.86/1.04 tff(tptp_fun_Y_4_type, type, (
% 0.86/1.04 tptp_fun_Y_4: $i)).
% 0.86/1.04 tff(tptp_fun_Z_3_type, type, (
% 0.86/1.04 tptp_fun_Z_3: $i)).
% 0.86/1.04 tff(lesseq_type, type, (
% 0.86/1.04 lesseq: ( $i * $i ) > $o)).
% 0.86/1.04 tff(model_ub_type, type, (
% 0.86/1.04 model_ub: ( $i * $i * $i ) > $o)).
% 0.86/1.04 tff(ub_type, type, (
% 0.86/1.04 ub: ( $i * $i * $i ) > $o)).
% 0.86/1.04 tff(tptp_fun_Z_0_type, type, (
% 0.86/1.04 tptp_fun_Z_0: ( $i * $i * $i ) > $i)).
% 0.86/1.04 tff(minsol_model_ub_type, type, (
% 0.86/1.04 minsol_model_ub: ( $i * $i * $i ) > $o)).
% 0.86/1.04 tff(minsol_model_max_type, type, (
% 0.86/1.04 minsol_model_max: ( $i * $i * $i ) > $o)).
% 0.86/1.04 tff(tptp_fun_Z_2_type, type, (
% 0.86/1.04 tptp_fun_Z_2: ( $i * $i * $i ) > $i)).
% 0.86/1.04 tff(1,assumption,(max(X!5, Y!4) = X!5), introduced(assumption)).
% 0.86/1.04 tff(2,plain,
% 0.86/1.04 (model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> model_ub(X!5, Y!4, max(X!5, Y!4))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1])).
% 0.86/1.04 tff(3,plain,
% 0.86/1.04 (model_ub(X!5, Y!4, max(X!5, Y!4)) <=> model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.86/1.04 inference(symmetry,[status(thm)],[2])).
% 0.86/1.04 tff(4,plain,
% 0.86/1.04 ((~model_ub(X!5, Y!4, max(X!5, Y!4))) <=> (~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[3])).
% 0.86/1.04 tff(5,assumption,(~model_ub(X!5, Y!4, max(X!5, Y!4))), introduced(assumption)).
% 0.86/1.04 tff(6,plain,
% 0.86/1.04 (~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.86/1.04 tff(7,plain,
% 0.86/1.04 (^[X: $i, Y: $i, N: $i] : refl((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))))),
% 0.86/1.04 inference(bind,[status(th)],[])).
% 0.86/1.04 tff(8,plain,
% 0.86/1.04 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.86/1.04 inference(quant_intro,[status(thm)],[7])).
% 0.86/1.04 tff(9,plain,
% 0.86/1.04 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))))),
% 0.86/1.04 inference(bind,[status(th)],[])).
% 0.86/1.04 tff(10,plain,
% 0.86/1.04 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.86/1.04 inference(quant_intro,[status(thm)],[9])).
% 0.86/1.04 tff(11,plain,
% 0.86/1.04 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[10, 8])).
% 0.86/1.04 tff(12,plain,
% 0.86/1.04 (^[X: $i, Y: $i, N: $i] : trans(monotonicity(rewrite(((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(tptp_fun_Z_0(N, Y, X), N))) <=> ((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))), rewrite((model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(Z, N)))) <=> (model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(tptp_fun_Z_0(N, Y, X), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(Z, N))))) <=> (((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))))), rewrite((((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(tptp_fun_Z_0(N, Y, X), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(Z, N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))))),
% 0.86/1.04 inference(bind,[status(th)],[])).
% 0.86/1.04 tff(13,plain,
% 0.86/1.04 (![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(tptp_fun_Z_0(N, Y, X), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(Z, N))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.86/1.04 inference(quant_intro,[status(thm)],[12])).
% 0.86/1.04 tff(14,plain,
% 0.86/1.04 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(Z, N))) <=> ![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(Z, N)))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(15,axiom,(![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(Z, N)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_ub_2')).
% 0.86/1.04 tff(16,plain,
% 0.86/1.04 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(Z, N)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.86/1.04 tff(17,plain,(
% 0.86/1.04 ![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(tptp_fun_Z_0(N, Y, X), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(Z, N)))))),
% 0.86/1.04 inference(skolemize,[status(sab)],[16])).
% 0.86/1.04 tff(18,plain,
% 0.86/1.04 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.86/1.04 tff(19,plain,
% 0.86/1.04 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.86/1.04 tff(20,plain,
% 0.86/1.04 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4))))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)))))))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(21,plain,
% 0.86/1.05 ((~((~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))))))) | (~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))))) <=> (~((~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4))))))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(22,plain,
% 0.86/1.05 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))))))) | (~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)))))))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[21])).
% 0.86/1.05 tff(23,plain,
% 0.86/1.05 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))))))) | (~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)))))))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[22, 20])).
% 0.86/1.05 tff(24,plain,
% 0.86/1.05 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))))))) | (~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(25,plain,
% 0.86/1.05 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4))))))))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.86/1.05 tff(26,plain,
% 0.86/1.05 (~((~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)))))))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.86/1.05 tff(27,plain,
% 0.86/1.05 (((~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~((~lesseq(tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4)), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(max(X!5, Y!4), Y!4, max(X!5, Y!4))))))))) | (model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))),
% 0.86/1.05 inference(tautology,[status(thm)],[])).
% 0.86/1.05 tff(28,plain,
% 0.86/1.05 (model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.86/1.05 tff(29,plain,
% 0.86/1.05 (lesseq(max(X!5, Y!4), max(X!5, Y!4)) <=> lesseq(X!5, X!5)),
% 0.86/1.05 inference(monotonicity,[status(thm)],[1, 1])).
% 0.86/1.05 tff(30,plain,
% 0.86/1.05 (lesseq(X!5, X!5) <=> lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.86/1.05 inference(symmetry,[status(thm)],[29])).
% 0.86/1.05 tff(31,assumption,(~lesseq(X!5, X!5)), introduced(assumption)).
% 0.86/1.05 tff(32,plain,
% 0.86/1.05 (^[X: $i, Y: $i] : refl((lesseq(X, Y) | lesseq(Y, X)) <=> (lesseq(X, Y) | lesseq(Y, X)))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(33,plain,
% 0.86/1.05 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[32])).
% 0.86/1.05 tff(34,plain,
% 0.86/1.05 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(35,axiom,(![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lesseq_total')).
% 0.86/1.05 tff(36,plain,
% 0.86/1.05 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.86/1.05 tff(37,plain,(
% 0.86/1.05 ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.86/1.05 inference(skolemize,[status(sab)],[36])).
% 0.86/1.05 tff(38,plain,
% 0.86/1.05 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.86/1.05 tff(39,plain,
% 0.86/1.05 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5)) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(40,plain,
% 0.86/1.05 ((lesseq(X!5, X!5) | lesseq(X!5, X!5)) <=> lesseq(X!5, X!5)),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(41,plain,
% 0.86/1.05 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[40])).
% 0.86/1.05 tff(42,plain,
% 0.86/1.05 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5))),
% 0.86/1.05 inference(transitivity,[status(thm)],[41, 39])).
% 0.86/1.05 tff(43,plain,
% 0.86/1.05 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, X!5) | lesseq(X!5, X!5))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(44,plain,
% 0.86/1.05 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, X!5)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.86/1.05 tff(45,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[44, 38, 31])).
% 0.86/1.05 tff(46,plain,(lesseq(X!5, X!5)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(47,plain,
% 0.86/1.05 (lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[46, 30])).
% 0.86/1.05 tff(48,assumption,(![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))), introduced(assumption)).
% 0.86/1.05 tff(49,assumption,(lesseq(max(X!5, Y!4), max(X!5, Y!4))), introduced(assumption)).
% 0.86/1.05 tff(50,assumption,((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))), introduced(assumption)).
% 0.86/1.05 tff(51,assumption,(lesseq(Y!4, X!5)), introduced(assumption)).
% 0.86/1.05 tff(52,plain,
% 0.86/1.05 (^[X: $i, Y: $i] : refl(((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(53,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[52])).
% 0.86/1.05 tff(54,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(55,plain,
% 0.86/1.05 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = X) | (~lesseq(Y, X))) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(56,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X))) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[55])).
% 0.86/1.05 tff(57,axiom,(![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_1')).
% 0.86/1.05 tff(58,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.86/1.05 tff(59,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.86/1.05 tff(60,plain,(
% 0.86/1.05 ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.86/1.05 inference(skolemize,[status(sab)],[59])).
% 0.86/1.05 tff(61,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.86/1.05 tff(62,plain,
% 0.86/1.05 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(63,plain,
% 0.86/1.05 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(64,plain,
% 0.86/1.05 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.86/1.05 tff(65,plain,
% 0.86/1.05 ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[64, 61])).
% 0.86/1.05 tff(66,plain,
% 0.86/1.05 (max(X!5, Y!4) = X!5),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[65, 51])).
% 0.86/1.05 tff(67,plain,
% 0.86/1.05 (lesseq(X!5, max(X!5, Y!4)) <=> lesseq(X!5, X!5)),
% 0.86/1.05 inference(monotonicity,[status(thm)],[66])).
% 0.86/1.05 tff(68,plain,
% 0.86/1.05 (lesseq(X!5, X!5) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.86/1.05 inference(symmetry,[status(thm)],[67])).
% 0.86/1.05 tff(69,plain,
% 0.86/1.05 (lesseq(X!5, max(X!5, Y!4))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[46, 68])).
% 0.86/1.05 tff(70,plain,
% 0.86/1.05 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(Y!4, X!5)),
% 0.86/1.05 inference(monotonicity,[status(thm)],[66])).
% 0.86/1.05 tff(71,plain,
% 0.86/1.05 (lesseq(Y!4, X!5) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(symmetry,[status(thm)],[70])).
% 0.86/1.05 tff(72,plain,
% 0.86/1.05 (lesseq(Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[51, 71])).
% 0.86/1.05 tff(73,plain,
% 0.86/1.05 ((~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4))))) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))),
% 0.86/1.05 inference(tautology,[status(thm)],[])).
% 0.86/1.05 tff(74,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[73, 72, 69, 50])).
% 0.86/1.05 tff(75,plain,((~lesseq(Y!4, X!5)) | (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(76,plain,
% 0.86/1.05 (~lesseq(Y!4, X!5)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[75, 50])).
% 0.86/1.05 tff(77,plain,
% 0.86/1.05 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, Y!4) | lesseq(Y!4, X!5))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, Y!4) | lesseq(Y!4, X!5))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(78,plain,
% 0.86/1.05 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, Y!4) | lesseq(Y!4, X!5))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(79,plain,
% 0.86/1.05 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, Y!4) | lesseq(Y!4, X!5)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.86/1.05 tff(80,plain,
% 0.86/1.05 (lesseq(X!5, Y!4)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[79, 38, 76])).
% 0.86/1.05 tff(81,plain,
% 0.86/1.05 (^[X: $i, Y: $i] : refl(((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(82,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[81])).
% 0.86/1.05 tff(83,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(84,plain,
% 0.86/1.05 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(85,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[84])).
% 0.86/1.05 tff(86,axiom,(![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_2')).
% 0.86/1.05 tff(87,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.86/1.05 tff(88,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.86/1.05 tff(89,plain,(
% 0.86/1.05 ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.86/1.05 inference(skolemize,[status(sab)],[88])).
% 0.86/1.05 tff(90,plain,
% 0.86/1.05 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.86/1.05 tff(91,plain,
% 0.86/1.05 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(92,plain,
% 0.86/1.05 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(93,plain,
% 0.86/1.05 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.86/1.05 tff(94,plain,
% 0.86/1.05 ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[93, 90])).
% 0.86/1.05 tff(95,plain,
% 0.86/1.05 (max(X!5, Y!4) = Y!4),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[94, 80])).
% 0.86/1.05 tff(96,plain,
% 0.86/1.05 (Y!4 = max(X!5, Y!4)),
% 0.86/1.05 inference(symmetry,[status(thm)],[95])).
% 0.86/1.05 tff(97,plain,
% 0.86/1.05 (lesseq(Y!4, Y!4) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[96])).
% 0.86/1.05 tff(98,plain,
% 0.86/1.05 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(Y!4, Y!4)),
% 0.86/1.05 inference(symmetry,[status(thm)],[97])).
% 0.86/1.05 tff(99,plain,
% 0.86/1.05 ((~lesseq(Y!4, max(X!5, Y!4))) <=> (~lesseq(Y!4, Y!4))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[98])).
% 0.86/1.05 tff(100,plain,
% 0.86/1.05 (lesseq(X!5, max(X!5, Y!4)) <=> lesseq(X!5, Y!4)),
% 0.86/1.05 inference(monotonicity,[status(thm)],[95])).
% 0.86/1.05 tff(101,plain,
% 0.86/1.05 (lesseq(X!5, Y!4) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.86/1.05 inference(symmetry,[status(thm)],[100])).
% 0.86/1.05 tff(102,plain,
% 0.86/1.05 (lesseq(X!5, max(X!5, Y!4))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[80, 101])).
% 0.86/1.05 tff(103,plain,
% 0.86/1.05 (~lesseq(Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[73, 102, 50])).
% 0.86/1.05 tff(104,plain,
% 0.86/1.05 (~lesseq(Y!4, Y!4)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.86/1.05 tff(105,plain,
% 0.86/1.05 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4)) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(106,plain,
% 0.86/1.05 ((lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4)) <=> lesseq(Y!4, Y!4)),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(107,plain,
% 0.86/1.05 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[106])).
% 0.86/1.05 tff(108,plain,
% 0.86/1.05 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4))),
% 0.86/1.05 inference(transitivity,[status(thm)],[107, 105])).
% 0.86/1.05 tff(109,plain,
% 0.86/1.05 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, Y!4) | lesseq(Y!4, Y!4))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(110,plain,
% 0.86/1.05 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, Y!4)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.86/1.05 tff(111,plain,
% 0.86/1.05 (lesseq(Y!4, Y!4)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[110, 38])).
% 0.86/1.05 tff(112,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[111, 104])).
% 0.86/1.05 tff(113,plain,(~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(114,plain,
% 0.86/1.05 (((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))) | lesseq(Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(tautology,[status(thm)],[])).
% 0.86/1.05 tff(115,plain,
% 0.86/1.05 (lesseq(Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.86/1.05 tff(116,plain,
% 0.86/1.05 ((~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.86/1.05 inference(tautology,[status(thm)],[])).
% 0.86/1.05 tff(117,plain,
% 0.86/1.05 ((~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.86/1.05 tff(118,plain,
% 0.86/1.05 (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[117, 49])).
% 0.86/1.05 tff(119,assumption,(((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))), introduced(assumption)).
% 0.86/1.05 tff(120,plain,
% 0.86/1.05 (^[X: $i, Y: $i, Z: $i] : refl((~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z))) <=> (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(121,plain,
% 0.86/1.05 (![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[120])).
% 0.86/1.05 tff(122,plain,
% 0.86/1.05 (^[X: $i, Y: $i, Z: $i] : trans(trans(monotonicity(rewrite((lesseq(X, Z) & lesseq(Y, Z)) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z))))), ((ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> (ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z))))))), rewrite((ub(X, Y, Z) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Z))))) <=> (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))), ((ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z))))), rewrite((~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z))) <=> (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))), ((ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(123,plain,
% 0.86/1.05 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[122])).
% 0.86/1.05 tff(124,plain,
% 0.86/1.05 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(125,axiom,(![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ub')).
% 0.86/1.05 tff(126,plain,
% 0.86/1.05 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.86/1.05 tff(127,plain,(
% 0.86/1.05 ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.86/1.05 inference(skolemize,[status(sab)],[126])).
% 0.86/1.05 tff(128,plain,
% 0.86/1.05 (![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.86/1.05 tff(129,plain,
% 0.86/1.05 (![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.86/1.05 tff(130,plain,
% 0.86/1.05 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(131,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[130, 129, 119])).
% 0.86/1.05 tff(132,plain,(~(((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(133,plain,
% 0.86/1.05 ((((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | ((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) | ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(tautology,[status(thm)],[])).
% 0.86/1.05 tff(134,plain,
% 0.86/1.05 (((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) | ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.86/1.05 tff(135,plain,
% 0.86/1.05 (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[134, 118])).
% 0.86/1.05 tff(136,plain,
% 0.86/1.05 (((~![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))) | ((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))))) <=> ((~![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(137,plain,
% 0.86/1.05 ((~![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))) | ((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(138,plain,
% 0.86/1.05 ((~![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.86/1.05 tff(139,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[138, 49, 135, 48])).
% 0.86/1.05 tff(140,plain,((~![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(141,plain,
% 0.86/1.05 (~![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[140, 47])).
% 0.86/1.05 tff(142,plain,
% 0.86/1.05 ((~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))) | model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z)))),
% 0.86/1.05 inference(tautology,[status(thm)],[])).
% 0.86/1.05 tff(143,plain,
% 0.86/1.05 ((~(model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(max(X!5, Y!4), Y!4, Z))))) | model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.86/1.05 tff(144,plain,
% 0.86/1.05 (model_ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[143, 28])).
% 0.86/1.05 tff(145,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[144, 6])).
% 0.86/1.05 tff(146,plain,(model_ub(X!5, Y!4, max(X!5, Y!4)) | (~(max(X!5, Y!4) = X!5))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(147,plain,
% 0.86/1.05 (model_ub(X!5, Y!4, max(X!5, Y!4))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[146, 1])).
% 0.86/1.05 tff(148,assumption,(~(model_max(X!5, Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3))), introduced(assumption)).
% 0.86/1.05 tff(149,plain,
% 0.86/1.05 (^[X: $i, Y: $i, N: $i] : refl((model_max(X, Y, N) <=> lesseq(max(X, Y), N)) <=> (model_max(X, Y, N) <=> lesseq(max(X, Y), N)))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(150,plain,
% 0.86/1.05 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[149])).
% 0.86/1.05 tff(151,plain,
% 0.86/1.05 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(152,axiom,(![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','model_max_2')).
% 0.86/1.05 tff(153,plain,
% 0.86/1.05 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.86/1.05 tff(154,plain,(
% 0.86/1.05 ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))),
% 0.86/1.05 inference(skolemize,[status(sab)],[153])).
% 0.86/1.05 tff(155,plain,
% 0.86/1.05 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.86/1.05 tff(156,plain,
% 0.86/1.05 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))) | (model_max(X!5, Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(157,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[156, 155, 148])).
% 0.86/1.05 tff(158,plain,(model_max(X!5, Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(159,assumption,(~lesseq(max(X!5, Y!4), Z!3)), introduced(assumption)).
% 0.86/1.05 tff(160,plain,
% 0.86/1.05 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(max(X!5, Y!4), Z!3)),
% 0.86/1.05 inference(tautology,[status(thm)],[])).
% 0.86/1.05 tff(161,plain,
% 0.86/1.05 (~model_max(X!5, Y!4, Z!3)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[160, 159, 158])).
% 0.86/1.05 tff(162,plain,
% 0.86/1.05 (((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | model_max(X!5, Y!4, Z!3)),
% 0.86/1.05 inference(tautology,[status(thm)],[])).
% 0.86/1.05 tff(163,plain,
% 0.86/1.05 ((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.86/1.05 tff(164,plain,
% 0.86/1.05 (^[X: $i, Y: $i, N: $i] : refl((~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.86/1.05 inference(bind,[status(th)],[])).
% 0.86/1.05 tff(165,plain,
% 0.86/1.05 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.86/1.05 inference(quant_intro,[status(thm)],[164])).
% 0.86/1.05 tff(166,plain,
% 0.86/1.05 (^[X: $i, Y: $i, N: $i] : rewrite((~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(167,plain,
% 0.86/1.06 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[166])).
% 0.86/1.06 tff(168,plain,
% 0.86/1.06 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[167, 165])).
% 0.86/1.06 tff(169,plain,
% 0.86/1.06 (^[X: $i, Y: $i, N: $i] : trans(monotonicity(rewrite(((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) <=> ((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))))), rewrite((minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))) <=> (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))), ((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))), rewrite((((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))), ((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(170,plain,
% 0.86/1.06 (![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[169])).
% 0.86/1.06 tff(171,plain,
% 0.86/1.06 (^[X: $i, Y: $i, N: $i] : rewrite((((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))) <=> (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(172,plain,
% 0.86/1.06 (![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))) <=> ![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[171])).
% 0.86/1.06 tff(173,plain,
% 0.86/1.06 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(174,plain,
% 0.86/1.06 (^[X: $i, Y: $i, N: $i] : rewrite((minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : (model_max(X, Y, Z) => lesseq(N, Z)))) <=> (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(175,plain,
% 0.86/1.06 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : (model_max(X, Y, Z) => lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[174])).
% 0.86/1.06 tff(176,axiom,(![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : (model_max(X, Y, Z) => lesseq(N, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','minsol_model_max')).
% 0.86/1.06 tff(177,plain,
% 0.86/1.06 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.86/1.06 tff(178,plain,
% 0.86/1.06 (![X: $i, Y: $i, N: $i] : (minsol_model_max(X, Y, N) <=> (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.86/1.06 tff(179,plain,(
% 0.86/1.06 ![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | ((~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))))),
% 0.86/1.06 inference(skolemize,[status(sab)],[178])).
% 0.86/1.06 tff(180,plain,
% 0.86/1.06 (![X: $i, Y: $i, N: $i] : (((~minsol_model_max(X, Y, N)) | (model_max(X, Y, N) & ![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.86/1.06 tff(181,plain,
% 0.86/1.06 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[180, 170])).
% 0.86/1.06 tff(182,plain,
% 0.86/1.06 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[181, 168])).
% 0.86/1.06 tff(183,plain,
% 0.86/1.06 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_max(X, Y, N) | (~model_max(X, Y, N)) | (~((~model_max(X, Y, tptp_fun_Z_1(N, Y, X))) | lesseq(N, tptp_fun_Z_1(N, Y, X)))))) | (~((~minsol_model_max(X, Y, N)) | (~((~model_max(X, Y, N)) | (~![Z: $i] : ((~model_max(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(184,plain,
% 0.86/1.06 (~((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.86/1.06 tff(185,plain,
% 0.86/1.06 (((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(186,plain,
% 0.86/1.06 ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.86/1.06 tff(187,plain,
% 0.86/1.06 ((~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))) | (~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(188,plain,
% 0.86/1.06 ((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.86/1.06 tff(189,plain,
% 0.86/1.06 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[188, 163])).
% 0.86/1.06 tff(190,plain,
% 0.86/1.06 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(191,plain,
% 0.86/1.06 (~(((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[190, 129])).
% 0.86/1.06 tff(192,assumption,(~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))), introduced(assumption)).
% 0.86/1.06 tff(193,plain,
% 0.86/1.06 (((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(194,plain,
% 0.86/1.06 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.86/1.06 tff(195,plain,
% 0.86/1.06 ((((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(196,plain,
% 0.86/1.06 ((((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.86/1.06 tff(197,plain,
% 0.86/1.06 (~((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[196, 191])).
% 0.86/1.06 tff(198,plain,
% 0.86/1.06 (((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(199,plain,
% 0.86/1.06 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.86/1.06 tff(200,plain,
% 0.86/1.06 (((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(201,plain,
% 0.86/1.06 (lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[200, 192])).
% 0.86/1.06 tff(202,plain,
% 0.86/1.06 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(203,plain,
% 0.86/1.06 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((lesseq(X, Y) & lesseq(Y, Z)) <=> (~((~lesseq(Y, Z)) | (~lesseq(X, Y))))), ((~(lesseq(X, Y) & lesseq(Y, Z))) <=> (~(~((~lesseq(Y, Z)) | (~lesseq(X, Y))))))), rewrite((~(~((~lesseq(Y, Z)) | (~lesseq(X, Y))))) <=> ((~lesseq(Y, Z)) | (~lesseq(X, Y)))), ((~(lesseq(X, Y) & lesseq(Y, Z))) <=> ((~lesseq(Y, Z)) | (~lesseq(X, Y))))), (((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> (((~lesseq(Y, Z)) | (~lesseq(X, Y))) | lesseq(X, Z)))), rewrite((((~lesseq(Y, Z)) | (~lesseq(X, Y))) | lesseq(X, Z)) <=> (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))), (((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(204,plain,
% 0.86/1.06 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[203])).
% 0.86/1.06 tff(205,plain,
% 0.86/1.06 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(206,plain,
% 0.86/1.06 (^[X: $i, Y: $i, Z: $i] : rewrite(((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z)) <=> ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z)))),
% 0.86/1.06 inference(bind,[status(th)],[])).
% 0.86/1.06 tff(207,plain,
% 0.86/1.06 (![X: $i, Y: $i, Z: $i] : ((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.86/1.06 inference(quant_intro,[status(thm)],[206])).
% 0.86/1.06 tff(208,axiom,(![X: $i, Y: $i, Z: $i] : ((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lesseq_trans')).
% 0.86/1.06 tff(209,plain,
% 0.86/1.06 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.86/1.06 tff(210,plain,
% 0.86/1.06 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.86/1.06 tff(211,plain,(
% 0.86/1.06 ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.86/1.06 inference(skolemize,[status(sab)],[210])).
% 0.86/1.06 tff(212,plain,
% 0.86/1.06 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[211, 204])).
% 0.86/1.06 tff(213,plain,
% 0.86/1.06 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[212, 202])).
% 0.86/1.06 tff(214,plain,
% 0.86/1.06 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(215,plain,
% 0.86/1.06 ((lesseq(Y!4, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(216,plain,
% 0.86/1.06 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[215])).
% 0.86/1.06 tff(217,plain,
% 0.86/1.06 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3))),
% 0.86/1.06 inference(transitivity,[status(thm)],[216, 214])).
% 0.86/1.06 tff(218,plain,
% 0.86/1.06 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(219,plain,
% 0.86/1.06 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(Y!4, Z!3)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.86/1.06 tff(220,plain,
% 0.86/1.06 (lesseq(Y!4, Z!3)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[219, 213, 201, 199])).
% 0.86/1.06 tff(221,assumption,(max(X!5, Y!4) = Y!4), introduced(assumption)).
% 0.86/1.06 tff(222,plain,
% 0.86/1.06 (Y!4 = max(X!5, Y!4)),
% 0.86/1.06 inference(symmetry,[status(thm)],[221])).
% 0.86/1.06 tff(223,plain,
% 0.86/1.06 (lesseq(Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[222])).
% 0.86/1.06 tff(224,plain,
% 0.86/1.06 (lesseq(max(X!5, Y!4), Z!3) <=> lesseq(Y!4, Z!3)),
% 0.86/1.06 inference(symmetry,[status(thm)],[223])).
% 0.86/1.06 tff(225,plain,
% 0.86/1.06 ((~lesseq(max(X!5, Y!4), Z!3)) <=> (~lesseq(Y!4, Z!3))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[224])).
% 0.86/1.06 tff(226,plain,
% 0.86/1.06 (~lesseq(Y!4, Z!3)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[159, 225])).
% 0.86/1.06 tff(227,assumption,(lesseq(Y!4, Z!3)), introduced(assumption)).
% 0.86/1.06 tff(228,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.86/1.06 tff(229,plain,((~(max(X!5, Y!4) = Y!4)) | (~lesseq(Y!4, Z!3)) | lesseq(max(X!5, Y!4), Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(230,plain,
% 0.86/1.06 (~(max(X!5, Y!4) = Y!4)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[229, 220, 159])).
% 0.86/1.06 tff(231,plain,
% 0.86/1.06 (~lesseq(X!5, Y!4)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[94, 230])).
% 0.86/1.06 tff(232,plain,
% 0.86/1.06 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, X!5) | lesseq(X!5, Y!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, X!5) | lesseq(X!5, Y!4))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(233,plain,
% 0.86/1.06 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, X!5) | lesseq(X!5, Y!4))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(234,plain,
% 0.86/1.06 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, X!5) | lesseq(X!5, Y!4)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.86/1.06 tff(235,plain,
% 0.86/1.06 (lesseq(Y!4, X!5)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[234, 38, 231])).
% 0.86/1.06 tff(236,plain,
% 0.86/1.06 (max(X!5, Y!4) = X!5),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[65, 235])).
% 0.86/1.06 tff(237,plain,
% 0.86/1.06 (X!5 = max(X!5, Y!4)),
% 0.86/1.06 inference(symmetry,[status(thm)],[236])).
% 0.86/1.06 tff(238,plain,
% 0.86/1.06 (lesseq(X!5, Z!3) <=> lesseq(max(X!5, Y!4), Z!3)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[237])).
% 0.86/1.06 tff(239,plain,
% 0.86/1.06 (lesseq(max(X!5, Y!4), Z!3) <=> lesseq(X!5, Z!3)),
% 0.86/1.06 inference(symmetry,[status(thm)],[238])).
% 0.86/1.06 tff(240,plain,
% 0.86/1.06 ((~lesseq(max(X!5, Y!4), Z!3)) <=> (~lesseq(X!5, Z!3))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[239])).
% 0.86/1.06 tff(241,plain,
% 0.86/1.06 (~lesseq(X!5, Z!3)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[159, 240])).
% 0.86/1.06 tff(242,plain,
% 0.86/1.06 (((~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.86/1.06 inference(tautology,[status(thm)],[])).
% 0.86/1.06 tff(243,plain,
% 0.86/1.06 (lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[242, 197])).
% 0.86/1.06 tff(244,plain,
% 0.86/1.06 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(245,plain,
% 0.86/1.06 ((lesseq(X!5, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))) <=> ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(246,plain,
% 0.86/1.06 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[245])).
% 0.86/1.06 tff(247,plain,
% 0.86/1.06 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3))),
% 0.86/1.06 inference(transitivity,[status(thm)],[246, 244])).
% 0.86/1.06 tff(248,plain,
% 0.86/1.06 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(249,plain,
% 0.86/1.06 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(X!5, Z!3)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.86/1.06 tff(250,plain,
% 0.86/1.06 (lesseq(X!5, Z!3)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[249, 213, 201, 243])).
% 0.86/1.06 tff(251,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[250, 241])).
% 0.86/1.06 tff(252,plain,(((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(max(X!5, Y!4), Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(253,plain,
% 0.86/1.06 ((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[252, 159])).
% 0.86/1.06 tff(254,assumption,((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))), introduced(assumption)).
% 0.86/1.06 tff(255,plain,
% 0.86/1.06 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(256,plain,
% 0.86/1.06 ((~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))))) <=> (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(257,plain,
% 0.86/1.06 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[256])).
% 0.86/1.06 tff(258,plain,
% 0.86/1.06 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[257, 255])).
% 0.86/1.06 tff(259,plain,
% 0.86/1.06 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(260,plain,
% 0.86/1.06 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.86/1.07 tff(261,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[260, 19, 254])).
% 0.86/1.07 tff(262,plain,(~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(263,plain,
% 0.86/1.07 (((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))) | ((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(264,plain,
% 0.86/1.07 ((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.86/1.07 tff(265,plain,
% 0.86/1.07 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))))))) | (~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(266,plain,
% 0.86/1.07 ((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[265, 264])).
% 0.86/1.07 tff(267,plain,
% 0.86/1.07 (~model_ub(X!5, Y!4, Z!3)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[266, 253])).
% 0.86/1.07 tff(268,plain,
% 0.86/1.07 (((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | model_ub(X!5, Y!4, Z!3)),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(269,plain,
% 0.86/1.07 ((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.86/1.07 tff(270,plain,
% 0.86/1.07 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(271,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[270])).
% 0.86/1.07 tff(272,plain,
% 0.86/1.07 (^[X: $i, Y: $i, N: $i] : refl((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(273,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[272])).
% 0.86/1.07 tff(274,plain,
% 0.86/1.07 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(275,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[274])).
% 0.86/1.07 tff(276,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[275, 273])).
% 0.86/1.07 tff(277,plain,
% 0.86/1.07 (^[X: $i, Y: $i, N: $i] : trans(monotonicity(rewrite(((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) <=> ((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))), rewrite((minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))) <=> (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))), ((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> (((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))), rewrite((((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))), ((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(278,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[277])).
% 0.86/1.07 tff(279,plain,
% 0.86/1.07 (^[X: $i, Y: $i, N: $i] : rewrite((((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))) <=> (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(280,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))) <=> ![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[279])).
% 0.86/1.07 tff(281,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(282,plain,
% 0.86/1.07 (^[X: $i, Y: $i, N: $i] : rewrite((minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : (model_ub(X, Y, Z) => lesseq(N, Z)))) <=> (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))),
% 0.86/1.07 inference(bind,[status(th)],[])).
% 0.86/1.07 tff(283,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : (model_ub(X, Y, Z) => lesseq(N, Z)))) <=> ![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.86/1.07 inference(quant_intro,[status(thm)],[282])).
% 0.86/1.07 tff(284,axiom,(![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : (model_ub(X, Y, Z) => lesseq(N, Z))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','minsol_model_ub')).
% 0.86/1.07 tff(285,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.86/1.07 tff(286,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (minsol_model_ub(X, Y, N) <=> (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[285, 281])).
% 0.86/1.07 tff(287,plain,(
% 0.86/1.07 ![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | ((~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))))),
% 0.86/1.07 inference(skolemize,[status(sab)],[286])).
% 0.86/1.07 tff(288,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (((~minsol_model_ub(X, Y, N)) | (model_ub(X, Y, N) & ![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))) & (minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[287, 280])).
% 0.86/1.07 tff(289,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[288, 278])).
% 0.86/1.07 tff(290,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (~((~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z))))))) | (~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X))))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[289, 276])).
% 0.86/1.07 tff(291,plain,
% 0.86/1.07 (![X: $i, Y: $i, N: $i] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[290, 271])).
% 0.86/1.07 tff(292,plain,
% 0.86/1.07 ((~![X: $i, Y: $i, N: $i] : (~((~(minsol_model_ub(X, Y, N) | (~model_ub(X, Y, N)) | (~((~model_ub(X, Y, tptp_fun_Z_2(N, Y, X))) | lesseq(N, tptp_fun_Z_2(N, Y, X)))))) | (~((~minsol_model_ub(X, Y, N)) | (~((~model_ub(X, Y, N)) | (~![Z: $i] : ((~model_ub(X, Y, Z)) | lesseq(N, Z)))))))))) | (~((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(293,plain,
% 0.86/1.07 (~((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[292, 291])).
% 0.86/1.07 tff(294,plain,
% 0.86/1.07 (((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(295,plain,
% 0.86/1.07 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[294, 293])).
% 0.86/1.07 tff(296,plain,
% 0.86/1.07 ((~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))))) | (~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(297,plain,
% 0.86/1.07 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[296, 295])).
% 0.86/1.07 tff(298,plain,
% 0.86/1.07 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[297, 269])).
% 0.86/1.07 tff(299,plain,
% 0.86/1.07 ((~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))) <=> (~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(300,plain,
% 0.86/1.07 ((~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))) <=> (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(301,axiom,(~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','max_is_ub_1')).
% 0.86/1.07 tff(302,plain,
% 0.86/1.07 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.86/1.07 tff(303,plain,
% 0.86/1.07 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[302, 300])).
% 0.86/1.07 tff(304,plain,
% 0.86/1.07 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[303, 300])).
% 0.86/1.07 tff(305,plain,
% 0.86/1.07 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[304, 300])).
% 0.86/1.07 tff(306,plain,(
% 0.86/1.07 ~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.86/1.07 inference(skolemize,[status(sab)],[305])).
% 0.86/1.07 tff(307,plain,
% 0.86/1.07 (~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[306, 299])).
% 0.86/1.07 tff(308,plain,
% 0.86/1.07 ((minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3)) | minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(309,plain,
% 0.86/1.07 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[308, 307])).
% 0.86/1.07 tff(310,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[309, 298, 189])).
% 0.86/1.07 tff(311,plain,(lesseq(max(X!5, Y!4), Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(312,plain,
% 0.86/1.07 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(max(X!5, Y!4), Z!3)) | (max(max(X!5, Y!4), Z!3) = Z!3))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(max(X!5, Y!4), Z!3)) | (max(max(X!5, Y!4), Z!3) = Z!3))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(313,plain,
% 0.86/1.07 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(max(X!5, Y!4), Z!3)) | (max(max(X!5, Y!4), Z!3) = Z!3))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(314,plain,
% 0.86/1.07 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(max(X!5, Y!4), Z!3)) | (max(max(X!5, Y!4), Z!3) = Z!3)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.86/1.07 tff(315,plain,
% 0.86/1.07 (max(max(X!5, Y!4), Z!3) = Z!3),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[314, 90, 311])).
% 0.86/1.07 tff(316,plain,
% 0.86/1.07 (X!5 = max(X!5, Y!4)),
% 0.86/1.07 inference(symmetry,[status(thm)],[1])).
% 0.86/1.07 tff(317,plain,
% 0.86/1.07 (model_max(X!5, Y!4, max(X!5, Y!4)) <=> model_max(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[316])).
% 0.86/1.07 tff(318,plain,
% 0.86/1.07 (model_max(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> model_max(X!5, Y!4, max(X!5, Y!4))),
% 0.86/1.07 inference(symmetry,[status(thm)],[317])).
% 0.86/1.07 tff(319,plain,
% 0.86/1.07 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))) | (model_max(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> lesseq(max(max(X!5, Y!4), Y!4), max(X!5, Y!4)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(320,plain,
% 0.86/1.07 (model_max(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> lesseq(max(max(X!5, Y!4), Y!4), max(X!5, Y!4))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[319, 155])).
% 0.86/1.07 tff(321,plain,
% 0.86/1.07 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, max(X!5, Y!4))) | (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, max(X!5, Y!4))) | (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(322,plain,
% 0.86/1.07 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, max(X!5, Y!4))) | (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(323,plain,
% 0.86/1.07 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, max(X!5, Y!4))) | (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.86/1.07 tff(324,plain,
% 0.86/1.07 (max(max(X!5, Y!4), Y!4) = max(X!5, Y!4)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[323, 61, 115])).
% 0.86/1.07 tff(325,plain,
% 0.86/1.07 (max(max(X!5, Y!4), Y!4) = X!5),
% 0.86/1.07 inference(transitivity,[status(thm)],[324, 1])).
% 0.86/1.07 tff(326,plain,
% 0.86/1.07 (lesseq(max(max(X!5, Y!4), Y!4), max(X!5, Y!4)) <=> lesseq(X!5, X!5)),
% 0.86/1.07 inference(monotonicity,[status(thm)],[325, 1])).
% 0.86/1.07 tff(327,plain,
% 0.86/1.07 (lesseq(X!5, X!5) <=> lesseq(max(max(X!5, Y!4), Y!4), max(X!5, Y!4))),
% 0.86/1.07 inference(symmetry,[status(thm)],[326])).
% 0.86/1.07 tff(328,plain,
% 0.86/1.07 (lesseq(max(max(X!5, Y!4), Y!4), max(X!5, Y!4))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[46, 327])).
% 0.86/1.07 tff(329,plain,
% 0.86/1.07 ((~(model_max(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> lesseq(max(max(X!5, Y!4), Y!4), max(X!5, Y!4)))) | model_max(max(X!5, Y!4), Y!4, max(X!5, Y!4)) | (~lesseq(max(max(X!5, Y!4), Y!4), max(X!5, Y!4)))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(330,plain,
% 0.86/1.07 (model_max(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[329, 328, 320])).
% 0.86/1.07 tff(331,plain,
% 0.86/1.07 (model_max(X!5, Y!4, max(X!5, Y!4))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[330, 318])).
% 0.86/1.07 tff(332,assumption,(~minsol_model_ub(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.86/1.07 tff(333,plain,
% 0.86/1.07 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[309, 332])).
% 0.86/1.07 tff(334,plain,
% 0.86/1.07 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[188, 333])).
% 0.86/1.07 tff(335,plain,
% 0.86/1.07 (((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | ![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(336,plain,
% 0.86/1.07 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[335, 334])).
% 0.86/1.07 tff(337,plain,
% 0.86/1.07 (((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, max(X!5, Y!4))) | lesseq(Z!3, max(X!5, Y!4)))) <=> ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, max(X!5, Y!4))) | lesseq(Z!3, max(X!5, Y!4)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(338,plain,
% 0.86/1.07 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, max(X!5, Y!4))) | lesseq(Z!3, max(X!5, Y!4)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(339,plain,
% 0.86/1.07 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, max(X!5, Y!4))) | lesseq(Z!3, max(X!5, Y!4))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.86/1.07 tff(340,plain,
% 0.86/1.07 ((~model_max(X!5, Y!4, max(X!5, Y!4))) | lesseq(Z!3, max(X!5, Y!4))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[339, 336])).
% 0.86/1.07 tff(341,plain,
% 0.86/1.07 (lesseq(Z!3, max(X!5, Y!4))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[340, 331])).
% 0.86/1.07 tff(342,plain,
% 0.86/1.07 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, max(X!5, Y!4))) | (max(max(X!5, Y!4), Z!3) = max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, max(X!5, Y!4))) | (max(max(X!5, Y!4), Z!3) = max(X!5, Y!4)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(343,plain,
% 0.86/1.07 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, max(X!5, Y!4))) | (max(max(X!5, Y!4), Z!3) = max(X!5, Y!4)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(344,plain,
% 0.86/1.07 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, max(X!5, Y!4))) | (max(max(X!5, Y!4), Z!3) = max(X!5, Y!4))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.86/1.07 tff(345,plain,
% 0.86/1.07 ((~lesseq(Z!3, max(X!5, Y!4))) | (max(max(X!5, Y!4), Z!3) = max(X!5, Y!4))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[344, 61])).
% 0.86/1.07 tff(346,plain,
% 0.86/1.07 (max(max(X!5, Y!4), Z!3) = max(X!5, Y!4)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[345, 341])).
% 0.86/1.07 tff(347,plain,
% 0.86/1.07 (max(X!5, Y!4) = max(max(X!5, Y!4), Z!3)),
% 0.86/1.07 inference(symmetry,[status(thm)],[346])).
% 0.86/1.07 tff(348,plain,
% 0.86/1.07 (max(X!5, Y!4) = Z!3),
% 0.86/1.07 inference(transitivity,[status(thm)],[347, 315])).
% 0.86/1.07 tff(349,plain,
% 0.86/1.07 (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)) <=> ub(X!5, Y!4, Z!3)),
% 0.86/1.07 inference(monotonicity,[status(thm)],[1, 348])).
% 0.86/1.07 tff(350,plain,
% 0.86/1.07 (ub(X!5, Y!4, Z!3) <=> ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.86/1.07 inference(symmetry,[status(thm)],[349])).
% 0.86/1.07 tff(351,assumption,((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))), introduced(assumption)).
% 0.86/1.07 tff(352,assumption,(lesseq(max(X!5, Y!4), Z!3)), introduced(assumption)).
% 0.86/1.07 tff(353,plain,
% 0.86/1.07 (X!5 = max(X!5, Y!4)),
% 0.86/1.07 inference(symmetry,[status(thm)],[66])).
% 0.86/1.07 tff(354,plain,
% 0.86/1.07 (lesseq(X!5, Z!3) <=> lesseq(max(X!5, Y!4), Z!3)),
% 0.86/1.07 inference(monotonicity,[status(thm)],[353])).
% 0.86/1.07 tff(355,plain,
% 0.86/1.07 (lesseq(max(X!5, Y!4), Z!3) <=> lesseq(X!5, Z!3)),
% 0.86/1.07 inference(symmetry,[status(thm)],[354])).
% 0.86/1.07 tff(356,plain,
% 0.86/1.07 (lesseq(X!5, Z!3)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[352, 355])).
% 0.86/1.07 tff(357,plain,
% 0.86/1.07 (lesseq(Y!4, X!5) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[353])).
% 0.86/1.07 tff(358,plain,
% 0.86/1.07 (lesseq(Y!4, max(X!5, Y!4))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[51, 357])).
% 0.86/1.07 tff(359,plain,
% 0.86/1.07 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(360,plain,
% 0.86/1.07 ((lesseq(Y!4, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(Y!4, max(X!5, Y!4)))) <=> (lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(361,plain,
% 0.86/1.07 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(Y!4, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[360])).
% 0.86/1.07 tff(362,plain,
% 0.86/1.07 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(Y!4, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[361, 359])).
% 0.86/1.07 tff(363,plain,
% 0.86/1.07 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(Y!4, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(Y!4, max(X!5, Y!4))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(364,plain,
% 0.86/1.07 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(Y!4, Z!3) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.86/1.07 tff(365,plain,
% 0.86/1.07 (lesseq(Y!4, Z!3)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[364, 213, 352, 358])).
% 0.86/1.07 tff(366,plain,
% 0.86/1.07 ((~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))) | (~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))),
% 0.86/1.07 inference(tautology,[status(thm)],[])).
% 0.86/1.07 tff(367,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[366, 365, 356, 351])).
% 0.86/1.07 tff(368,plain,((~lesseq(Y!4, X!5)) | (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))) | (~lesseq(max(X!5, Y!4), Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(369,plain,
% 0.86/1.07 (~lesseq(Y!4, X!5)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[368, 351, 352])).
% 0.86/1.07 tff(370,plain,
% 0.86/1.07 (lesseq(X!5, Y!4)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[79, 38, 369])).
% 0.86/1.07 tff(371,plain,
% 0.86/1.07 (max(X!5, Y!4) = Y!4),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[94, 370])).
% 0.86/1.08 tff(372,plain,
% 0.86/1.08 (Y!4 = max(X!5, Y!4)),
% 0.86/1.08 inference(symmetry,[status(thm)],[371])).
% 0.86/1.08 tff(373,plain,
% 0.86/1.08 (lesseq(Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3)),
% 0.86/1.08 inference(monotonicity,[status(thm)],[372])).
% 0.86/1.08 tff(374,plain,
% 0.86/1.08 (lesseq(max(X!5, Y!4), Z!3) <=> lesseq(Y!4, Z!3)),
% 0.86/1.08 inference(symmetry,[status(thm)],[373])).
% 0.86/1.08 tff(375,plain,
% 0.86/1.08 (lesseq(Y!4, Z!3)),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[352, 374])).
% 0.86/1.08 tff(376,plain,
% 0.86/1.08 (lesseq(X!5, Y!4) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[372])).
% 0.86/1.08 tff(377,plain,
% 0.86/1.08 (lesseq(X!5, max(X!5, Y!4))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[370, 376])).
% 0.86/1.08 tff(378,plain,
% 0.86/1.08 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(379,plain,
% 0.86/1.08 ((lesseq(X!5, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(X!5, max(X!5, Y!4)))) <=> (lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(380,plain,
% 0.86/1.08 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(X!5, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[379])).
% 0.86/1.08 tff(381,plain,
% 0.86/1.08 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(X!5, max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3)))),
% 0.86/1.08 inference(transitivity,[status(thm)],[380, 378])).
% 0.86/1.08 tff(382,plain,
% 0.86/1.08 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(X!5, Z!3) | (~lesseq(max(X!5, Y!4), Z!3)) | (~lesseq(X!5, max(X!5, Y!4))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(383,plain,
% 0.86/1.08 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(X!5, Z!3) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), Z!3))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.86/1.08 tff(384,plain,
% 0.86/1.08 (lesseq(X!5, Z!3)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[383, 213, 352, 377])).
% 0.86/1.08 tff(385,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[366, 384, 375, 351])).
% 0.86/1.08 tff(386,plain,((~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))) | (~lesseq(max(X!5, Y!4), Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(387,plain,
% 0.86/1.08 (~((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[386, 311])).
% 0.86/1.08 tff(388,assumption,(((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.86/1.08 tff(389,plain,
% 0.86/1.08 (((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(390,plain,
% 0.86/1.08 ((~(((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3))) <=> (~(((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(391,plain,
% 0.86/1.08 ((((~lesseq(Y!4, Z!3)) | (~lesseq(X!5, Z!3))) <=> ub(X!5, Y!4, Z!3)) <=> (((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(392,plain,
% 0.86/1.08 ((~(((~lesseq(Y!4, Z!3)) | (~lesseq(X!5, Z!3))) <=> ub(X!5, Y!4, Z!3))) <=> (~(((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3)))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[391])).
% 0.91/1.08 tff(393,plain,
% 0.91/1.08 ((~(((~lesseq(Y!4, Z!3)) | (~lesseq(X!5, Z!3))) <=> ub(X!5, Y!4, Z!3))) <=> (~(((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[392, 390])).
% 0.91/1.08 tff(394,plain,
% 0.91/1.08 (((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, Z!3)) | (~lesseq(X!5, Z!3))) <=> ub(X!5, Y!4, Z!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[393])).
% 0.91/1.08 tff(395,plain,
% 0.91/1.08 (((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, Z!3)) | (~lesseq(X!5, Z!3))) <=> ub(X!5, Y!4, Z!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3))))),
% 0.91/1.08 inference(transitivity,[status(thm)],[394, 389])).
% 0.91/1.08 tff(396,plain,
% 0.91/1.08 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, Z!3)) | (~lesseq(X!5, Z!3))) <=> ub(X!5, Y!4, Z!3)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(397,plain,
% 0.91/1.08 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3)))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.91/1.08 tff(398,plain,
% 0.91/1.08 ($false),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[397, 129, 388])).
% 0.91/1.08 tff(399,plain,(~(((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.08 tff(400,plain,
% 0.91/1.08 ((((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) <=> ub(X!5, Y!4, Z!3)) | ((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) | ub(X!5, Y!4, Z!3)),
% 0.91/1.08 inference(tautology,[status(thm)],[])).
% 0.91/1.08 tff(401,plain,
% 0.91/1.08 (((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) | ub(X!5, Y!4, Z!3)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[400, 399])).
% 0.91/1.08 tff(402,plain,
% 0.91/1.08 (ub(X!5, Y!4, Z!3)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[401, 387])).
% 0.91/1.08 tff(403,plain,
% 0.91/1.08 (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[402, 350])).
% 0.91/1.08 tff(404,plain,
% 0.91/1.08 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))))))))))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(405,plain,
% 0.91/1.08 ((~((~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)))))) | (~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))))) <=> (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))))))))))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(406,plain,
% 0.91/1.08 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)))))) | (~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))))))))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[405])).
% 0.91/1.08 tff(407,plain,
% 0.91/1.08 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)))))) | (~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))))))))))),
% 0.91/1.08 inference(transitivity,[status(thm)],[406, 404])).
% 0.91/1.08 tff(408,plain,
% 0.91/1.08 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))) | (~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)))))) | (~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))))))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(409,plain,
% 0.91/1.08 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))))))))))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.91/1.08 tff(410,plain,
% 0.91/1.08 (~((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)))))))))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[409, 19])).
% 0.91/1.08 tff(411,plain,
% 0.91/1.08 (((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))) | (~((~model_ub(max(X!5, Y!4), Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4)), Z!3)) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(Z!3, Y!4, max(X!5, Y!4))))))))) | (model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))),
% 0.91/1.08 inference(tautology,[status(thm)],[])).
% 0.91/1.08 tff(412,plain,
% 0.91/1.08 (model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[411, 410])).
% 0.91/1.08 tff(413,plain,
% 0.91/1.08 (model_ub(max(X!5, Y!4), Y!4, Z!3) <=> model_ub(X!5, Y!4, Z!3)),
% 0.91/1.08 inference(monotonicity,[status(thm)],[1])).
% 0.91/1.08 tff(414,plain,
% 0.91/1.08 (model_ub(X!5, Y!4, Z!3) <=> model_ub(max(X!5, Y!4), Y!4, Z!3)),
% 0.91/1.08 inference(symmetry,[status(thm)],[413])).
% 0.91/1.08 tff(415,plain,
% 0.91/1.08 ((~model_ub(X!5, Y!4, Z!3)) <=> (~model_ub(max(X!5, Y!4), Y!4, Z!3))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[414])).
% 0.91/1.08 tff(416,plain,
% 0.91/1.08 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(max(X!5, Y!4), Z!3))) | model_max(X!5, Y!4, Z!3) | (~lesseq(max(X!5, Y!4), Z!3))),
% 0.91/1.08 inference(tautology,[status(thm)],[])).
% 0.91/1.08 tff(417,plain,
% 0.91/1.08 (model_max(X!5, Y!4, Z!3)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[416, 311, 158])).
% 0.91/1.08 tff(418,plain,
% 0.91/1.08 (((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3))) <=> ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(419,plain,
% 0.91/1.08 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(420,plain,
% 0.91/1.08 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(Z!3, Z!3)),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.91/1.08 tff(421,plain,
% 0.91/1.08 (lesseq(Z!3, Z!3)),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[420, 417, 336])).
% 0.91/1.08 tff(422,assumption,(~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.91/1.08 tff(423,plain,
% 0.91/1.08 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))) | (model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(424,plain,
% 0.91/1.08 (model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[423, 155])).
% 0.91/1.08 tff(425,assumption,(![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))), introduced(assumption)).
% 0.91/1.08 tff(426,plain,
% 0.91/1.08 (((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))) <=> ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(427,plain,
% 0.91/1.08 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(428,plain,
% 0.91/1.08 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.91/1.08 tff(429,plain,
% 0.91/1.08 (~model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[428, 425, 422])).
% 0.91/1.08 tff(430,plain,
% 0.91/1.08 ((~(model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.91/1.08 inference(tautology,[status(thm)],[])).
% 0.91/1.08 tff(431,plain,
% 0.91/1.08 ((~(model_max(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[430, 429])).
% 0.91/1.08 tff(432,plain,
% 0.91/1.08 (~lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[431, 424])).
% 0.91/1.08 tff(433,plain,
% 0.91/1.08 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(434,plain,
% 0.91/1.08 ((lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4)) | lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4)))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(435,plain,
% 0.91/1.08 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4)) | lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4))))),
% 0.91/1.08 inference(monotonicity,[status(thm)],[434])).
% 0.91/1.08 tff(436,plain,
% 0.91/1.08 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4)) | lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4)))),
% 0.91/1.08 inference(transitivity,[status(thm)],[435, 433])).
% 0.91/1.08 tff(437,plain,
% 0.91/1.08 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4)) | lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.91/1.08 inference(quant_inst,[status(thm)],[])).
% 0.91/1.08 tff(438,plain,
% 0.91/1.08 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) | lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4))),
% 0.91/1.08 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.91/1.08 tff(439,plain,
% 0.91/1.08 (lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4))),
% 0.91/1.08 inference(unit_resolution,[status(thm)],[438, 38, 432])).
% 0.91/1.08 tff(440,plain,
% 0.91/1.08 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5)))))))))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(441,plain,
% 0.91/1.08 ((~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, Z))))))) <=> (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))))))))),
% 0.91/1.08 inference(rewrite,[status(thm)],[])).
% 0.91/1.08 tff(442,plain,
% 0.91/1.08 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5)))))))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[441])).
% 0.91/1.09 tff(443,plain,
% 0.91/1.09 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5)))))))))),
% 0.91/1.09 inference(transitivity,[status(thm)],[442, 440])).
% 0.91/1.09 tff(444,plain,
% 0.91/1.09 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, Z)))))))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(445,plain,
% 0.91/1.09 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))))))))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.91/1.09 tff(446,plain,
% 0.91/1.09 (~((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5)))))))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[445, 19])).
% 0.91/1.09 tff(447,plain,
% 0.91/1.09 (((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(Z, tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))),
% 0.91/1.09 inference(tautology,[status(thm)],[])).
% 0.91/1.09 tff(448,plain,
% 0.91/1.09 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[447, 446])).
% 0.91/1.09 tff(449,assumption,(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.91/1.09 tff(450,plain,
% 0.91/1.09 ((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.91/1.09 inference(tautology,[status(thm)],[])).
% 0.91/1.09 tff(451,plain,
% 0.91/1.09 ((~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))))) | (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[450, 449])).
% 0.91/1.09 tff(452,plain,
% 0.91/1.09 (~((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[451, 448])).
% 0.91/1.09 tff(453,plain,
% 0.91/1.09 (((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) | lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.09 inference(tautology,[status(thm)],[])).
% 0.91/1.09 tff(454,plain,
% 0.91/1.09 (lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[453, 452])).
% 0.91/1.09 tff(455,plain,
% 0.91/1.09 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4))))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(456,plain,
% 0.91/1.09 ((lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5)))) <=> ((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4))))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(457,plain,
% 0.91/1.09 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4)))))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[456])).
% 0.91/1.09 tff(458,plain,
% 0.91/1.09 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4))))),
% 0.91/1.09 inference(transitivity,[status(thm)],[457, 455])).
% 0.91/1.09 tff(459,plain,
% 0.91/1.09 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(460,plain,
% 0.91/1.09 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) | (~lesseq(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4)))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.91/1.09 tff(461,plain,
% 0.91/1.09 (lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[460, 213, 454, 439])).
% 0.91/1.09 tff(462,plain,
% 0.91/1.09 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = max(X!5, Y!4)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(463,plain,
% 0.91/1.09 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = max(X!5, Y!4)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(464,plain,
% 0.91/1.09 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = max(X!5, Y!4))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.91/1.09 tff(465,plain,
% 0.91/1.09 (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = max(X!5, Y!4)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[464, 90, 461])).
% 0.91/1.09 tff(466,plain,
% 0.91/1.09 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(467,plain,
% 0.91/1.09 (~(((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[466, 129])).
% 0.91/1.09 tff(468,plain,
% 0.91/1.09 (((~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) | ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(tautology,[status(thm)],[])).
% 0.91/1.09 tff(469,plain,
% 0.91/1.09 (ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[468, 452])).
% 0.91/1.09 tff(470,plain,
% 0.91/1.09 ((((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))) | (~ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.91/1.09 inference(tautology,[status(thm)],[])).
% 0.91/1.09 tff(471,plain,
% 0.91/1.09 ((((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ub(X!5, Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[470, 469])).
% 0.91/1.09 tff(472,plain,
% 0.91/1.09 (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[471, 467])).
% 0.91/1.09 tff(473,plain,
% 0.91/1.09 (((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) | lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(tautology,[status(thm)],[])).
% 0.91/1.09 tff(474,plain,
% 0.91/1.09 (lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[473, 472])).
% 0.91/1.09 tff(475,plain,
% 0.91/1.09 (((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) | lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(tautology,[status(thm)],[])).
% 0.91/1.09 tff(476,plain,
% 0.91/1.09 (lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[475, 472])).
% 0.91/1.09 tff(477,assumption,(lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), introduced(assumption)).
% 0.91/1.09 tff(478,assumption,(~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), introduced(assumption)).
% 0.91/1.09 tff(479,plain,
% 0.91/1.09 (lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[222])).
% 0.91/1.09 tff(480,plain,
% 0.91/1.09 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(symmetry,[status(thm)],[479])).
% 0.91/1.09 tff(481,plain,
% 0.91/1.09 ((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) <=> (~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[480])).
% 0.91/1.09 tff(482,plain,
% 0.91/1.09 (~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[478, 481])).
% 0.91/1.09 tff(483,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[477, 482])).
% 0.91/1.09 tff(484,plain,((~(max(X!5, Y!4) = Y!4)) | (~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(485,plain,
% 0.91/1.09 (~(max(X!5, Y!4) = Y!4)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[484, 478, 477])).
% 0.91/1.09 tff(486,plain,
% 0.91/1.09 (~lesseq(X!5, Y!4)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[94, 485])).
% 0.91/1.09 tff(487,plain,
% 0.91/1.09 (lesseq(Y!4, X!5)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[234, 38, 486])).
% 0.91/1.09 tff(488,plain,
% 0.91/1.09 (max(X!5, Y!4) = X!5),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[65, 487])).
% 0.91/1.09 tff(489,plain,
% 0.91/1.09 (X!5 = max(X!5, Y!4)),
% 0.91/1.09 inference(symmetry,[status(thm)],[488])).
% 0.91/1.09 tff(490,plain,
% 0.91/1.09 (lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[489])).
% 0.91/1.09 tff(491,plain,
% 0.91/1.09 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) <=> lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(symmetry,[status(thm)],[490])).
% 0.91/1.09 tff(492,plain,
% 0.91/1.09 ((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) <=> (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[491])).
% 0.91/1.09 tff(493,plain,
% 0.91/1.09 (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[478, 492])).
% 0.91/1.09 tff(494,assumption,(lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))), introduced(assumption)).
% 0.91/1.09 tff(495,plain,
% 0.91/1.09 ($false),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[494, 493])).
% 0.91/1.09 tff(496,plain,(lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.09 tff(497,plain,
% 0.91/1.09 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[496, 476, 474])).
% 0.91/1.09 tff(498,plain,
% 0.91/1.09 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.91/1.09 inference(rewrite,[status(thm)],[])).
% 0.91/1.09 tff(499,plain,
% 0.91/1.09 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)))),
% 0.91/1.09 inference(quant_inst,[status(thm)],[])).
% 0.91/1.09 tff(500,plain,
% 0.91/1.09 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.91/1.09 tff(501,plain,
% 0.91/1.09 ((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))) | (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5))),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[500, 61])).
% 0.91/1.09 tff(502,plain,
% 0.91/1.09 (max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4)) = tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5)),
% 0.91/1.09 inference(unit_resolution,[status(thm)],[501, 497])).
% 0.91/1.09 tff(503,plain,
% 0.91/1.09 (tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5) = max(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), max(X!5, Y!4))),
% 0.91/1.09 inference(symmetry,[status(thm)],[502])).
% 0.91/1.09 tff(504,plain,
% 0.91/1.09 (tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5) = max(X!5, Y!4)),
% 0.91/1.09 inference(transitivity,[status(thm)],[503, 465])).
% 0.91/1.09 tff(505,plain,
% 0.91/1.09 (lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.09 inference(monotonicity,[status(thm)],[504])).
% 0.91/1.09 tff(506,plain,
% 0.91/1.09 (lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.09 inference(symmetry,[status(thm)],[505])).
% 0.91/1.09 tff(507,plain,
% 0.91/1.09 ((~lesseq(max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[506])).
% 0.91/1.10 tff(508,plain,
% 0.91/1.10 (~lesseq(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, X!5), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[432, 507])).
% 0.91/1.10 tff(509,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[454, 508])).
% 0.91/1.10 tff(510,plain,((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(511,plain,
% 0.91/1.10 (~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[510, 336, 422])).
% 0.91/1.10 tff(512,plain,
% 0.91/1.10 (((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))) | model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(513,plain,
% 0.91/1.10 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[512, 511])).
% 0.91/1.10 tff(514,plain,
% 0.91/1.10 (((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | (~((~minsol_model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(515,plain,
% 0.91/1.10 (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[514, 293])).
% 0.91/1.10 tff(516,plain,
% 0.91/1.10 ((~(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))))) | minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(517,plain,
% 0.91/1.10 (minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3)) | (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[516, 515])).
% 0.91/1.10 tff(518,plain,
% 0.91/1.10 (~model_ub(X!5, Y!4, Z!3)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[517, 513, 332])).
% 0.91/1.10 tff(519,plain,
% 0.91/1.10 (((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~lesseq(tptp_fun_Z_0(Z!3, Y!4, X!5), Z!3)) | (~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)))))))) | (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(520,plain,
% 0.91/1.10 (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[519, 262])).
% 0.91/1.10 tff(521,plain,
% 0.91/1.10 ((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z))))) | model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(522,plain,
% 0.91/1.10 (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[521, 520])).
% 0.91/1.10 tff(523,plain,
% 0.91/1.10 (![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[522, 518])).
% 0.91/1.10 tff(524,plain,
% 0.91/1.10 (((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))) | ((~lesseq(Z!3, Z!3)) | (~ub(X!5, Y!4, Z!3)))) <=> ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))) | (~lesseq(Z!3, Z!3)) | (~ub(X!5, Y!4, Z!3)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(525,plain,
% 0.91/1.10 ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))) | ((~lesseq(Z!3, Z!3)) | (~ub(X!5, Y!4, Z!3)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(526,plain,
% 0.91/1.10 ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, Y!4, Z)))) | (~lesseq(Z!3, Z!3)) | (~ub(X!5, Y!4, Z!3))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.91/1.10 tff(527,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[526, 402, 523, 421])).
% 0.91/1.10 tff(528,plain,(minsol_model_ub(X!5, Y!4, Z!3) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(529,plain,
% 0.91/1.10 (lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[528, 332])).
% 0.91/1.10 tff(530,plain,
% 0.91/1.10 (((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(531,plain,
% 0.91/1.10 ((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[530, 529])).
% 0.91/1.10 tff(532,plain,
% 0.91/1.10 (~model_ub(X!5, Y!4, Z!3)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[517, 531, 332])).
% 0.91/1.10 tff(533,plain,
% 0.91/1.10 (~model_ub(max(X!5, Y!4), Y!4, Z!3)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[532, 415])).
% 0.91/1.10 tff(534,plain,
% 0.91/1.10 ((~(model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z))))) | model_ub(max(X!5, Y!4), Y!4, Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(535,plain,
% 0.91/1.10 (![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[534, 533, 412])).
% 0.91/1.10 tff(536,plain,
% 0.91/1.10 (((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))) | ((~lesseq(max(X!5, Y!4), Z!3)) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))))) <=> ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))) | (~lesseq(max(X!5, Y!4), Z!3)) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(537,plain,
% 0.91/1.10 ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))) | ((~lesseq(max(X!5, Y!4), Z!3)) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(538,plain,
% 0.91/1.10 ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(max(X!5, Y!4), Y!4, Z)))) | (~lesseq(max(X!5, Y!4), Z!3)) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.91/1.10 tff(539,plain,
% 0.91/1.10 (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[538, 311, 535])).
% 0.91/1.10 tff(540,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[539, 403])).
% 0.91/1.10 tff(541,plain,(minsol_model_ub(X!5, Y!4, Z!3) | (~(max(X!5, Y!4) = X!5))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(542,plain,
% 0.91/1.10 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[541, 1])).
% 0.91/1.10 tff(543,plain,
% 0.91/1.10 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[297, 542])).
% 0.91/1.10 tff(544,plain,
% 0.91/1.10 (((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))) | ![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(545,plain,
% 0.91/1.10 (![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[544, 543])).
% 0.91/1.10 tff(546,plain,
% 0.91/1.10 (((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, max(X!5, Y!4))) | lesseq(Z!3, max(X!5, Y!4)))) <=> ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, max(X!5, Y!4))) | lesseq(Z!3, max(X!5, Y!4)))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(547,plain,
% 0.91/1.10 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, max(X!5, Y!4))) | lesseq(Z!3, max(X!5, Y!4)))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(548,plain,
% 0.91/1.10 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, max(X!5, Y!4))) | lesseq(Z!3, max(X!5, Y!4))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.91/1.10 tff(549,plain,
% 0.91/1.10 (lesseq(Z!3, max(X!5, Y!4))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[548, 545, 147])).
% 0.91/1.10 tff(550,plain,
% 0.91/1.10 (max(max(X!5, Y!4), Z!3) = max(X!5, Y!4)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[345, 549])).
% 0.91/1.10 tff(551,plain,
% 0.91/1.10 (Z!3 = max(max(X!5, Y!4), Z!3)),
% 0.91/1.10 inference(symmetry,[status(thm)],[315])).
% 0.91/1.10 tff(552,plain,
% 0.91/1.10 (Z!3 = max(X!5, Y!4)),
% 0.91/1.10 inference(transitivity,[status(thm)],[551, 550])).
% 0.91/1.10 tff(553,plain,
% 0.91/1.10 (model_max(Z!3, Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) <=> model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[552])).
% 0.91/1.10 tff(554,plain,
% 0.91/1.10 (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) <=> model_max(Z!3, Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(symmetry,[status(thm)],[553])).
% 0.91/1.10 tff(555,plain,
% 0.91/1.10 (tptp_fun_Z_1(Z!3, Y!4, X!5) = tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[316])).
% 0.91/1.10 tff(556,plain,
% 0.91/1.10 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[316, 555])).
% 0.91/1.10 tff(557,plain,
% 0.91/1.10 ((minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3)) | (~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(558,plain,
% 0.91/1.10 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[557, 307])).
% 0.91/1.10 tff(559,plain,
% 0.91/1.10 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[558, 542])).
% 0.91/1.10 tff(560,plain,
% 0.91/1.10 (((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | (~((~minsol_model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))))))) | (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(561,plain,
% 0.91/1.10 (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[560, 184])).
% 0.91/1.10 tff(562,plain,
% 0.91/1.10 ((~(minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))))) | minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(563,plain,
% 0.91/1.10 (minsol_model_max(X!5, Y!4, Z!3) | (~model_max(X!5, Y!4, Z!3)) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[562, 561])).
% 0.91/1.10 tff(564,plain,
% 0.91/1.10 (minsol_model_max(X!5, Y!4, Z!3) | (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[563, 417])).
% 0.91/1.10 tff(565,plain,
% 0.91/1.10 (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[564, 559])).
% 0.91/1.10 tff(566,plain,
% 0.91/1.10 (((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))) | model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(567,plain,
% 0.91/1.10 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[566, 565])).
% 0.91/1.10 tff(568,plain,
% 0.91/1.10 (model_max(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[567, 556])).
% 0.91/1.10 tff(569,plain,
% 0.91/1.10 (model_max(Z!3, Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[568, 554])).
% 0.91/1.10 tff(570,plain,
% 0.91/1.10 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))) | (model_max(Z!3, Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) <=> lesseq(max(Z!3, Y!4), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(571,plain,
% 0.91/1.10 (model_max(Z!3, Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) <=> lesseq(max(Z!3, Y!4), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[570, 155])).
% 0.91/1.10 tff(572,plain,
% 0.91/1.10 (((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) | lesseq(Y!4, Z!3)),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(573,plain,
% 0.91/1.10 (lesseq(Y!4, Z!3)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[572, 387])).
% 0.91/1.10 tff(574,plain,
% 0.91/1.10 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, Z!3)) | (max(Z!3, Y!4) = Z!3))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, Z!3)) | (max(Z!3, Y!4) = Z!3))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(575,plain,
% 0.91/1.10 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, Z!3)) | (max(Z!3, Y!4) = Z!3))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(576,plain,
% 0.91/1.10 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, Z!3)) | (max(Z!3, Y!4) = Z!3)),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.91/1.10 tff(577,plain,
% 0.91/1.10 (max(Z!3, Y!4) = Z!3),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[576, 61, 573])).
% 0.91/1.10 tff(578,plain,
% 0.91/1.10 (lesseq(max(Z!3, Y!4), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) <=> lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[577])).
% 0.91/1.10 tff(579,plain,
% 0.91/1.10 (lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) <=> lesseq(max(Z!3, Y!4), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(symmetry,[status(thm)],[578])).
% 0.91/1.10 tff(580,plain,
% 0.91/1.10 ((~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))) <=> (~lesseq(max(Z!3, Y!4), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[579])).
% 0.91/1.10 tff(581,plain,
% 0.91/1.10 (lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[555])).
% 0.91/1.10 tff(582,plain,
% 0.91/1.10 ((~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))) <=> (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[581])).
% 0.91/1.10 tff(583,plain,
% 0.91/1.10 (((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))) | (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(584,plain,
% 0.91/1.10 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[583, 565])).
% 0.91/1.10 tff(585,plain,
% 0.91/1.10 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[584, 582])).
% 0.91/1.10 tff(586,plain,
% 0.91/1.10 (~lesseq(max(Z!3, Y!4), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[585, 580])).
% 0.91/1.10 tff(587,plain,
% 0.91/1.10 ((~(model_max(Z!3, Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) <=> lesseq(max(Z!3, Y!4), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))))) | (~model_max(Z!3, Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))) | lesseq(max(Z!3, Y!4), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(588,plain,
% 0.91/1.10 (~model_max(Z!3, Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[587, 586, 571])).
% 0.91/1.10 tff(589,plain,
% 0.91/1.10 ($false),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[588, 569])).
% 0.91/1.10 tff(590,plain,(~(max(X!5, Y!4) = X!5)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.10 tff(591,plain,
% 0.91/1.10 (~lesseq(Y!4, X!5)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[65, 590])).
% 0.91/1.10 tff(592,plain,
% 0.91/1.10 (lesseq(X!5, Y!4)),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[79, 38, 591])).
% 0.91/1.10 tff(593,plain,
% 0.91/1.10 (max(X!5, Y!4) = Y!4),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[94, 592])).
% 0.91/1.10 tff(594,plain,
% 0.91/1.10 (model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) <=> model_ub(X!5, Y!4, max(X!5, Y!4))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[593])).
% 0.91/1.10 tff(595,plain,
% 0.91/1.10 (model_ub(X!5, Y!4, max(X!5, Y!4)) <=> model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 0.91/1.10 inference(symmetry,[status(thm)],[594])).
% 0.91/1.10 tff(596,plain,
% 0.91/1.10 ((~model_ub(X!5, Y!4, max(X!5, Y!4))) <=> (~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[595])).
% 0.91/1.10 tff(597,plain,
% 0.91/1.10 (~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[5, 596])).
% 0.91/1.10 tff(598,plain,
% 0.91/1.10 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4)))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4))))))))))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(599,plain,
% 0.91/1.10 ((~((~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4))))))) | (~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))))) <=> (~((~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4)))))))))),
% 0.91/1.10 inference(rewrite,[status(thm)],[])).
% 0.91/1.10 tff(600,plain,
% 0.91/1.10 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4))))))) | (~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4))))))))))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[599])).
% 0.91/1.10 tff(601,plain,
% 0.91/1.10 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4))))))) | (~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4))))))))))),
% 0.91/1.10 inference(transitivity,[status(thm)],[600, 598])).
% 0.91/1.10 tff(602,plain,
% 0.91/1.10 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4))))))) | (~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z)))))))),
% 0.91/1.10 inference(quant_inst,[status(thm)],[])).
% 0.91/1.10 tff(603,plain,
% 0.91/1.10 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4)))))))))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.91/1.10 tff(604,plain,
% 0.91/1.10 (~((~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4))))))))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[603, 19])).
% 0.91/1.10 tff(605,plain,
% 0.91/1.10 (((~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(max(X!5, Y!4), max(X!5, Y!4), X!5), max(X!5, Y!4)))))))) | (model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(606,plain,
% 0.91/1.10 (model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z)))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[605, 604])).
% 0.91/1.10 tff(607,assumption,(![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z)))), introduced(assumption)).
% 0.91/1.10 tff(608,plain,
% 0.91/1.10 (Y!4 = max(X!5, Y!4)),
% 0.91/1.10 inference(symmetry,[status(thm)],[593])).
% 0.91/1.10 tff(609,plain,
% 0.91/1.10 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.91/1.10 inference(monotonicity,[status(thm)],[608])).
% 0.91/1.10 tff(610,plain,
% 0.91/1.10 (lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.91/1.10 inference(modus_ponens,[status(thm)],[115, 609])).
% 0.91/1.10 tff(611,plain,
% 0.91/1.10 (((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(Y!4, max(X!5, Y!4)))) | lesseq(X!5, max(X!5, Y!4))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(612,plain,
% 0.91/1.10 (lesseq(X!5, max(X!5, Y!4))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[611, 113])).
% 0.91/1.10 tff(613,plain,
% 0.91/1.10 ((~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))) | (~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.91/1.10 inference(tautology,[status(thm)],[])).
% 0.91/1.10 tff(614,plain,
% 0.91/1.10 ((~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.91/1.10 inference(unit_resolution,[status(thm)],[613, 612])).
% 0.91/1.10 tff(615,plain,
% 0.91/1.10 (~((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[614, 610])).
% 0.91/1.11 tff(616,assumption,(((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))), introduced(assumption)).
% 0.91/1.11 tff(617,plain,
% 0.91/1.11 (((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(618,plain,
% 0.91/1.11 ((~(((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))) <=> (~(((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(619,plain,
% 0.91/1.11 ((((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) <=> (((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(620,plain,
% 0.91/1.11 ((~(((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))) <=> (~(((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[619])).
% 0.91/1.11 tff(621,plain,
% 0.91/1.11 ((~(((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))) <=> (~(((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))),
% 0.91/1.11 inference(transitivity,[status(thm)],[620, 618])).
% 0.91/1.11 tff(622,plain,
% 0.91/1.11 (((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[621])).
% 0.91/1.11 tff(623,plain,
% 0.91/1.11 (((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))))),
% 0.91/1.11 inference(transitivity,[status(thm)],[622, 617])).
% 0.91/1.11 tff(624,plain,
% 0.91/1.11 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(625,plain,
% 0.91/1.11 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.91/1.11 tff(626,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[625, 129, 616])).
% 0.91/1.11 tff(627,plain,(~(((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(628,plain,
% 0.91/1.11 ((((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | ((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) | ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 0.91/1.11 inference(tautology,[status(thm)],[])).
% 0.91/1.11 tff(629,plain,
% 0.91/1.11 (((~lesseq(X!5, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) | ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[628, 627])).
% 0.91/1.11 tff(630,plain,
% 0.91/1.11 (ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[629, 615])).
% 0.91/1.11 tff(631,plain,
% 0.91/1.11 (((~![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z)))) | ((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))) <=> ((~![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z)))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(632,plain,
% 0.91/1.11 ((~![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z)))) | ((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(633,plain,
% 0.91/1.11 ((~![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z)))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4)))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.91/1.11 tff(634,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[633, 610, 630, 607])).
% 0.91/1.11 tff(635,plain,(~![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z)))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(636,plain,
% 0.91/1.11 ((~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))) | model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z)))),
% 0.91/1.11 inference(tautology,[status(thm)],[])).
% 0.91/1.11 tff(637,plain,
% 0.91/1.11 ((~(model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4)) | ![Z: $i] : ((~lesseq(Z, max(X!5, Y!4))) | (~ub(X!5, max(X!5, Y!4), Z))))) | model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[636, 635])).
% 0.91/1.11 tff(638,plain,
% 0.91/1.11 (model_ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[637, 606])).
% 0.91/1.11 tff(639,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[638, 597])).
% 0.91/1.11 tff(640,plain,(model_ub(X!5, Y!4, max(X!5, Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(641,assumption,(~model_ub(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.91/1.11 tff(642,plain,
% 0.91/1.11 ((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[268, 641])).
% 0.91/1.11 tff(643,plain,
% 0.91/1.11 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[297, 642])).
% 0.91/1.11 tff(644,plain,
% 0.91/1.11 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[309, 643])).
% 0.91/1.11 tff(645,plain,
% 0.91/1.11 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[188, 644])).
% 0.91/1.11 tff(646,plain,
% 0.91/1.11 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[335, 645])).
% 0.91/1.11 tff(647,plain,
% 0.91/1.11 (lesseq(Z!3, Z!3)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[420, 417, 646])).
% 0.91/1.11 tff(648,plain,
% 0.91/1.11 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3))))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3)))))))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(649,plain,
% 0.91/1.11 ((~((~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3)))))) | (~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))))) <=> (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3))))))))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(650,plain,
% 0.91/1.11 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3)))))) | (~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3)))))))))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[649])).
% 0.91/1.11 tff(651,plain,
% 0.91/1.11 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3)))))) | (~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3)))))))))),
% 0.91/1.11 inference(transitivity,[status(thm)],[650, 648])).
% 0.91/1.11 tff(652,plain,
% 0.91/1.11 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3)))))) | (~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))))))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(653,plain,
% 0.91/1.11 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(tptp_fun_Z_0(N, Y, X), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~lesseq(Z, N)) | (~ub(X, Y, Z)))))))) | (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3))))))))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.91/1.11 tff(654,plain,
% 0.91/1.11 (~((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3)))))))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[653, 19])).
% 0.91/1.11 tff(655,plain,
% 0.91/1.11 (((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | (~((~model_ub(X!5, max(X!5, Y!4), Z!3)) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5))) | (~lesseq(tptp_fun_Z_0(Z!3, max(X!5, Y!4), X!5), Z!3))))))) | (model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))),
% 0.91/1.11 inference(tautology,[status(thm)],[])).
% 0.91/1.11 tff(656,plain,
% 0.91/1.11 (model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[655, 654])).
% 0.91/1.11 tff(657,plain,
% 0.91/1.11 (model_ub(X!5, max(X!5, Y!4), Z!3) <=> model_ub(X!5, Y!4, Z!3)),
% 0.91/1.11 inference(monotonicity,[status(thm)],[221])).
% 0.91/1.11 tff(658,plain,
% 0.91/1.11 (model_ub(X!5, Y!4, Z!3) <=> model_ub(X!5, max(X!5, Y!4), Z!3)),
% 0.91/1.11 inference(symmetry,[status(thm)],[657])).
% 0.91/1.11 tff(659,plain,
% 0.91/1.11 ((~model_ub(X!5, Y!4, Z!3)) <=> (~model_ub(X!5, max(X!5, Y!4), Z!3))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[658])).
% 0.91/1.11 tff(660,plain,
% 0.91/1.11 (~model_ub(X!5, max(X!5, Y!4), Z!3)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[641, 659])).
% 0.91/1.11 tff(661,plain,
% 0.91/1.11 ((~(model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z))))) | model_ub(X!5, max(X!5, Y!4), Z!3) | ![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))),
% 0.91/1.11 inference(tautology,[status(thm)],[])).
% 0.91/1.11 tff(662,plain,
% 0.91/1.11 (![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[661, 660, 656])).
% 0.91/1.11 tff(663,plain,
% 0.91/1.11 (ub(X!5, max(X!5, Y!4), Z!3) <=> ub(X!5, Y!4, Z!3)),
% 0.91/1.11 inference(monotonicity,[status(thm)],[221])).
% 0.91/1.11 tff(664,plain,
% 0.91/1.11 (ub(X!5, Y!4, Z!3) <=> ub(X!5, max(X!5, Y!4), Z!3)),
% 0.91/1.11 inference(symmetry,[status(thm)],[663])).
% 0.91/1.11 tff(665,plain,
% 0.91/1.11 (ub(X!5, max(X!5, Y!4), Z!3)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[402, 664])).
% 0.91/1.11 tff(666,assumption,(~ub(X!5, max(X!5, Y!4), Z!3)), introduced(assumption)).
% 0.91/1.11 tff(667,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[666, 665])).
% 0.91/1.11 tff(668,plain,(ub(X!5, max(X!5, Y!4), Z!3) | (~(max(X!5, Y!4) = Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(669,plain,
% 0.91/1.11 (ub(X!5, max(X!5, Y!4), Z!3)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[668, 221])).
% 0.91/1.11 tff(670,plain,
% 0.91/1.11 (((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))) | ((~lesseq(Z!3, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z!3)))) <=> ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))) | (~lesseq(Z!3, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z!3)))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(671,plain,
% 0.91/1.11 ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))) | ((~lesseq(Z!3, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z!3)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(672,plain,
% 0.91/1.11 ((~![Z: $i] : ((~lesseq(Z, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z)))) | (~lesseq(Z!3, Z!3)) | (~ub(X!5, max(X!5, Y!4), Z!3))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[671, 670])).
% 0.91/1.11 tff(673,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[672, 669, 662, 647])).
% 0.91/1.11 tff(674,plain,(model_ub(X!5, Y!4, Z!3) | (~(max(X!5, Y!4) = Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(675,plain,
% 0.91/1.11 (model_ub(X!5, Y!4, Z!3)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[674, 593])).
% 0.91/1.11 tff(676,assumption,(model_ub(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.91/1.11 tff(677,plain,
% 0.91/1.11 (~((~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[517, 332, 676])).
% 0.91/1.11 tff(678,plain,
% 0.91/1.11 ($false),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[530, 677, 529])).
% 0.91/1.11 tff(679,plain,(minsol_model_ub(X!5, Y!4, Z!3) | (~model_ub(X!5, Y!4, Z!3))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.11 tff(680,plain,
% 0.91/1.11 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[679, 675])).
% 0.91/1.11 tff(681,plain,
% 0.91/1.11 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[297, 680])).
% 0.91/1.11 tff(682,plain,
% 0.91/1.11 (![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[544, 681])).
% 0.91/1.11 tff(683,plain,
% 0.91/1.11 (lesseq(Z!3, max(X!5, Y!4))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[548, 682, 640])).
% 0.91/1.11 tff(684,plain,
% 0.91/1.11 (max(max(X!5, Y!4), Z!3) = max(X!5, Y!4)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[345, 683])).
% 0.91/1.11 tff(685,plain,
% 0.91/1.11 (Z!3 = max(X!5, Y!4)),
% 0.91/1.11 inference(transitivity,[status(thm)],[551, 684])).
% 0.91/1.11 tff(686,plain,
% 0.91/1.11 (model_max(X!5, Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[685])).
% 0.91/1.11 tff(687,plain,
% 0.91/1.11 (model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> model_max(X!5, Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.11 inference(symmetry,[status(thm)],[686])).
% 0.91/1.11 tff(688,plain,
% 0.91/1.11 (tptp_fun_Z_1(Z!3, Y!4, X!5) = tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)),
% 0.91/1.11 inference(monotonicity,[status(thm)],[608])).
% 0.91/1.11 tff(689,plain,
% 0.91/1.11 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[608, 688])).
% 0.91/1.11 tff(690,plain,
% 0.91/1.11 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[558, 680])).
% 0.91/1.11 tff(691,plain,
% 0.91/1.11 (~((~model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[564, 690])).
% 0.91/1.11 tff(692,plain,
% 0.91/1.11 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[566, 691])).
% 0.91/1.11 tff(693,plain,
% 0.91/1.11 (model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[692, 689])).
% 0.91/1.11 tff(694,plain,
% 0.91/1.11 (model_max(X!5, Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[693, 687])).
% 0.91/1.11 tff(695,plain,
% 0.91/1.11 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(max(X, Y), N))) | (model_max(X!5, Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> lesseq(max(X!5, Z!3), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(696,plain,
% 0.91/1.11 (model_max(X!5, Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> lesseq(max(X!5, Z!3), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[695, 155])).
% 0.91/1.11 tff(697,plain,
% 0.91/1.11 (((~lesseq(X!5, Z!3)) | (~lesseq(Y!4, Z!3))) | lesseq(X!5, Z!3)),
% 0.91/1.11 inference(tautology,[status(thm)],[])).
% 0.91/1.11 tff(698,plain,
% 0.91/1.11 (lesseq(X!5, Z!3)),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[697, 387])).
% 0.91/1.11 tff(699,plain,
% 0.91/1.11 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Z!3)) | (max(X!5, Z!3) = Z!3))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Z!3)) | (max(X!5, Z!3) = Z!3))),
% 0.91/1.11 inference(rewrite,[status(thm)],[])).
% 0.91/1.11 tff(700,plain,
% 0.91/1.11 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Z!3)) | (max(X!5, Z!3) = Z!3))),
% 0.91/1.11 inference(quant_inst,[status(thm)],[])).
% 0.91/1.11 tff(701,plain,
% 0.91/1.11 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Z!3)) | (max(X!5, Z!3) = Z!3)),
% 0.91/1.11 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.91/1.11 tff(702,plain,
% 0.91/1.11 (max(X!5, Z!3) = Z!3),
% 0.91/1.11 inference(unit_resolution,[status(thm)],[701, 90, 698])).
% 0.91/1.11 tff(703,plain,
% 0.91/1.11 (lesseq(max(X!5, Z!3), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> lesseq(Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.11 inference(monotonicity,[status(thm)],[702])).
% 0.91/1.11 tff(704,plain,
% 0.91/1.11 (lesseq(Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> lesseq(max(X!5, Z!3), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.11 inference(symmetry,[status(thm)],[703])).
% 0.91/1.11 tff(705,plain,
% 0.91/1.11 ((~lesseq(Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))) <=> (~lesseq(max(X!5, Z!3), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[704])).
% 0.91/1.12 tff(706,plain,
% 0.91/1.12 (lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[688])).
% 0.91/1.12 tff(707,plain,
% 0.91/1.12 ((~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))) <=> (~lesseq(Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)))),
% 0.91/1.12 inference(monotonicity,[status(thm)],[706])).
% 0.91/1.12 tff(708,plain,
% 0.91/1.12 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[583, 691])).
% 0.91/1.12 tff(709,plain,
% 0.91/1.12 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.91/1.12 tff(710,plain,
% 0.91/1.12 (~lesseq(max(X!5, Z!3), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.12 inference(modus_ponens,[status(thm)],[709, 705])).
% 0.91/1.12 tff(711,plain,
% 0.91/1.12 ((~(model_max(X!5, Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> lesseq(max(X!5, Z!3), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)))) | (~model_max(X!5, Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))) | lesseq(max(X!5, Z!3), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.12 inference(tautology,[status(thm)],[])).
% 0.91/1.12 tff(712,plain,
% 0.91/1.12 (~model_max(X!5, Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[711, 710, 696])).
% 0.91/1.12 tff(713,plain,
% 0.91/1.12 ($false),
% 0.91/1.12 inference(unit_resolution,[status(thm)],[712, 694])).
% 0.91/1.12 % SZS output end Proof
% 0.91/1.12 % E exiting
%------------------------------------------------------------------------------