%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM862+1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:22:16 AM UTC 2025
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM862+1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 02:02:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(lesseq_type, type, (
% 0.20/0.44 lesseq: ( $i * $i ) > $o)).
% 0.20/0.44 tff(tptp_fun_Y_4_type, type, (
% 0.20/0.44 tptp_fun_Y_4: $i)).
% 0.20/0.44 tff(tptp_fun_X_5_type, type, (
% 0.20/0.44 tptp_fun_X_5: $i)).
% 0.20/0.44 tff(max_type, type, (
% 0.20/0.44 max: ( $i * $i ) > $i)).
% 0.20/0.44 tff(tptp_fun_Z_2_type, type, (
% 0.20/0.44 tptp_fun_Z_2: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(tptp_fun_Z_3_type, type, (
% 0.20/0.44 tptp_fun_Z_3: $i)).
% 0.20/0.44 tff(model_ub_type, type, (
% 0.20/0.44 model_ub: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(sum_type, type, (
% 0.20/0.44 sum: ( $i * $i ) > $i)).
% 0.20/0.44 tff(summation_type, type, (
% 0.20/0.44 summation: $i > $i)).
% 0.20/0.44 tff(c_type, type, (
% 0.20/0.44 c: $i)).
% 0.20/0.44 tff(ub_type, type, (
% 0.20/0.44 ub: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(tptp_fun_Z_0_type, type, (
% 0.20/0.44 tptp_fun_Z_0: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(model_max_type, type, (
% 0.20/0.44 model_max: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(minsol_model_ub_type, type, (
% 0.20/0.44 minsol_model_ub: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(minsol_model_max_type, type, (
% 0.20/0.44 minsol_model_max: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(tptp_fun_Z_1_type, type, (
% 0.20/0.44 tptp_fun_Z_1: ( $i * $i * $i ) > $i)).
% 0.20/0.44 tff(1,assumption,((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))))))), introduced(assumption)).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 (^[X: $i, Y: $i, N: $i] : refl((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 (^[X: $i, Y: $i, N: $i] : rewrite((~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (^[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(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))) <=> ((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))), rewrite((model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N)))) <=> (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N))))) <=> (((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))))), rewrite((((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))))) & (model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))), ((((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N))))) <=> (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N))))) <=> ![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N))) <=> ![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(10,axiom,(![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','model_ub_5')).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 (![X: $i, Y: $i, N: $i] : (model_ub(X, Y, N) <=> ?[Z: $i] : (ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.44 tff(12,plain,(
% 0.20/0.44 ![X: $i, Y: $i, N: $i] : (((~model_ub(X, Y, N)) | (ub(X, Y, tptp_fun_Z_0(N, Y, X)) & lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N))) & (model_ub(X, Y, N) | ![Z: $i] : (~(ub(X, Y, Z) & lesseq(sum(c, summation(Z)), N)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[11])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.44 tff(14,plain,
% 0.20/0.44 (![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, 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(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 ((~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))))) <=> (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))))))) <=> ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[17, 15])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))))) | (~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[20, 14, 1])).
% 0.20/0.45 tff(22,plain,(~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))))))) | (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.45 tff(25,assumption,(![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))), introduced(assumption)).
% 0.20/0.45 tff(26,assumption,(((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, Y!4, max(X!5, Y!4))), introduced(assumption)).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (^[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))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(32,axiom,(![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ub')).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.45 tff(34,plain,(
% 0.20/0.45 ![X: $i, Y: $i, Z: $i] : (ub(X, Y, Z) <=> (lesseq(X, Z) & lesseq(Y, Z)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[33])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 (![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, Y!4, max(X!5, Y!4))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[37, 36, 26])).
% 0.20/0.45 tff(39,plain,(~(((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, Y!4, max(X!5, Y!4)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(40,assumption,((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))), introduced(assumption)).
% 0.20/0.45 tff(41,assumption,(lesseq(Y!4, X!5)), introduced(assumption)).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : refl(((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X)) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = X) | (~lesseq(Y, X))) <=> ((~lesseq(Y, X)) | (max(X, Y) = X)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X))) <=> ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.45 tff(47,axiom,(![X: $i, Y: $i] : ((max(X, Y) = X) | (~lesseq(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_1')).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.45 tff(50,plain,(
% 0.20/0.45 ![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.20/0.45 inference(skolemize,[status(sab)],[49])).
% 0.20/0.45 tff(51,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (((~![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))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(54,plain,
% 0.20/0.45 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 ((~lesseq(Y!4, X!5)) | (max(X!5, Y!4) = X!5)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (max(X!5, Y!4) = X!5),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[55, 41])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 (X!5 = max(X!5, Y!4)),
% 0.20/0.45 inference(symmetry,[status(thm)],[56])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 (lesseq(Y!4, X!5) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (lesseq(Y!4, max(X!5, Y!4))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[41, 58])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (lesseq(X!5, max(X!5, Y!4)) <=> lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (lesseq(max(X!5, Y!4), max(X!5, Y!4)) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.20/0.45 inference(symmetry,[status(thm)],[60])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : refl((lesseq(X, Y) | lesseq(Y, X)) <=> (lesseq(X, Y) | lesseq(Y, X)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X)) <=> ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(65,axiom,(![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lesseq_total')).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.46 tff(67,plain,(
% 0.20/0.46 ![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.20/0.46 inference(skolemize,[status(sab)],[66])).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 (![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(max(X!5, Y!4), max(X!5, Y!4))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 ((lesseq(max(X!5, 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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(max(X!5, Y!4), max(X!5, Y!4)) | lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[70])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(max(X!5, Y!4), max(X!5, Y!4)) | lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.20/0.46 inference(transitivity,[status(thm)],[71, 69])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(max(X!5, Y!4), max(X!5, Y!4)) | lesseq(max(X!5, Y!4), max(X!5, Y!4)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 (lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[74, 68])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (lesseq(X!5, max(X!5, Y!4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[75, 61])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 ((~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4))))) | (~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[77, 76, 59, 40])).
% 0.20/0.46 tff(79,plain,((~lesseq(Y!4, X!5)) | (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (~lesseq(Y!4, X!5)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[79, 40])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (((~![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(X!5, Y!4) | lesseq(Y!4, X!5))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(X!5, Y!4) | lesseq(Y!4, X!5)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (lesseq(X!5, Y!4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[83, 68, 80])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (^[X: $i, Y: $i] : refl(((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y)) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (^[X: $i, Y: $i] : rewrite(((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ((~lesseq(X, Y)) | (max(X, Y) = Y)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y))) <=> ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.46 tff(90,axiom,(![X: $i, Y: $i] : ((max(X, Y) = Y) | (~lesseq(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_2')).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.46 tff(93,plain,(
% 0.20/0.46 ![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.20/0.46 inference(skolemize,[status(sab)],[92])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 (((~![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 ((~lesseq(X!5, Y!4)) | (max(X!5, Y!4) = Y!4)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (max(X!5, Y!4) = Y!4),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[98, 84])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (Y!4 = max(X!5, Y!4)),
% 0.20/0.46 inference(symmetry,[status(thm)],[99])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (lesseq(X!5, Y!4) <=> lesseq(X!5, max(X!5, Y!4))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (lesseq(X!5, max(X!5, Y!4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[84, 101])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (lesseq(Y!4, max(X!5, Y!4)) <=> lesseq(max(X!5, Y!4), max(X!5, Y!4))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (lesseq(max(X!5, Y!4), max(X!5, Y!4)) <=> lesseq(Y!4, max(X!5, Y!4))),
% 0.20/0.46 inference(symmetry,[status(thm)],[103])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 (lesseq(Y!4, max(X!5, Y!4))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[75, 104])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[77, 105, 102, 40])).
% 0.20/0.46 tff(107,plain,(~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 ((((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, Y!4, max(X!5, Y!4))) | ((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) | ub(X!5, Y!4, max(X!5, Y!4))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 ((((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, Y!4, max(X!5, Y!4))) | ub(X!5, Y!4, max(X!5, Y!4))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 (ub(X!5, Y!4, max(X!5, Y!4))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[109, 39])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (^[X: $i, Y: $i, N: $i] : refl((model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N)) <=> (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N)) <=> ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(114,axiom,(![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','model_max_5')).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.46 tff(116,plain,(
% 0.20/0.46 ![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))),
% 0.20/0.46 inference(skolemize,[status(sab)],[115])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(X!5, Y!4, Z!3) <=> lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 (model_max(X!5, Y!4, Z!3) <=> lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (~((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[20, 14])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | (~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))))))) | ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 ((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.20/0.46 tff(123,assumption,(~model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (((~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)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 ((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (^[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))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (![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)))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 (^[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))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (![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)))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 (![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)))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[129, 127])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 (^[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)))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (![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)))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 (^[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)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 (![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))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.46 tff(138,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/sandbox/benchmark/theBenchmark.p','minsol_model_max')).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.20/0.46 tff(141,plain,(
% 0.20/0.46 ![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)))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[140])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (![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))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 (![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)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (![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)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[143, 130])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 ((~![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)))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (~((~(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))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (((~(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))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 ((~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)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 ((~((~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)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 ((~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)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[150, 125])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 ((~(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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 ((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(154,axiom,(~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','max_is_ub_1')).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[155, 153])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[156, 153])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (~![X: $i, Y: $i, Z: $i] : (minsol_model_ub(X, Y, Z) <=> minsol_model_max(X, Y, Z))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.20/0.47 tff(159,plain,(
% 0.20/0.47 ~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.20/0.47 inference(skolemize,[status(sab)],[158])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (~(minsol_model_ub(X!5, Y!4, Z!3) <=> minsol_model_max(X!5, Y!4, Z!3))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[159, 152])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 ((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)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 (minsol_model_ub(X!5, Y!4, Z!3) | minsol_model_max(X!5, Y!4, Z!3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[162, 151])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 (^[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))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (![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)))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 (^[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)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(167,plain,
% 0.20/0.47 (![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))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.47 tff(168,plain,
% 0.20/0.47 (^[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)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(169,plain,
% 0.20/0.47 (![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))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 (![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))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[169, 167])).
% 0.20/0.47 tff(171,plain,
% 0.20/0.47 (^[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))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(172,plain,
% 0.20/0.47 (![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))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[171])).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 (^[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)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[173])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[176])).
% 0.20/0.47 tff(178,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/sandbox/benchmark/theBenchmark.p','minsol_model_ub')).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.20/0.47 tff(181,plain,(
% 0.20/0.47 ![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)))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[180])).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.20/0.47 tff(183,plain,
% 0.20/0.47 (![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))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[182, 172])).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 (![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))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[183, 170])).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 (![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)))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[184, 165])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 ((~![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)))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(187,plain,
% 0.20/0.47 (~((~(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))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.20/0.47 tff(188,plain,
% 0.20/0.47 (((~(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))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(189,plain,
% 0.20/0.47 ((~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)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.20/0.47 tff(190,plain,
% 0.20/0.47 ((~((~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)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(191,plain,
% 0.20/0.47 ((~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)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.20/0.47 tff(192,plain,
% 0.20/0.47 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[191, 163])).
% 0.20/0.47 tff(193,plain,
% 0.20/0.47 (((~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)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(194,plain,
% 0.20/0.47 (model_ub(X!5, Y!4, Z!3)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.20/0.47 tff(195,plain,
% 0.20/0.47 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))))) | (~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(196,plain,
% 0.20/0.47 ((~((~model_ub(X!5, Y!4, Z!3)) | (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(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(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.20/0.47 tff(197,plain,
% 0.20/0.47 (~((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[196, 122])).
% 0.20/0.47 tff(198,plain,
% 0.20/0.47 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3))) | lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 (lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.20/0.48 tff(200,plain,
% 0.20/0.48 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))) | model_max(X!5, Y!4, Z!3) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(201,plain,
% 0.20/0.48 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[200, 123])).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[201, 119])).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 (^[X: $i, Y: $i, Z: $i] : refl((lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))) <=> (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(204,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[203])).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y))) <=> ![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(206,axiom,(![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sum_monotone_1')).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.20/0.48 tff(208,plain,(
% 0.20/0.48 ![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[207])).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.20/0.48 tff(210,plain,
% 0.20/0.48 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))) | (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 (^[X: $i, Y: $i] : refl((lesseq(X, Y) <=> lesseq(summation(X), summation(Y))) <=> (lesseq(X, Y) <=> lesseq(summation(X), summation(Y))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y))) <=> ![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[212])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y))) <=> ![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(215,axiom,(![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','summation_monotone')).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.20/0.48 tff(217,plain,(
% 0.20/0.48 ![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[216])).
% 0.20/0.48 tff(218,plain,
% 0.20/0.48 (![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.20/0.48 tff(219,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))) | (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(220,plain,
% 0.20/0.48 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.20/0.48 tff(221,plain,
% 0.20/0.48 ((~![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))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(222,plain,
% 0.20/0.48 (~(((~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)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[221, 36])).
% 0.20/0.48 tff(223,plain,
% 0.20/0.48 (((~ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(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))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 (ub(X!5, Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[223, 197])).
% 0.20/0.48 tff(225,plain,
% 0.20/0.48 ((((~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)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(226,plain,
% 0.20/0.48 ((((~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)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.20/0.48 tff(227,plain,
% 0.20/0.48 (~((~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))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[226, 222])).
% 0.20/0.48 tff(228,plain,
% 0.20/0.48 (((~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))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(229,plain,
% 0.20/0.48 (lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 (((~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))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(231,plain,
% 0.20/0.48 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[230, 227])).
% 0.20/0.48 tff(232,assumption,(lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.20/0.48 tff(233,assumption,(~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.20/0.48 tff(234,assumption,(max(X!5, Y!4) = Y!4), introduced(assumption)).
% 0.20/0.48 tff(235,plain,
% 0.20/0.48 (Y!4 = max(X!5, Y!4)),
% 0.20/0.48 inference(symmetry,[status(thm)],[234])).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 (lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[235])).
% 0.20/0.48 tff(237,plain,
% 0.20/0.48 (lesseq(max(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))),
% 0.20/0.48 inference(symmetry,[status(thm)],[236])).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 ((~lesseq(max(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)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[237])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[233, 238])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[232, 239])).
% 0.20/0.48 tff(241,plain,((~(max(X!5, Y!4) = Y!4)) | (~lesseq(Y!4, tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 (~(max(X!5, Y!4) = Y!4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[241, 233, 232])).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 (~lesseq(X!5, Y!4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[98, 242])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 (((~![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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(Y!4, X!5) | lesseq(X!5, Y!4))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(Y!4, X!5) | lesseq(X!5, Y!4)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (lesseq(Y!4, X!5)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[246, 68, 243])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 (max(X!5, Y!4) = X!5),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[55, 247])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 (X!5 = max(X!5, Y!4)),
% 0.20/0.48 inference(symmetry,[status(thm)],[248])).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 (lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[249])).
% 0.20/0.48 tff(251,plain,
% 0.20/0.48 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.20/0.48 inference(symmetry,[status(thm)],[250])).
% 0.20/0.48 tff(252,plain,
% 0.20/0.48 ((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[251])).
% 0.20/0.48 tff(253,plain,
% 0.20/0.48 (~lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[233, 252])).
% 0.20/0.48 tff(254,assumption,(lesseq(X!5, tptp_fun_Z_0(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.20/0.48 tff(255,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.20/0.48 tff(256,plain,(lesseq(max(X!5, 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)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[256, 231, 229])).
% 0.20/0.48 tff(258,plain,
% 0.20/0.48 ((~(lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5)) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(Z!3, Y!4, X!5))) | lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[258, 257, 220])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 ((~(lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(261,plain,
% 0.20/0.48 (lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[260, 259, 211])).
% 0.20/0.48 tff(262,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(263,plain,
% 0.20/0.48 (^[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)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(264,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[263])).
% 0.20/0.48 tff(265,plain,
% 0.20/0.48 (![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))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 (^[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)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(267,plain,
% 0.20/0.48 (![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))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[266])).
% 0.20/0.48 tff(268,axiom,(![X: $i, Y: $i, Z: $i] : ((lesseq(X, Y) & lesseq(Y, Z)) => lesseq(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lesseq_trans')).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.20/0.48 tff(270,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[269, 265])).
% 0.20/0.48 tff(271,plain,(
% 0.20/0.48 ![X: $i, Y: $i, Z: $i] : ((~(lesseq(X, Y) & lesseq(Y, Z))) | lesseq(X, Z))),
% 0.20/0.48 inference(skolemize,[status(sab)],[270])).
% 0.20/0.48 tff(272,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[271, 264])).
% 0.20/0.48 tff(273,plain,
% 0.20/0.48 (![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[272, 262])).
% 0.20/0.48 tff(274,plain,
% 0.20/0.48 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | ((~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(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(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(275,plain,
% 0.20/0.48 ((lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))) <=> ((~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(276,plain,
% 0.20/0.48 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(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(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[275])).
% 0.20/0.48 tff(277,plain,
% 0.20/0.48 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(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(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[276, 274])).
% 0.20/0.48 tff(278,plain,
% 0.20/0.48 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(279,plain,
% 0.20/0.48 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5))), Z!3)) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(Z!3, Y!4, X!5)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.20/0.48 tff(280,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[279, 273, 261, 202, 199])).
% 0.20/0.48 tff(281,plain,(model_max(X!5, Y!4, Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(282,plain,
% 0.20/0.48 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))) | (~model_max(X!5, Y!4, Z!3)) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(283,plain,
% 0.20/0.48 ((~(model_max(X!5, Y!4, Z!3) <=> lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))) | lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.20/0.48 tff(284,plain,
% 0.20/0.48 (lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[283, 119])).
% 0.20/0.48 tff(285,plain,
% 0.20/0.48 (((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)))) <=> ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(286,plain,
% 0.20/0.48 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | ((~ub(X!5, Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(287,plain,
% 0.20/0.48 ((~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))) | (~ub(X!5, Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.20/0.48 tff(288,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[287, 284, 110, 25])).
% 0.20/0.48 tff(289,plain,(~![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(290,plain,
% 0.20/0.48 ((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(291,plain,
% 0.20/0.48 ((~(model_ub(X!5, Y!4, Z!3) | ![Z: $i] : ((~ub(X!5, Y!4, Z)) | (~lesseq(sum(c, summation(Z)), Z!3))))) | model_ub(X!5, Y!4, Z!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[290, 289])).
% 0.20/0.48 tff(292,plain,
% 0.20/0.48 (model_ub(X!5, Y!4, Z!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[291, 24])).
% 0.20/0.48 tff(293,plain,
% 0.20/0.48 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)), Y!4, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(294,plain,
% 0.20/0.48 (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)), Y!4, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[293, 14])).
% 0.20/0.49 tff(295,plain,
% 0.20/0.49 (((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)), Y!4, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))))) | (model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(296,plain,
% 0.20/0.49 (model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[295, 294])).
% 0.20/0.49 tff(297,assumption,(minsol_model_ub(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.20/0.49 tff(298,plain,
% 0.20/0.49 ((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))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(299,plain,
% 0.20/0.49 ((~minsol_model_ub(X!5, Y!4, Z!3)) | (~minsol_model_max(X!5, Y!4, Z!3))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[298, 160])).
% 0.20/0.49 tff(300,plain,
% 0.20/0.49 (~minsol_model_max(X!5, Y!4, Z!3)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[299, 297])).
% 0.20/0.49 tff(301,plain,
% 0.20/0.49 (((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) | lesseq(X!5, max(X!5, Y!4))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(302,plain,
% 0.20/0.49 (lesseq(X!5, max(X!5, Y!4))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[301, 107])).
% 0.20/0.49 tff(303,plain,
% 0.20/0.49 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, max(X!5, Y!4))) | (max(X!5, max(X!5, Y!4)) = max(X!5, Y!4)))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, max(X!5, Y!4))) | (max(X!5, max(X!5, Y!4)) = max(X!5, Y!4)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(304,plain,
% 0.20/0.49 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(X!5, max(X!5, Y!4))) | (max(X!5, max(X!5, Y!4)) = max(X!5, Y!4)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(305,plain,
% 0.20/0.49 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(X!5, max(X!5, Y!4))) | (max(X!5, max(X!5, Y!4)) = max(X!5, Y!4))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.20/0.49 tff(306,plain,
% 0.20/0.49 (max(X!5, max(X!5, Y!4)) = max(X!5, Y!4)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[305, 94, 302])).
% 0.20/0.49 tff(307,plain,
% 0.20/0.49 (summation(max(X!5, max(X!5, Y!4))) = summation(max(X!5, Y!4))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[306])).
% 0.20/0.49 tff(308,plain,
% 0.20/0.49 (sum(c, summation(max(X!5, max(X!5, Y!4)))) = sum(c, summation(max(X!5, Y!4)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[307])).
% 0.20/0.49 tff(309,plain,
% 0.20/0.49 (sum(c, summation(max(X!5, Y!4))) = sum(c, summation(max(X!5, max(X!5, Y!4))))),
% 0.20/0.49 inference(symmetry,[status(thm)],[308])).
% 0.20/0.49 tff(310,plain,
% 0.20/0.49 (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[309])).
% 0.20/0.49 tff(311,plain,
% 0.20/0.49 (lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.49 inference(symmetry,[status(thm)],[310])).
% 0.20/0.49 tff(312,plain,
% 0.20/0.49 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(313,plain,
% 0.20/0.49 (model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[312, 117])).
% 0.20/0.49 tff(314,plain,
% 0.20/0.49 (tptp_fun_Z_1(Z!3, Y!4, X!5) = tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[235])).
% 0.20/0.49 tff(315,plain,
% 0.20/0.49 (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))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[235, 314])).
% 0.20/0.49 tff(316,assumption,(~minsol_model_max(X!5, Y!4, Z!3)), introduced(assumption)).
% 0.20/0.49 tff(317,plain,
% 0.20/0.49 (((~(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)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(318,plain,
% 0.20/0.49 (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))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[317, 146])).
% 0.20/0.49 tff(319,plain,
% 0.20/0.49 ((~(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))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(320,plain,
% 0.20/0.49 (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))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[319, 318])).
% 0.20/0.49 tff(321,plain,
% 0.20/0.49 (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))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[320, 281])).
% 0.20/0.49 tff(322,plain,
% 0.20/0.49 (~((~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)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[321, 316])).
% 0.20/0.49 tff(323,plain,
% 0.20/0.49 (((~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))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(324,plain,
% 0.20/0.49 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[323, 322])).
% 0.20/0.49 tff(325,plain,
% 0.20/0.49 (model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[324, 315])).
% 0.20/0.49 tff(326,plain,
% 0.20/0.49 ((~(model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> lesseq(sum(c, summation(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, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))) | lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(327,plain,
% 0.20/0.49 ((~(model_max(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)))) | lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[326, 325])).
% 0.20/0.49 tff(328,plain,
% 0.20/0.49 (lesseq(sum(c, summation(max(X!5, max(X!5, Y!4)))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[327, 313])).
% 0.20/0.49 tff(329,plain,
% 0.20/0.49 (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[328, 311])).
% 0.20/0.49 tff(330,plain,
% 0.20/0.49 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))))) | (~(model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(331,plain,
% 0.20/0.49 (~((~((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))))) | (~(model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[330, 14])).
% 0.20/0.49 tff(332,plain,
% 0.20/0.49 (((~((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))))) | (~(model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))))) | (model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(333,plain,
% 0.20/0.49 (model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[332, 331])).
% 0.20/0.49 tff(334,plain,
% 0.20/0.49 (model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[234])).
% 0.20/0.49 tff(335,plain,
% 0.20/0.49 (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) <=> model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.49 inference(symmetry,[status(thm)],[334])).
% 0.20/0.49 tff(336,plain,
% 0.20/0.49 ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))) <=> (~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[335])).
% 0.20/0.49 tff(337,plain,
% 0.20/0.49 (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))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[314])).
% 0.20/0.49 tff(338,plain,
% 0.20/0.49 ((~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)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[337])).
% 0.20/0.49 tff(339,plain,
% 0.20/0.49 (((~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)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(340,plain,
% 0.20/0.49 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[339, 322])).
% 0.20/0.49 tff(341,plain,
% 0.20/0.49 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[340, 338])).
% 0.20/0.50 tff(342,plain,
% 0.20/0.50 (minsol_model_ub(X!5, Y!4, Z!3)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[162, 316])).
% 0.20/0.50 tff(343,plain,
% 0.20/0.50 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[191, 342])).
% 0.20/0.50 tff(344,plain,
% 0.20/0.50 (((~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))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(345,plain,
% 0.20/0.50 (![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[344, 343])).
% 0.20/0.50 tff(346,plain,
% 0.20/0.50 (((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, 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)))) <=> ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, 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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(347,plain,
% 0.20/0.50 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(X!5, Y!4, 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)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(348,plain,
% 0.20/0.50 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, 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))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.20/0.50 tff(349,plain,
% 0.20/0.50 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[348, 345, 341])).
% 0.20/0.50 tff(350,plain,
% 0.20/0.50 (~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[349, 336])).
% 0.20/0.50 tff(351,plain,
% 0.20/0.50 ((~(model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)))))) | model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(352,plain,
% 0.20/0.50 (![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[351, 350, 333])).
% 0.20/0.50 tff(353,assumption,(((~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))), introduced(assumption)).
% 0.20/0.50 tff(354,plain,
% 0.20/0.50 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) <=> ub(X!5, max(X!5, Y!4), max(X!5, Y!4))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(355,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[354, 36, 353])).
% 0.20/0.50 tff(356,plain,(~(((~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)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(357,plain,
% 0.20/0.50 ((~((~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))) | (~lesseq(X!5, max(X!5, Y!4)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(358,plain,
% 0.20/0.50 (~((~lesseq(max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[357, 75, 302])).
% 0.20/0.50 tff(359,plain,
% 0.20/0.50 ((((~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(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))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(360,plain,
% 0.20/0.50 ((((~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))) | ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[359, 358])).
% 0.20/0.50 tff(361,plain,
% 0.20/0.50 (ub(X!5, max(X!5, Y!4), max(X!5, Y!4))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[360, 356])).
% 0.20/0.50 tff(362,plain,
% 0.20/0.50 (((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))) | ((~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))) <=> ((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(363,plain,
% 0.20/0.50 ((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))) | ((~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(364,plain,
% 0.20/0.50 ((~![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5))))) | (~ub(X!5, max(X!5, Y!4), max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, max(X!5, Y!4), X!5)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.20/0.50 tff(365,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[364, 361, 352, 329])).
% 0.20/0.50 tff(366,plain,(minsol_model_max(X!5, Y!4, Z!3) | (~(max(X!5, Y!4) = Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(367,plain,
% 0.20/0.50 (~(max(X!5, Y!4) = Y!4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[366, 300])).
% 0.20/0.50 tff(368,plain,
% 0.20/0.50 (~lesseq(X!5, Y!4)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[98, 367])).
% 0.20/0.50 tff(369,plain,
% 0.20/0.50 (lesseq(Y!4, X!5)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[246, 68, 368])).
% 0.20/0.50 tff(370,plain,
% 0.20/0.50 (max(X!5, Y!4) = X!5),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[55, 369])).
% 0.20/0.50 tff(371,plain,
% 0.20/0.50 (X!5 = max(X!5, Y!4)),
% 0.20/0.50 inference(symmetry,[status(thm)],[370])).
% 0.20/0.50 tff(372,plain,
% 0.20/0.50 (tptp_fun_Z_1(Z!3, Y!4, X!5) = tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[371])).
% 0.20/0.50 tff(373,plain,
% 0.20/0.50 (tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)) = tptp_fun_Z_1(Z!3, Y!4, X!5)),
% 0.20/0.50 inference(symmetry,[status(thm)],[372])).
% 0.20/0.50 tff(374,plain,
% 0.20/0.50 (model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) <=> model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[370, 373])).
% 0.20/0.50 tff(375,plain,
% 0.20/0.50 (model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.20/0.50 inference(symmetry,[status(thm)],[374])).
% 0.20/0.50 tff(376,plain,
% 0.20/0.50 ((~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))) <=> (~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[375])).
% 0.20/0.50 tff(377,plain,
% 0.20/0.50 (~((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[191, 297])).
% 0.20/0.50 tff(378,plain,
% 0.20/0.50 (![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[344, 377])).
% 0.20/0.50 tff(379,plain,
% 0.20/0.50 (~((~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)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[321, 300])).
% 0.20/0.50 tff(380,plain,
% 0.20/0.50 (~lesseq(Z!3, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[339, 379])).
% 0.20/0.50 tff(381,plain,
% 0.20/0.50 (((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(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)))) <=> ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(382,plain,
% 0.20/0.50 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_ub(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)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(383,plain,
% 0.20/0.50 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(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))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.20/0.50 tff(384,plain,
% 0.20/0.50 (~model_ub(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[383, 380, 378])).
% 0.20/0.50 tff(385,plain,
% 0.20/0.50 (~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[384, 376])).
% 0.20/0.50 tff(386,plain,
% 0.20/0.50 ((~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))))))) | model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(387,plain,
% 0.20/0.50 (![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[386, 385, 296])).
% 0.20/0.50 tff(388,plain,
% 0.20/0.50 (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[373])).
% 0.20/0.50 tff(389,plain,
% 0.20/0.50 (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.20/0.50 inference(symmetry,[status(thm)],[388])).
% 0.20/0.50 tff(390,plain,
% 0.20/0.50 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(391,plain,
% 0.20/0.50 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[390, 117])).
% 0.20/0.50 tff(392,plain,
% 0.20/0.50 (model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[323, 379])).
% 0.20/0.50 tff(393,plain,
% 0.20/0.50 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), 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))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(394,plain,
% 0.20/0.50 ((~(model_max(X!5, Y!4, tptp_fun_Z_1(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5)))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[393, 392])).
% 0.20/0.50 tff(395,plain,
% 0.20/0.50 (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, X!5))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[394, 391])).
% 0.20/0.50 tff(396,plain,
% 0.20/0.50 (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[395, 389])).
% 0.20/0.50 tff(397,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)).
% 0.20/0.50 tff(398,plain,
% 0.20/0.50 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4)))) <=> ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(399,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[398, 36, 397])).
% 0.20/0.50 tff(400,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,[]))).
% 0.20/0.50 tff(401,plain,
% 0.20/0.50 (((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(X!5, max(X!5, Y!4)))) | lesseq(Y!4, max(X!5, Y!4))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(402,plain,
% 0.20/0.50 (lesseq(Y!4, max(X!5, Y!4))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[401, 107])).
% 0.20/0.50 tff(403,plain,
% 0.20/0.50 ((~((~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)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(404,plain,
% 0.20/0.50 (~((~lesseq(Y!4, max(X!5, Y!4))) | (~lesseq(max(X!5, Y!4), max(X!5, Y!4))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[403, 75, 402])).
% 0.20/0.50 tff(405,plain,
% 0.20/0.50 ((((~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))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(406,plain,
% 0.20/0.50 ((((~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))) | ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[405, 404])).
% 0.20/0.50 tff(407,plain,
% 0.20/0.50 (ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[406, 400])).
% 0.20/0.50 tff(408,plain,
% 0.20/0.50 (((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))) | ((~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))) <=> ((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(409,plain,
% 0.20/0.50 ((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))) | ((~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(410,plain,
% 0.20/0.50 ((~![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4)))))) | (~ub(max(X!5, Y!4), Y!4, max(X!5, Y!4))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_1(Z!3, Y!4, max(X!5, Y!4))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.20/0.50 tff(411,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[410, 407, 396, 387])).
% 0.20/0.50 tff(412,plain,(~minsol_model_ub(X!5, Y!4, Z!3)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(413,plain,
% 0.20/0.50 (((~(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)))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(414,plain,
% 0.20/0.50 (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))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[413, 187])).
% 0.20/0.50 tff(415,plain,
% 0.20/0.50 ((~(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))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(416,plain,
% 0.20/0.50 (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))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[415, 414])).
% 0.20/0.50 tff(417,plain,
% 0.20/0.50 (~((~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)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[416, 412, 292])).
% 0.20/0.50 tff(418,plain,
% 0.20/0.51 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))) | (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(419,plain,
% 0.20/0.51 (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[418, 209])).
% 0.20/0.51 tff(420,plain,
% 0.20/0.51 ((~![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))) | (lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(421,plain,
% 0.20/0.51 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[420, 218])).
% 0.20/0.51 tff(422,plain,
% 0.20/0.51 ((~![X: $i, Y: $i, Z: $i] : (~(((~lesseq(Y, Z)) | (~lesseq(X, Z))) <=> ub(X, Y, Z)))) | (~(((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))) <=> ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(423,plain,
% 0.20/0.51 (~(((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))) <=> ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[422, 36])).
% 0.20/0.51 tff(424,plain,
% 0.20/0.51 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(425,plain,
% 0.20/0.51 (~((~((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[424, 14])).
% 0.20/0.51 tff(426,plain,
% 0.20/0.51 (((~((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(X!5, max(X!5, Y!4), Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | ((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(427,plain,
% 0.20/0.51 ((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[426, 425])).
% 0.20/0.51 tff(428,plain,
% 0.20/0.51 (model_ub(X!5, max(X!5, Y!4), 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))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[234])).
% 0.20/0.51 tff(429,plain,
% 0.20/0.51 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.51 inference(symmetry,[status(thm)],[428])).
% 0.20/0.51 tff(430,assumption,(~((~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)))), introduced(assumption)).
% 0.20/0.51 tff(431,plain,
% 0.20/0.51 (((~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))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(432,plain,
% 0.20/0.51 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[431, 430])).
% 0.20/0.51 tff(433,plain,
% 0.20/0.51 (model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[432, 429])).
% 0.20/0.51 tff(434,plain,
% 0.20/0.51 ((~((~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~model_ub(X!5, max(X!5, Y!4), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(435,plain,
% 0.20/0.51 (~((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[434, 433, 427])).
% 0.20/0.51 tff(436,plain,
% 0.20/0.51 (((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(437,plain,
% 0.20/0.51 (ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[436, 435])).
% 0.20/0.51 tff(438,plain,
% 0.20/0.51 ((((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))) <=> ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(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), max(X!5, Y!4), X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))))) | (~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(439,plain,
% 0.20/0.51 ((((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))) <=> ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(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), max(X!5, Y!4), X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[438, 437])).
% 0.20/0.51 tff(440,plain,
% 0.20/0.51 (~((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[439, 423])).
% 0.20/0.51 tff(441,plain,
% 0.20/0.51 (((~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(X!5, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(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), max(X!5, Y!4), X!5))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(442,plain,
% 0.20/0.51 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[441, 440])).
% 0.20/0.51 tff(443,plain,
% 0.20/0.51 ((~(lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(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), max(X!5, Y!4), X!5))) | lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(444,plain,
% 0.20/0.51 (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[443, 442, 421])).
% 0.20/0.51 tff(445,plain,
% 0.20/0.51 ((~(lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))))) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(446,plain,
% 0.20/0.51 (lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[445, 444, 419])).
% 0.20/0.51 tff(447,plain,
% 0.20/0.51 (((~ub(X!5, max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(448,plain,
% 0.20/0.51 (lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[447, 435])).
% 0.20/0.51 tff(449,plain,
% 0.20/0.51 (((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)) | (max(sum(c, summation(max(X!5, Y!4))), Z!3) = Z!3))) <=> ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)) | (max(sum(c, summation(max(X!5, Y!4))), Z!3) = Z!3))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(450,plain,
% 0.20/0.51 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | ((~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)) | (max(sum(c, summation(max(X!5, Y!4))), Z!3) = Z!3))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(451,plain,
% 0.20/0.51 ((~![X: $i, Y: $i] : ((~lesseq(X, Y)) | (max(X, Y) = Y))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), Z!3)) | (max(sum(c, summation(max(X!5, Y!4))), Z!3) = Z!3)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.20/0.51 tff(452,plain,
% 0.20/0.51 (max(sum(c, summation(max(X!5, Y!4))), Z!3) = Z!3),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[451, 94, 284])).
% 0.20/0.51 tff(453,plain,
% 0.20/0.51 ((~![X: $i, Y: $i, N: $i] : (model_max(X, Y, N) <=> lesseq(sum(c, summation(max(X, Y))), N))) | (model_max(X!5, Y!4, sum(c, summation(max(X!5, Y!4)))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(454,plain,
% 0.20/0.51 (model_max(X!5, Y!4, sum(c, summation(max(X!5, Y!4)))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[453, 117])).
% 0.20/0.51 tff(455,plain,
% 0.20/0.51 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(456,plain,
% 0.20/0.51 ((lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4))))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(457,plain,
% 0.20/0.51 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[456])).
% 0.20/0.51 tff(458,plain,
% 0.20/0.51 (((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))))) <=> ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[457, 455])).
% 0.20/0.51 tff(459,plain,
% 0.20/0.51 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | (lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(460,plain,
% 0.20/0.51 ((~![X: $i, Y: $i] : (lesseq(X, Y) | lesseq(Y, X))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.20/0.51 tff(461,plain,
% 0.20/0.51 (lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[460, 68])).
% 0.20/0.51 tff(462,plain,
% 0.20/0.51 ((~(model_max(X!5, Y!4, sum(c, summation(max(X!5, Y!4)))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))))) | model_max(X!5, Y!4, sum(c, summation(max(X!5, Y!4)))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(max(X!5, Y!4)))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(463,plain,
% 0.20/0.51 (model_max(X!5, Y!4, sum(c, summation(max(X!5, Y!4))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[462, 461, 454])).
% 0.20/0.51 tff(464,plain,
% 0.20/0.51 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[366, 234])).
% 0.20/0.51 tff(465,plain,
% 0.20/0.51 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[150, 464])).
% 0.20/0.51 tff(466,plain,
% 0.20/0.51 (((~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))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(467,plain,
% 0.20/0.51 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[466, 465])).
% 0.20/0.51 tff(468,plain,
% 0.20/0.51 (((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, sum(c, summation(max(X!5, Y!4))))) | lesseq(Z!3, sum(c, summation(max(X!5, Y!4)))))) <=> ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, sum(c, summation(max(X!5, Y!4))))) | lesseq(Z!3, sum(c, summation(max(X!5, Y!4)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(469,plain,
% 0.20/0.51 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~model_max(X!5, Y!4, sum(c, summation(max(X!5, Y!4))))) | lesseq(Z!3, sum(c, summation(max(X!5, Y!4)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(470,plain,
% 0.20/0.51 ((~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_max(X!5, Y!4, sum(c, summation(max(X!5, Y!4))))) | lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.20/0.52 tff(471,plain,
% 0.20/0.52 (lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[470, 467, 463])).
% 0.20/0.52 tff(472,plain,
% 0.20/0.52 (((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | (max(sum(c, summation(max(X!5, Y!4))), Z!3) = sum(c, summation(max(X!5, Y!4)))))) <=> ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | (max(sum(c, summation(max(X!5, Y!4))), Z!3) = sum(c, summation(max(X!5, Y!4)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(473,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | ((~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | (max(sum(c, summation(max(X!5, Y!4))), Z!3) = sum(c, summation(max(X!5, Y!4)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(474,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : ((~lesseq(Y, X)) | (max(X, Y) = X))) | (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | (max(sum(c, summation(max(X!5, Y!4))), Z!3) = sum(c, summation(max(X!5, Y!4))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.20/0.52 tff(475,plain,
% 0.20/0.52 ((~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))) | (max(sum(c, summation(max(X!5, Y!4))), Z!3) = sum(c, summation(max(X!5, Y!4))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[474, 51])).
% 0.20/0.52 tff(476,plain,
% 0.20/0.52 (max(sum(c, summation(max(X!5, Y!4))), Z!3) = sum(c, summation(max(X!5, Y!4)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[475, 471])).
% 0.20/0.52 tff(477,plain,
% 0.20/0.52 (sum(c, summation(max(X!5, Y!4))) = max(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.20/0.52 inference(symmetry,[status(thm)],[476])).
% 0.20/0.52 tff(478,plain,
% 0.20/0.52 (sum(c, summation(max(X!5, Y!4))) = Z!3),
% 0.20/0.52 inference(transitivity,[status(thm)],[477, 452])).
% 0.20/0.52 tff(479,plain,
% 0.20/0.52 (lesseq(sum(c, summation(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))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[478])).
% 0.20/0.52 tff(480,plain,
% 0.20/0.52 (lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.52 inference(symmetry,[status(thm)],[479])).
% 0.20/0.52 tff(481,plain,
% 0.20/0.52 ((~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[480])).
% 0.20/0.52 tff(482,plain,
% 0.20/0.52 (((~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)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(483,plain,
% 0.20/0.52 (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[482, 430])).
% 0.20/0.52 tff(484,plain,
% 0.20/0.52 (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[483, 481])).
% 0.20/0.52 tff(485,plain,
% 0.20/0.52 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(486,plain,
% 0.20/0.52 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(487,plain,
% 0.20/0.52 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), max(X!5, Y!4), X!5)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.20/0.52 tff(488,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[487, 273, 484, 448, 446])).
% 0.20/0.52 tff(489,plain,(((~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))) | (~(max(X!5, Y!4) = Y!4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(490,plain,
% 0.20/0.52 (~(max(X!5, Y!4) = Y!4)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[489, 417])).
% 0.20/0.52 tff(491,plain,
% 0.20/0.52 (~lesseq(X!5, Y!4)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[98, 490])).
% 0.20/0.52 tff(492,plain,
% 0.20/0.52 (~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[482, 417])).
% 0.20/0.52 tff(493,assumption,(max(X!5, Y!4) = X!5), introduced(assumption)).
% 0.20/0.52 tff(494,plain,
% 0.20/0.52 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Y) <=> lesseq(sum(Z, X), sum(Z, Y)))) | (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(495,plain,
% 0.20/0.52 (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[494, 209])).
% 0.20/0.52 tff(496,plain,
% 0.20/0.52 ((~![X: $i, Y: $i] : (lesseq(X, Y) <=> lesseq(summation(X), summation(Y)))) | (lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(497,plain,
% 0.20/0.52 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[496, 218])).
% 0.20/0.52 tff(498,plain,
% 0.20/0.52 ((~![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, max(X!5, Y!4)))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))) <=> ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(499,plain,
% 0.20/0.52 (~(((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))) <=> ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[498, 36])).
% 0.20/0.52 tff(500,plain,
% 0.20/0.52 ((~![X: $i, Y: $i, N: $i] : (~((~((~model_ub(X, Y, N)) | (~((~ub(X, Y, tptp_fun_Z_0(N, Y, X))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(N, Y, X))), N)))))) | (~(model_ub(X, Y, N) | ![Z: $i] : ((~ub(X, Y, Z)) | (~lesseq(sum(c, summation(Z)), N)))))))) | (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(501,plain,
% 0.20/0.52 (~((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_2(Z!3, Y!4, X!5)))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[500, 14])).
% 0.20/0.52 tff(502,plain,
% 0.20/0.52 (((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~(model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) | ![Z: $i] : ((~ub(max(X!5, Y!4), Y!4, Z)) | (~lesseq(sum(c, summation(Z)), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | ((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(503,plain,
% 0.20/0.52 ((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[502, 501])).
% 0.20/0.52 tff(504,plain,
% 0.20/0.52 (model_ub(max(X!5, Y!4), Y!4, 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))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[493])).
% 0.20/0.52 tff(505,plain,
% 0.20/0.52 (model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.52 inference(symmetry,[status(thm)],[504])).
% 0.20/0.52 tff(506,plain,
% 0.20/0.52 (model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[432, 505])).
% 0.20/0.52 tff(507,plain,
% 0.20/0.52 ((~((~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))))))) | (~model_ub(max(X!5, Y!4), Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5)))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(508,plain,
% 0.20/0.52 (~((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[507, 506, 503])).
% 0.20/0.52 tff(509,plain,
% 0.20/0.52 (((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(510,plain,
% 0.20/0.52 (ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[509, 508])).
% 0.20/0.52 tff(511,plain,
% 0.20/0.52 ((((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))) <=> ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))))) | (~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(512,plain,
% 0.20/0.52 ((((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))) <=> ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[511, 510])).
% 0.20/0.52 tff(513,plain,
% 0.20/0.52 (~((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[512, 499])).
% 0.20/0.52 tff(514,plain,
% 0.20/0.52 (((~lesseq(Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))) | lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(515,plain,
% 0.20/0.52 (lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[514, 513])).
% 0.20/0.52 tff(516,plain,
% 0.20/0.52 ((~(lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))) <=> lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))))) | (~lesseq(max(X!5, Y!4), tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(517,plain,
% 0.20/0.52 (lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[516, 515, 497])).
% 0.20/0.52 tff(518,plain,
% 0.20/0.52 ((~(lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) <=> lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))))) | (~lesseq(summation(max(X!5, Y!4)), summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))) | lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(519,plain,
% 0.20/0.52 (lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[518, 517, 495])).
% 0.20/0.52 tff(520,plain,
% 0.20/0.52 (((~ub(max(X!5, Y!4), Y!4, tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5)))) | lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(521,plain,
% 0.20/0.52 (lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[520, 508])).
% 0.20/0.52 tff(522,assumption,(max(sum(c, summation(max(X!5, Y!4))), Z!3) = sum(c, summation(max(X!5, Y!4)))), introduced(assumption)).
% 0.20/0.52 tff(523,plain,
% 0.20/0.52 (sum(c, summation(max(X!5, Y!4))) = max(sum(c, summation(max(X!5, Y!4))), Z!3)),
% 0.20/0.52 inference(symmetry,[status(thm)],[522])).
% 0.20/0.52 tff(524,plain,
% 0.20/0.52 (sum(c, summation(max(X!5, Y!4))) = Z!3),
% 0.20/0.52 inference(transitivity,[status(thm)],[523, 452])).
% 0.20/0.52 tff(525,plain,
% 0.20/0.52 (lesseq(sum(c, summation(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))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[524])).
% 0.20/0.52 tff(526,plain,
% 0.20/0.52 (lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5)) <=> lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.53 inference(symmetry,[status(thm)],[525])).
% 0.20/0.53 tff(527,plain,
% 0.20/0.53 ((~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))) <=> (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[526])).
% 0.20/0.53 tff(528,plain,
% 0.20/0.53 (~lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[483, 527])).
% 0.20/0.53 tff(529,plain,
% 0.20/0.53 (((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))))))) <=> ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(530,plain,
% 0.20/0.53 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | (lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(531,plain,
% 0.20/0.53 ((~![X: $i, Y: $i, Z: $i] : (lesseq(X, Z) | (~lesseq(Y, Z)) | (~lesseq(X, Y)))) | lesseq(sum(c, summation(max(X!5, Y!4))), tptp_fun_Z_2(Z!3, Y!4, X!5)) | (~lesseq(sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4)))), tptp_fun_Z_2(Z!3, Y!4, X!5))) | (~lesseq(sum(c, summation(max(X!5, Y!4))), sum(c, summation(tptp_fun_Z_0(tptp_fun_Z_2(Z!3, Y!4, X!5), Y!4, max(X!5, Y!4))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.20/0.53 tff(532,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[531, 273, 528, 521, 519])).
% 0.20/0.53 tff(533,plain,(((~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))) | (~(max(X!5, Y!4) = X!5)) | (~(max(sum(c, summation(max(X!5, Y!4))), Z!3) = sum(c, summation(max(X!5, Y!4)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(534,plain,
% 0.20/0.53 (~(max(sum(c, summation(max(X!5, Y!4))), Z!3) = sum(c, summation(max(X!5, Y!4))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[533, 430, 493])).
% 0.20/0.53 tff(535,plain,
% 0.20/0.53 (~lesseq(Z!3, sum(c, summation(max(X!5, Y!4))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[475, 534])).
% 0.20/0.53 tff(536,assumption,(~lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.20/0.53 tff(537,assumption,(![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))), introduced(assumption)).
% 0.20/0.53 tff(538,assumption,(model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))), introduced(assumption)).
% 0.20/0.53 tff(539,plain,
% 0.20/0.53 (((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~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)))) <=> ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(540,plain,
% 0.20/0.53 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | ((~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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(541,plain,
% 0.20/0.53 ((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~model_ub(X!5, Y!4, tptp_fun_Z_2(Z!3, Y!4, X!5))) | lesseq(Z!3, tptp_fun_Z_2(Z!3, Y!4, X!5))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[540, 539])).
% 0.20/0.53 tff(542,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[541, 538, 536, 537])).
% 0.20/0.53 tff(543,plain,((~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))) | (~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))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(544,plain,
% 0.20/0.53 (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[543, 432, 536])).
% 0.20/0.53 tff(545,plain,
% 0.20/0.53 ((~model_ub(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_ub(X!5, Y!4, Z)) | lesseq(Z!3, Z)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[344, 544])).
% 0.20/0.53 tff(546,plain,
% 0.20/0.53 (~minsol_model_ub(X!5, Y!4, Z!3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[191, 545])).
% 0.20/0.53 tff(547,plain,
% 0.20/0.53 (minsol_model_max(X!5, Y!4, Z!3)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[162, 546])).
% 0.20/0.53 tff(548,plain,
% 0.20/0.53 (~((~model_max(X!5, Y!4, Z!3)) | (~![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[150, 547])).
% 0.20/0.53 tff(549,plain,
% 0.20/0.53 (![Z: $i] : ((~model_max(X!5, Y!4, Z)) | lesseq(Z!3, Z))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[466, 548])).
% 0.20/0.53 tff(550,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[470, 549, 535, 463])).
% 0.20/0.53 tff(551,plain,(((~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)) | (~(max(X!5, Y!4) = X!5))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(552,plain,
% 0.20/0.53 (~(max(X!5, Y!4) = X!5)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[551, 417, 492])).
% 0.20/0.53 tff(553,plain,
% 0.20/0.53 (~lesseq(Y!4, X!5)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[55, 552])).
% 0.20/0.53 tff(554,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[246, 68, 553, 491])).
% 0.20/0.53 % SZS output end Proof
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------