%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN077+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:38:10 AM UTC 2025
% Result : Theorem 0.90s 1.07s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN077+1 : TPTP v9.0.0. Released v2.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:28:12 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.90/1.07 % SZS status Theorem
% 0.90/1.07 % SZS output start Proof
% 0.90/1.07 tff(big_f_type, type, (
% 0.90/1.07 big_f: ( $i * $i ) > $o)).
% 0.90/1.07 tff(tptp_fun_Y_2_type, type, (
% 0.90/1.07 tptp_fun_Y_2: $i > $i)).
% 0.90/1.07 tff(tptp_fun_U_3_type, type, (
% 0.90/1.07 tptp_fun_U_3: $i > $i)).
% 0.90/1.07 tff(tptp_fun_W_1_type, type, (
% 0.90/1.07 tptp_fun_W_1: $i)).
% 0.90/1.07 tff(tptp_fun_Z_4_type, type, (
% 0.90/1.07 tptp_fun_Z_4: ( $i * $i ) > $i)).
% 0.90/1.07 tff(tptp_fun_Z_0_type, type, (
% 0.90/1.07 tptp_fun_Z_0: $i > $i)).
% 0.90/1.07 tff(1,plain,
% 0.90/1.07 (^[X: $i] : refl((~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))))))) <=> (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))))))))),
% 0.90/1.07 inference(bind,[status(th)],[])).
% 0.90/1.07 tff(2,plain,
% 0.90/1.07 (![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))))))) <=> ![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))),
% 0.90/1.07 inference(quant_intro,[status(thm)],[1])).
% 0.90/1.07 tff(3,plain,
% 0.90/1.07 (^[X: $i] : rewrite((~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))))))) <=> (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))))))))),
% 0.90/1.07 inference(bind,[status(th)],[])).
% 0.90/1.07 tff(4,plain,
% 0.90/1.07 (![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))))))) <=> ![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))),
% 0.90/1.07 inference(quant_intro,[status(thm)],[3])).
% 0.90/1.07 tff(5,plain,
% 0.90/1.07 (![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))))))) <=> ![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))),
% 0.90/1.07 inference(transitivity,[status(thm)],[4, 2])).
% 0.90/1.07 tff(6,plain,
% 0.90/1.07 (^[X: $i] : trans(monotonicity(rewrite(((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (big_f(tptp_fun_Y_2(U), U) & ![Z: $i] : (~(big_f(Z, U) & big_f(Z, tptp_fun_Y_2(U))))))) <=> ((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((~big_f(Y, tptp_fun_U_3(X))) | (big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X)) & big_f(tptp_fun_Z_4(Y, X), Y))) <=> ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))), (![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X)) & big_f(tptp_fun_Z_4(Y, X), Y))) <=> ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))), ((big_f(X, tptp_fun_U_3(X)) & ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X)) & big_f(tptp_fun_Z_4(Y, X), Y)))) <=> (big_f(X, tptp_fun_U_3(X)) & ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))), rewrite((big_f(X, tptp_fun_U_3(X)) & ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))) <=> (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))), ((big_f(X, tptp_fun_U_3(X)) & ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X)) & big_f(tptp_fun_Z_4(Y, X), Y)))) <=> (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))))), ((big_f(X, W!1) | (big_f(X, tptp_fun_U_3(X)) & ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X)) & big_f(tptp_fun_Z_4(Y, X), Y))))) <=> (big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))), rewrite((big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))) <=> (big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))))), ((big_f(X, W!1) | (big_f(X, tptp_fun_U_3(X)) & ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X)) & big_f(tptp_fun_Z_4(Y, X), Y))))) <=> (big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))), ((((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (big_f(tptp_fun_Y_2(U), U) & ![Z: $i] : (~(big_f(Z, U) & big_f(Z, tptp_fun_Y_2(U))))))) & (big_f(X, W!1) | (big_f(X, tptp_fun_U_3(X)) & ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X)) & big_f(tptp_fun_Z_4(Y, X), Y)))))) <=> (((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))) & (big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))))))), rewrite((((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))) & (big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y)))))))))) <=> (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))), ((((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (big_f(tptp_fun_Y_2(U), U) & ![Z: $i] : (~(big_f(Z, U) & big_f(Z, tptp_fun_Y_2(U))))))) & (big_f(X, W!1) | (big_f(X, tptp_fun_U_3(X)) & ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X)) & big_f(tptp_fun_Z_4(Y, X), Y)))))) <=> (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))))),
% 0.90/1.07 inference(bind,[status(th)],[])).
% 0.90/1.07 tff(7,plain,
% 0.90/1.07 (![X: $i] : (((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (big_f(tptp_fun_Y_2(U), U) & ![Z: $i] : (~(big_f(Z, U) & big_f(Z, tptp_fun_Y_2(U))))))) & (big_f(X, W!1) | (big_f(X, tptp_fun_U_3(X)) & ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X)) & big_f(tptp_fun_Z_4(Y, X), Y)))))) <=> ![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))),
% 0.90/1.07 inference(quant_intro,[status(thm)],[6])).
% 0.90/1.07 tff(8,plain,
% 0.90/1.07 (?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : ((~big_f(X, U)) | ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y)))))) <=> ?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : ((~big_f(X, U)) | ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y))))))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(9,plain,
% 0.90/1.07 ((~(~?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : ((~big_f(X, U)) | ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y)))))))) <=> ?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : ((~big_f(X, U)) | ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y))))))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(10,plain,
% 0.90/1.07 ((~?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : (big_f(X, U) => ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y))))))) <=> (~?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : ((~big_f(X, U)) | ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y)))))))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(11,plain,
% 0.90/1.07 ((~(~?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : (big_f(X, U) => ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y)))))))) <=> (~(~?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : ((~big_f(X, U)) | ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y))))))))),
% 0.90/1.07 inference(monotonicity,[status(thm)],[10])).
% 0.90/1.07 tff(12,plain,
% 0.90/1.07 ((~(~?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : (big_f(X, U) => ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y)))))))) <=> ?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : ((~big_f(X, U)) | ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y))))))),
% 0.90/1.07 inference(transitivity,[status(thm)],[11, 9])).
% 0.90/1.07 tff(13,axiom,(~(~?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : (big_f(X, U) => ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel54')).
% 0.90/1.07 tff(14,plain,
% 0.90/1.07 (?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : ((~big_f(X, U)) | ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y))))))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.90/1.07 tff(15,plain,
% 0.90/1.07 (?[W: $i] : ![X: $i] : (big_f(X, W) <=> ![U: $i] : ((~big_f(X, U)) | ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y))))))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.90/1.07 tff(16,plain,(
% 0.90/1.07 $oeq(![X: $i] : (big_f(X, W!1) <=> ![U: $i] : ((~big_f(X, U)) | ?[Y: $i] : (big_f(Y, U) & (~?[Z: $i] : (big_f(Z, U) & big_f(Z, Y)))))), ![X: $i] : (((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (big_f(tptp_fun_Y_2(U), U) & ![Z: $i] : (~(big_f(Z, U) & big_f(Z, tptp_fun_Y_2(U))))))) & (big_f(X, W!1) | (big_f(X, tptp_fun_U_3(X)) & ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X)) & big_f(tptp_fun_Z_4(Y, X), Y)))))))),
% 0.90/1.07 inference(transitivity,[status(sab)],[15])).
% 0.90/1.07 tff(17,plain,
% 0.90/1.07 (![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[16, 7])).
% 0.90/1.07 tff(18,plain,
% 0.90/1.07 (![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))),
% 0.90/1.07 inference(modus_ponens,[status(thm)],[17, 5])).
% 0.90/1.07 tff(19,plain,
% 0.90/1.07 (((~![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y)))))))) | big_f(tptp_fun_Z_4(W!1, W!1), W!1)))))) <=> ((~![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y)))))))) | big_f(tptp_fun_Z_4(W!1, W!1), W!1))))))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(20,plain,
% 0.90/1.07 ((~((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(tptp_fun_Z_4(W!1, W!1), W!1) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y)))))))))))) <=> (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y)))))))) | big_f(tptp_fun_Z_4(W!1, W!1), W!1)))))),
% 0.90/1.07 inference(rewrite,[status(thm)],[])).
% 0.90/1.07 tff(21,plain,
% 0.90/1.07 (((~![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(tptp_fun_Z_4(W!1, W!1), W!1) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y))))))))))))) <=> ((~![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y)))))))) | big_f(tptp_fun_Z_4(W!1, W!1), W!1))))))),
% 0.90/1.07 inference(monotonicity,[status(thm)],[20])).
% 0.90/1.07 tff(22,plain,
% 0.90/1.07 (((~![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(tptp_fun_Z_4(W!1, W!1), W!1) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y))))))))))))) <=> ((~![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y)))))))) | big_f(tptp_fun_Z_4(W!1, W!1), W!1))))))),
% 0.90/1.08 inference(transitivity,[status(thm)],[21, 19])).
% 0.90/1.08 tff(23,plain,
% 0.90/1.08 ((~![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(tptp_fun_Z_4(W!1, W!1), W!1) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y))))))))))))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(24,plain,
% 0.90/1.08 ((~![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y)))))))) | big_f(tptp_fun_Z_4(W!1, W!1), W!1)))))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.90/1.08 tff(25,plain,
% 0.90/1.08 (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y)))))))) | big_f(tptp_fun_Z_4(W!1, W!1), W!1))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[24, 18])).
% 0.90/1.08 tff(26,plain,
% 0.90/1.08 (((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~((~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~((~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), tptp_fun_U_3(tptp_fun_Z_4(W!1, W!1)))) | (~big_f(tptp_fun_Z_4(Y, tptp_fun_Z_4(W!1, W!1)), Y)))))))) | big_f(tptp_fun_Z_4(W!1, W!1), W!1)))) | ((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(27,plain,
% 0.90/1.08 ((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.90/1.08 tff(28,plain,
% 0.90/1.08 (![Y: $i] : ![X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y)) <=> ![Y: $i, X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))),
% 0.90/1.08 inference(pull_quant,[status(thm)],[])).
% 0.90/1.08 tff(29,plain,
% 0.90/1.08 (![Y: $i] : ?[Z: $i] : ![X: $i] : (big_f(X, Z) <=> (X = Y)) <=> ![Y: $i] : ?[Z: $i] : ![X: $i] : (big_f(X, Z) <=> (X = Y))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(30,axiom,(![Y: $i] : ?[Z: $i] : ![X: $i] : (big_f(X, Z) <=> (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel54_1')).
% 0.90/1.08 tff(31,plain,
% 0.90/1.08 (![Y: $i] : ?[Z: $i] : ![X: $i] : (big_f(X, Z) <=> (X = Y))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.90/1.08 tff(32,plain,(
% 0.90/1.08 ![Y: $i] : ![X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))),
% 0.90/1.08 inference(skolemize,[status(sab)],[31])).
% 0.90/1.08 tff(33,plain,
% 0.90/1.08 (![Y: $i, X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.90/1.08 tff(34,plain,
% 0.90/1.08 (((~![Y: $i, X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))) | big_f(W!1, tptp_fun_Z_0(W!1))) <=> ((~![Y: $i, X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))) | big_f(W!1, tptp_fun_Z_0(W!1)))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(35,plain,
% 0.90/1.08 ((big_f(W!1, tptp_fun_Z_0(W!1)) <=> $true) <=> big_f(W!1, tptp_fun_Z_0(W!1))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(36,plain,
% 0.90/1.08 ((W!1 = W!1) <=> $true),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(37,plain,
% 0.90/1.08 ((big_f(W!1, tptp_fun_Z_0(W!1)) <=> (W!1 = W!1)) <=> (big_f(W!1, tptp_fun_Z_0(W!1)) <=> $true)),
% 0.90/1.08 inference(monotonicity,[status(thm)],[36])).
% 0.90/1.08 tff(38,plain,
% 0.90/1.08 ((big_f(W!1, tptp_fun_Z_0(W!1)) <=> (W!1 = W!1)) <=> big_f(W!1, tptp_fun_Z_0(W!1))),
% 0.90/1.08 inference(transitivity,[status(thm)],[37, 35])).
% 0.90/1.08 tff(39,plain,
% 0.90/1.08 (((~![Y: $i, X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))) | (big_f(W!1, tptp_fun_Z_0(W!1)) <=> (W!1 = W!1))) <=> ((~![Y: $i, X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))) | big_f(W!1, tptp_fun_Z_0(W!1)))),
% 0.90/1.08 inference(monotonicity,[status(thm)],[38])).
% 0.90/1.08 tff(40,plain,
% 0.90/1.08 (((~![Y: $i, X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))) | (big_f(W!1, tptp_fun_Z_0(W!1)) <=> (W!1 = W!1))) <=> ((~![Y: $i, X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))) | big_f(W!1, tptp_fun_Z_0(W!1)))),
% 0.90/1.08 inference(transitivity,[status(thm)],[39, 34])).
% 0.90/1.08 tff(41,plain,
% 0.90/1.08 ((~![Y: $i, X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))) | (big_f(W!1, tptp_fun_Z_0(W!1)) <=> (W!1 = W!1))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(42,plain,
% 0.90/1.08 ((~![Y: $i, X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))) | big_f(W!1, tptp_fun_Z_0(W!1))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.90/1.08 tff(43,plain,
% 0.90/1.08 (big_f(W!1, tptp_fun_Z_0(W!1))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[42, 33])).
% 0.90/1.08 tff(44,assumption,(big_f(W!1, W!1)), introduced(assumption)).
% 0.90/1.08 tff(45,plain,
% 0.90/1.08 ((~![X: $i] : (~((~((~big_f(X, W!1)) | ![U: $i] : ((~big_f(X, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(X, W!1) | (~((~big_f(X, tptp_fun_U_3(X))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(X))) | (~((~big_f(tptp_fun_Z_4(Y, X), tptp_fun_U_3(X))) | (~big_f(tptp_fun_Z_4(Y, X), Y))))))))))))) | (~((~((~big_f(W!1, W!1)) | ![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(W!1, W!1) | (~((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y))))))))))))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(46,plain,
% 0.90/1.08 (~((~((~big_f(W!1, W!1)) | ![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(W!1, W!1) | (~((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[45, 18])).
% 0.90/1.08 tff(47,plain,
% 0.90/1.08 (((~((~big_f(W!1, W!1)) | ![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(W!1, W!1) | (~((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y))))))))))) | ((~big_f(W!1, W!1)) | ![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(48,plain,
% 0.90/1.08 ((~big_f(W!1, W!1)) | ![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.90/1.08 tff(49,plain,
% 0.90/1.08 ((~((~big_f(W!1, W!1)) | ![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~big_f(W!1, W!1)) | ![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(50,plain,
% 0.90/1.08 ((~big_f(W!1, W!1)) | ![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.90/1.08 tff(51,plain,
% 0.90/1.08 (![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[50, 44])).
% 0.90/1.08 tff(52,plain,
% 0.90/1.08 (((~![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))) | ((~big_f(W!1, tptp_fun_Z_0(W!1))) | (~((~big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))))))) <=> ((~![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))) | (~big_f(W!1, tptp_fun_Z_0(W!1))) | (~((~big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))))))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(53,plain,
% 0.90/1.08 ((~![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))) | ((~big_f(W!1, tptp_fun_Z_0(W!1))) | (~((~big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))))))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(54,plain,
% 0.90/1.08 ((~![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))) | (~big_f(W!1, tptp_fun_Z_0(W!1))) | (~((~big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1))))))))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.90/1.08 tff(55,plain,
% 0.90/1.08 (~((~big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[54, 51, 43])).
% 0.90/1.08 tff(56,plain,
% 0.90/1.08 (((~big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1))))))) | big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(57,plain,
% 0.90/1.08 (big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.90/1.08 tff(58,plain,
% 0.90/1.08 ((~![Y: $i, X: $i] : (big_f(X, tptp_fun_Z_0(Y)) <=> (X = Y))) | (big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1)) <=> (tptp_fun_Y_2(tptp_fun_Z_0(W!1)) = W!1))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(59,plain,
% 0.90/1.08 (big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1)) <=> (tptp_fun_Y_2(tptp_fun_Z_0(W!1)) = W!1)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[58, 33])).
% 0.90/1.08 tff(60,plain,
% 0.90/1.08 ((~(big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1)) <=> (tptp_fun_Y_2(tptp_fun_Z_0(W!1)) = W!1))) | (~big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1))) | (tptp_fun_Y_2(tptp_fun_Z_0(W!1)) = W!1)),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(61,plain,
% 0.90/1.08 ((~big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1))) | (tptp_fun_Y_2(tptp_fun_Z_0(W!1)) = W!1)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.90/1.08 tff(62,plain,
% 0.90/1.08 (tptp_fun_Y_2(tptp_fun_Z_0(W!1)) = W!1),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[61, 57])).
% 0.90/1.08 tff(63,plain,
% 0.90/1.08 (big_f(W!1, tptp_fun_Y_2(tptp_fun_Z_0(W!1))) <=> big_f(W!1, W!1)),
% 0.90/1.08 inference(monotonicity,[status(thm)],[62])).
% 0.90/1.08 tff(64,plain,
% 0.90/1.08 (big_f(W!1, W!1) <=> big_f(W!1, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))),
% 0.90/1.08 inference(symmetry,[status(thm)],[63])).
% 0.90/1.08 tff(65,plain,
% 0.90/1.08 (big_f(W!1, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[44, 64])).
% 0.90/1.08 tff(66,plain,
% 0.90/1.08 (((~big_f(tptp_fun_Y_2(tptp_fun_Z_0(W!1)), tptp_fun_Z_0(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1))))))) | ![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(67,plain,
% 0.90/1.08 (![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[66, 55])).
% 0.90/1.08 tff(68,plain,
% 0.90/1.08 (((~![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))) | ((~big_f(W!1, tptp_fun_Z_0(W!1))) | (~big_f(W!1, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))) <=> ((~![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))) | (~big_f(W!1, tptp_fun_Z_0(W!1))) | (~big_f(W!1, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(69,plain,
% 0.90/1.08 ((~![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))) | ((~big_f(W!1, tptp_fun_Z_0(W!1))) | (~big_f(W!1, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(70,plain,
% 0.90/1.08 ((~![Z: $i] : ((~big_f(Z, tptp_fun_Z_0(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))))) | (~big_f(W!1, tptp_fun_Z_0(W!1))) | (~big_f(W!1, tptp_fun_Y_2(tptp_fun_Z_0(W!1))))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.90/1.08 tff(71,plain,
% 0.90/1.08 (~big_f(W!1, tptp_fun_Y_2(tptp_fun_Z_0(W!1)))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[70, 43, 67])).
% 0.90/1.08 tff(72,plain,
% 0.90/1.08 ($false),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[71, 65])).
% 0.90/1.08 tff(73,plain,(~big_f(W!1, W!1)), inference(lemma,lemma(discharge,[]))).
% 0.90/1.08 tff(74,plain,
% 0.90/1.08 (((~((~big_f(W!1, W!1)) | ![U: $i] : ((~big_f(W!1, U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~(big_f(W!1, W!1) | (~((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y))))))))))) | (big_f(W!1, W!1) | (~((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))))))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(75,plain,
% 0.90/1.08 (big_f(W!1, W!1) | (~((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y))))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[74, 46])).
% 0.90/1.08 tff(76,plain,
% 0.90/1.08 ((~(big_f(W!1, W!1) | (~((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))))))) | big_f(W!1, W!1) | (~((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y))))))))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(77,plain,
% 0.90/1.08 (big_f(W!1, W!1) | (~((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y))))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.90/1.08 tff(78,plain,
% 0.90/1.08 (~((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[77, 73])).
% 0.90/1.08 tff(79,plain,
% 0.90/1.08 (((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y))))))) | ![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(80,plain,
% 0.90/1.08 (![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.90/1.08 tff(81,plain,
% 0.90/1.08 (((~big_f(W!1, tptp_fun_U_3(W!1))) | (~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y))))))) | big_f(W!1, tptp_fun_U_3(W!1))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(82,plain,
% 0.90/1.08 (big_f(W!1, tptp_fun_U_3(W!1))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[81, 78])).
% 0.90/1.08 tff(83,plain,
% 0.90/1.08 (((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | ((~big_f(W!1, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | (~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))))))) <=> ((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | (~big_f(W!1, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | (~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))))))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(84,plain,
% 0.90/1.08 (((~big_f(W!1, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(W!1, W!1), W!1))))) <=> ((~big_f(W!1, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | (~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))))))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(85,plain,
% 0.90/1.08 (((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | ((~big_f(W!1, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(W!1, W!1), W!1)))))) <=> ((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | ((~big_f(W!1, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | (~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1)))))))),
% 0.90/1.08 inference(monotonicity,[status(thm)],[84])).
% 0.90/1.08 tff(86,plain,
% 0.90/1.08 (((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | ((~big_f(W!1, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(W!1, W!1), W!1)))))) <=> ((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | (~big_f(W!1, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | (~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))))))),
% 0.90/1.08 inference(transitivity,[status(thm)],[85, 83])).
% 0.90/1.08 tff(87,plain,
% 0.90/1.08 ((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | ((~big_f(W!1, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(W!1, W!1), W!1)))))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(88,plain,
% 0.90/1.08 ((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | (~big_f(W!1, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | (~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1)))))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.90/1.08 tff(89,plain,
% 0.90/1.08 (~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | (~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[88, 82, 80])).
% 0.90/1.08 tff(90,plain,
% 0.90/1.08 (((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | (~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1)))) | big_f(tptp_fun_Z_4(W!1, W!1), W!1)),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(91,plain,
% 0.90/1.08 (big_f(tptp_fun_Z_4(W!1, W!1), W!1)),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.90/1.08 tff(92,plain,
% 0.90/1.08 ((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | (~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(93,plain,
% 0.90/1.08 ((~((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U)))))))))) | ![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.90/1.08 tff(94,plain,
% 0.90/1.08 (![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[93, 27])).
% 0.90/1.08 tff(95,plain,
% 0.90/1.08 (((~big_f(tptp_fun_Z_4(W!1, W!1), W!1)) | (~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1)))) | big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(96,plain,
% 0.90/1.08 (big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[95, 89])).
% 0.90/1.08 tff(97,plain,
% 0.90/1.08 (((~![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))) | ((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1)))))))))) <=> ((~![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))) | (~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1)))))))))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(98,plain,
% 0.90/1.08 ((~![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))) | ((~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1)))))))))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(99,plain,
% 0.90/1.08 ((~![U: $i] : ((~big_f(tptp_fun_Z_4(W!1, W!1), U)) | (~((~big_f(tptp_fun_Y_2(U), U)) | (~![Z: $i] : ((~big_f(Z, U)) | (~big_f(Z, tptp_fun_Y_2(U))))))))) | (~big_f(tptp_fun_Z_4(W!1, W!1), tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1))))))))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.90/1.08 tff(100,plain,
% 0.90/1.08 (~((~big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1)))))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[99, 96, 94])).
% 0.90/1.08 tff(101,plain,
% 0.90/1.08 (((~big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1))))))) | big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(102,plain,
% 0.90/1.08 (big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.90/1.08 tff(103,plain,
% 0.90/1.08 (((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | ((~big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1)))))))) <=> ((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | (~big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1)))))))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(104,plain,
% 0.90/1.08 ((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | ((~big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1)))))))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(105,plain,
% 0.90/1.08 ((~![Y: $i] : ((~big_f(Y, tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(Y, W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(Y, W!1), Y)))))) | (~big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))) | (~((~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1))))))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.90/1.08 tff(106,plain,
% 0.90/1.08 (~((~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1)))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[105, 80, 102])).
% 0.90/1.08 tff(107,plain,
% 0.90/1.08 (((~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1))))) | big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1)))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(108,plain,
% 0.90/1.08 (big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1)))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.90/1.08 tff(109,plain,
% 0.90/1.08 (((~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1))))) | big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(110,plain,
% 0.90/1.08 (big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.90/1.08 tff(111,plain,
% 0.90/1.08 (((~big_f(tptp_fun_Y_2(tptp_fun_U_3(W!1)), tptp_fun_U_3(W!1))) | (~![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1))))))) | ![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1)))))),
% 0.90/1.08 inference(tautology,[status(thm)],[])).
% 0.90/1.08 tff(112,plain,
% 0.90/1.08 (![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1)))))),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[111, 100])).
% 0.90/1.08 tff(113,plain,
% 0.90/1.08 (((~![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1)))))) | ((~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1)))))) <=> ((~![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1)))))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1)))))),
% 0.90/1.08 inference(rewrite,[status(thm)],[])).
% 0.90/1.08 tff(114,plain,
% 0.90/1.08 ((~![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1)))))) | ((~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1)))))),
% 0.90/1.08 inference(quant_inst,[status(thm)],[])).
% 0.90/1.08 tff(115,plain,
% 0.90/1.08 ((~![Z: $i] : ((~big_f(Z, tptp_fun_U_3(W!1))) | (~big_f(Z, tptp_fun_Y_2(tptp_fun_U_3(W!1)))))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_U_3(W!1))) | (~big_f(tptp_fun_Z_4(tptp_fun_Y_2(tptp_fun_U_3(W!1)), W!1), tptp_fun_Y_2(tptp_fun_U_3(W!1))))),
% 0.90/1.08 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.90/1.08 tff(116,plain,
% 0.90/1.08 ($false),
% 0.90/1.08 inference(unit_resolution,[status(thm)],[115, 112, 110, 108])).
% 0.90/1.08 % SZS output end Proof
% 0.90/1.08 % E exiting
%------------------------------------------------------------------------------