%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN345+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:50 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN345+1 : TPTP v9.0.0. Released v2.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.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 12:31:55 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(big_f_type, type, (
% 0.19/0.39 big_f: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_Z_2_type, type, (
% 0.19/0.39 tptp_fun_Z_2: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_X2_0_type, type, (
% 0.19/0.39 tptp_fun_X2_0: $i)).
% 0.19/0.39 tff(tptp_fun_X1_1_type, type, (
% 0.19/0.39 tptp_fun_X1_1: $i)).
% 0.19/0.39 tff(elem_3_type, type, (
% 0.19/0.39 elem_3: $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[Y1: $i, Y2: $i] : refl((~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))))) <=> (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))))) <=> ![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[Y1: $i, Y2: $i] : rewrite((~((big_f(X2!0, X2!0, Y1) & (big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))))) <=> (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![Y1: $i, Y2: $i] : (~((big_f(X2!0, X2!0, Y1) & (big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))))) <=> ![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 ((~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))) <=> (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 ((~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (((big_f(X1, X2, Y1) => big_f(Y2, Y1, Z)) => (big_f(X1, X1, X2) => big_f(X1, X2, X2))) => (((big_f(X2, Y1, Y2) => big_f(Y1, Z, Z)) => (big_f(X1, X2, X2) => big_f(X1, X1, X2))) => (big_f(Y1, Y2, Z) => (big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))))))) <=> (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(7,axiom,(~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : (((big_f(X1, X2, Y1) => big_f(Y2, Y1, Z)) => (big_f(X1, X1, X2) => big_f(X1, X2, X2))) => (((big_f(X2, Y1, Y2) => big_f(Y1, Z, Z)) => (big_f(X1, X2, X2) => big_f(X1, X1, X2))) => (big_f(Y1, Y2, Z) => (big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','church_46_16_4')).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (~![X1: $i, X2: $i] : ?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2, X2, Y1) & (big_f(X1, X1, X2) <=> big_f(X1, X2, X2))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1, X1, X2) | (~big_f(X1, X2, X2)) | (~((~big_f(X2, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1, X2, X2) | (~big_f(X1, X1, X2)) | (~((~big_f(X1, X2, Y1)) | big_f(Y2, Y1, Z))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.19/0.39 tff(12,plain,(
% 0.19/0.39 $oeq((~?[Y1: $i, Y2: $i] : ![Z: $i] : ((big_f(X2!0, X2!0, Y1) & (big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(Y1, Y2, Z)) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, Z, Z))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, Z))))))), ![Y1: $i, Y2: $i] : (~((big_f(X2!0, X2!0, Y1) & (big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))))))),
% 0.19/0.39 inference(transitivity,[status(sab)],[11])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 ((~((~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))))) <=> (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[16])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[20, 14])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~big_f(X2!0, X1!1, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))))))) | (big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.19/0.40 tff(24,assumption,((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))), introduced(assumption)).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 ((~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))))) <=> (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[26])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[27, 25])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | (~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[30, 14, 24])).
% 0.19/0.41 tff(32,plain,(~((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (((~((~big_f(X2!0, X2!0, X2!0)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X2!0)) | big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(X2!0, X2!0)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, X2!0)) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))) | big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 (big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.42 tff(35,assumption,((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))), introduced(assumption)).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 ((~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))))) <=> (~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[38, 36])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[41, 14, 35])).
% 0.21/0.43 tff(43,plain,(~((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (((~big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0))) | big_f(tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X2!0, X2!0))) | big_f(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(tptp_fun_Z_2(X2!0, X2!0), X2!0), tptp_fun_Z_2(X2!0, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))))) | ((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 ((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 ((~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0))))) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 ((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X2!0, X2!0)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[47, 34])).
% 0.21/0.44 tff(49,assumption,(big_f(X1!1, X1!1, X2!0)), introduced(assumption)).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 ((big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)) | (~big_f(X1!1, X1!1, X2!0)) | (~big_f(X1!1, X2!0, X2!0))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (~big_f(X1!1, X2!0, X2!0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[50, 49, 48])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 ((~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))))) <=> (~((~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[54, 52])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (~((~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3)))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[57, 14])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (((~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))) | (big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 (big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 (((~((~big_f(X2!0, X2!0, elem!3)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | (~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, elem!3, elem!3)) | big_f(elem!3, tptp_fun_Z_2(elem!3, elem!3), tptp_fun_Z_2(elem!3, elem!3))))))) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 (big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 (((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))) | (~big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 ((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 ((~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3)))))) | big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, elem!3)) | big_f(elem!3, elem!3, tptp_fun_Z_2(elem!3, elem!3))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[65, 64, 60])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[66, 51, 49])).
% 0.21/0.45 tff(68,plain,(~big_f(X1!1, X1!1, X2!0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 ((big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)) | big_f(X1!1, X1!1, X2!0) | big_f(X1!1, X2!0, X2!0)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (big_f(X1!1, X2!0, X2!0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[69, 68, 48])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 ((~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 ((~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))) | (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[71, 68, 70])).
% 0.21/0.45 tff(73,plain,
% 0.21/0.45 (~((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[72, 23])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (((~big_f(X2!0, X2!0, X1!1)) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | (~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.45 tff(76,plain,
% 0.21/0.45 (((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 ((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 ((~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[78, 68, 70, 77])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))) | (big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 ((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(83,plain,
% 0.21/0.46 ((~((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))))))) <=> (~((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.46 tff(85,plain,
% 0.21/0.46 (((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) <=> ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[84, 82])).
% 0.21/0.46 tff(86,plain,
% 0.21/0.46 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(87,plain,
% 0.21/0.47 ((~![Y1: $i, Y2: $i] : (~((~big_f(Y1, Y2, tptp_fun_Z_2(Y2, Y1))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, Y1, Y2)) | big_f(Y1, tptp_fun_Z_2(Y2, Y1), tptp_fun_Z_2(Y2, Y1)))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, Y1)) | big_f(Y2, Y1, tptp_fun_Z_2(Y2, Y1)))))) | (~((~big_f(X2!0, X2!0, Y1)) | (~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0)))))))) | (~((~big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)))) | (~(big_f(X1!1, X1!1, X2!0) | (~big_f(X1!1, X2!0, X2!0)) | (~((~big_f(X2!0, tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0)), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~(big_f(X1!1, X2!0, X2!0) | (~big_f(X1!1, X1!1, X2!0)) | (~((~big_f(X1!1, X2!0, tptp_fun_Z_2(X1!1, X2!0))) | big_f(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(tptp_fun_Z_2(X1!1, X2!0), tptp_fun_Z_2(X1!1, X2!0))))))) | (~((~(big_f(X1!1, X1!1, X2!0) <=> big_f(X1!1, X2!0, X2!0))) | (~big_f(X2!0, X2!0, tptp_fun_Z_2(X1!1, X2!0)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.47 tff(88,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[87, 14, 81])).
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------