%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN074+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:38:09 AM UTC 2025
% Result : Theorem 0.17s 0.36s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN074+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n006.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 12:27:35 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.17/0.36 % SZS status Theorem
% 0.17/0.36 % SZS output start Proof
% 0.17/0.36 tff(big_f_type, type, (
% 0.17/0.36 big_f: ( $i * $i ) > $o)).
% 0.17/0.36 tff(tptp_fun_W_3_type, type, (
% 0.17/0.36 tptp_fun_W_3: $i > $i)).
% 0.17/0.36 tff(tptp_fun_Z_1_type, type, (
% 0.17/0.36 tptp_fun_Z_1: $i)).
% 0.17/0.36 tff(tptp_fun_X_2_type, type, (
% 0.17/0.36 tptp_fun_X_2: $i > $i)).
% 0.17/0.36 tff(tptp_fun_W_0_type, type, (
% 0.17/0.36 tptp_fun_W_0: $i)).
% 0.17/0.36 tff(tptp_fun_Y_4_type, type, (
% 0.17/0.36 tptp_fun_Y_4: ( $i * $i ) > $i)).
% 0.17/0.36 tff(1,assumption,(tptp_fun_X_2(Z!1) = Z!1), introduced(assumption)).
% 0.17/0.36 tff(2,plain,
% 0.17/0.36 (Z!1 = tptp_fun_X_2(Z!1)),
% 0.17/0.36 inference(symmetry,[status(thm)],[1])).
% 0.17/0.36 tff(3,plain,
% 0.17/0.36 (big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)) <=> big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1))),
% 0.17/0.36 inference(monotonicity,[status(thm)],[2])).
% 0.17/0.36 tff(4,plain,
% 0.17/0.36 (big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1)) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))),
% 0.17/0.36 inference(symmetry,[status(thm)],[3])).
% 0.17/0.36 tff(5,plain,
% 0.17/0.36 ((~big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1))) <=> (~big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))),
% 0.17/0.36 inference(monotonicity,[status(thm)],[4])).
% 0.17/0.36 tff(6,assumption,(~big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1))), introduced(assumption)).
% 0.17/0.36 tff(7,plain,
% 0.17/0.36 (~big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.17/0.36 tff(8,plain,
% 0.17/0.36 (^[X: $i, Y: $i] : refl((~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y))) <=> (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(9,plain,
% 0.17/0.36 (![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y))) <=> ![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[8])).
% 0.17/0.36 tff(10,plain,
% 0.17/0.36 (^[X: $i, Y: $i] : trans(trans(monotonicity(rewrite(((X = Z!1) & (Y = W!0)) <=> (~((~(X = Z!1)) | (~(Y = W!0))))), ((big_f(X, Y) <=> ((X = Z!1) & (Y = W!0))) <=> (big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0))))))), rewrite((big_f(X, Y) <=> (~((~(X = Z!1)) | (~(Y = W!0))))) <=> (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))), ((big_f(X, Y) <=> ((X = Z!1) & (Y = W!0))) <=> (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y))))), rewrite((~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y))) <=> (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))), ((big_f(X, Y) <=> ((X = Z!1) & (Y = W!0))) <=> (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(11,plain,
% 0.17/0.36 (![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z!1) & (Y = W!0))) <=> ![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.17/0.36 tff(12,plain,
% 0.17/0.36 (?[Z: $i, W: $i] : ![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z) & (Y = W))) <=> ?[Z: $i, W: $i] : ![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z) & (Y = W)))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(13,axiom,(?[Z: $i, W: $i] : ![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z) & (Y = W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel51_1')).
% 0.17/0.36 tff(14,plain,
% 0.17/0.36 (?[Z: $i, W: $i] : ![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z) & (Y = W)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.17/0.36 tff(15,plain,(
% 0.17/0.36 $oeq(![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z!1) & (Y = W!0))), ![X: $i, Y: $i] : (big_f(X, Y) <=> ((X = Z!1) & (Y = W!0))))),
% 0.17/0.36 inference(transitivity,[status(sab)],[14])).
% 0.17/0.36 tff(16,plain,
% 0.17/0.36 (![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.17/0.36 tff(17,plain,
% 0.17/0.36 (![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.17/0.36 tff(18,plain,
% 0.17/0.36 (((~![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))) | ((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))) <=> ((~![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))) | ((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(19,plain,
% 0.17/0.36 ((~(~((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))))) <=> ((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(20,plain,
% 0.17/0.37 ((~((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))) <=> (~((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(21,plain,
% 0.17/0.37 (((~(tptp_fun_Y_4(W!0, Z!1) = W!0)) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))) <=> (~((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(22,plain,
% 0.17/0.37 (($false | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))) <=> (~(tptp_fun_Y_4(W!0, Z!1) = W!0))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(23,plain,
% 0.17/0.37 ((~$true) <=> $false),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(24,plain,
% 0.17/0.37 ((Z!1 = Z!1) <=> $true),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(25,plain,
% 0.17/0.37 ((~(Z!1 = Z!1)) <=> (~$true)),
% 0.17/0.37 inference(monotonicity,[status(thm)],[24])).
% 0.17/0.37 tff(26,plain,
% 0.17/0.37 ((~(Z!1 = Z!1)) <=> $false),
% 0.17/0.37 inference(transitivity,[status(thm)],[25, 23])).
% 0.17/0.37 tff(27,plain,
% 0.17/0.37 (((~(Z!1 = Z!1)) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))) <=> ($false | (~(tptp_fun_Y_4(W!0, Z!1) = W!0)))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[26])).
% 0.17/0.37 tff(28,plain,
% 0.17/0.37 (((~(Z!1 = Z!1)) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))) <=> (~(tptp_fun_Y_4(W!0, Z!1) = W!0))),
% 0.17/0.37 inference(transitivity,[status(thm)],[27, 22])).
% 0.17/0.37 tff(29,plain,
% 0.17/0.37 ((((~(Z!1 = Z!1)) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))) <=> ((~(tptp_fun_Y_4(W!0, Z!1) = W!0)) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[28])).
% 0.17/0.37 tff(30,plain,
% 0.17/0.37 ((((~(Z!1 = Z!1)) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))) <=> (~((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[29, 21])).
% 0.17/0.37 tff(31,plain,
% 0.17/0.37 ((((~(Z!1 = Z!1)) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))) <=> (~((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[30, 20])).
% 0.17/0.37 tff(32,plain,
% 0.17/0.37 ((~(((~(Z!1 = Z!1)) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))) <=> (~(~((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[31])).
% 0.17/0.37 tff(33,plain,
% 0.17/0.37 ((~(((~(Z!1 = Z!1)) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))) <=> ((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))),
% 0.17/0.37 inference(transitivity,[status(thm)],[32, 19])).
% 0.17/0.37 tff(34,plain,
% 0.17/0.37 (((~![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))) | (~(((~(Z!1 = Z!1)) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))))) <=> ((~![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))) | ((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[33])).
% 0.17/0.37 tff(35,plain,
% 0.17/0.37 (((~![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))) | (~(((~(Z!1 = Z!1)) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))))) <=> ((~![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))) | ((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[34, 18])).
% 0.17/0.37 tff(36,plain,
% 0.17/0.37 ((~![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))) | (~(((~(Z!1 = Z!1)) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(37,plain,
% 0.17/0.37 ((~![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))) | ((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.17/0.37 tff(38,plain,
% 0.17/0.37 ((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[37, 17])).
% 0.17/0.37 tff(39,plain,
% 0.17/0.37 (^[Z: $i] : trans(monotonicity(rewrite(((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) <=> ((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))), rewrite((![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))) <=> (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))), ((((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))) <=> (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))))), rewrite((((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))) <=> (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))), ((((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))) <=> (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(40,plain,
% 0.17/0.37 (![Z: $i] : (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))) <=> ![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[39])).
% 0.17/0.37 tff(41,plain,
% 0.17/0.37 (^[Z: $i] : rewrite(((![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))) | (tptp_fun_X_2(Z) = Z)) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))) <=> (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(42,plain,
% 0.17/0.37 (![Z: $i] : ((![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))) | (tptp_fun_X_2(Z) = Z)) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))) <=> ![Z: $i] : (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[41])).
% 0.17/0.37 tff(43,plain,
% 0.17/0.37 ((~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))) <=> (~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z)))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(44,axiom,(~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel51')).
% 0.17/0.37 tff(45,plain,
% 0.17/0.37 (~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.17/0.37 tff(46,plain,
% 0.17/0.37 (~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[45, 43])).
% 0.17/0.37 tff(47,plain,
% 0.17/0.37 (~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[46, 43])).
% 0.17/0.37 tff(48,plain,
% 0.17/0.37 (~?[Z: $i] : ![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.17/0.37 tff(49,plain,
% 0.17/0.37 (^[Z: $i] : trans(sk($oeq((~![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))), (~(?[W: $i] : ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = W)) <=> (tptp_fun_X_2(Z) = Z))))), nnf_neg(trans(sk($oeq(?[W: $i] : ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = W)), ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))), nnf_pos(proof_bind(^[Y: $i] : refl($oeq((big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))), (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))))), $oeq(![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))), ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))), $oeq(?[W: $i] : ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = W)), ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))), nnf_neg(proof_bind(^[W: $i] : sk($oeq((~![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = W))), (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W)))))), $oeq((~?[W: $i] : ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = W))), ![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))))), refl($oeq((tptp_fun_X_2(Z) = Z), (tptp_fun_X_2(Z) = Z))), refl($oeq((~(tptp_fun_X_2(Z) = Z)), (~(tptp_fun_X_2(Z) = Z)))), $oeq((~(?[W: $i] : ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = W)) <=> (tptp_fun_X_2(Z) = Z))), ((![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))) | (tptp_fun_X_2(Z) = Z)) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z)))))), $oeq((~![X: $i] : (?[W: $i] : ![Y: $i] : (big_f(X, Y) <=> (Y = W)) <=> (X = Z))), ((![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))) | (tptp_fun_X_2(Z) = Z)) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(50,plain,(
% 0.17/0.37 ![Z: $i] : ((![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))) | (tptp_fun_X_2(Z) = Z)) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))),
% 0.17/0.37 inference(nnf-neg,[status(sab)],[48, 49])).
% 0.17/0.37 tff(51,plain,
% 0.17/0.37 (![Z: $i] : (((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z)))) & (![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[50, 42])).
% 0.17/0.37 tff(52,plain,
% 0.17/0.37 (![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[51, 40])).
% 0.17/0.37 tff(53,plain,
% 0.17/0.37 (((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))) | (~((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W)))))))) <=> ((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))) | (~((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W))))))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(54,plain,
% 0.17/0.37 ((~((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W))) | (~(tptp_fun_X_2(Z!1) = Z!1)))))) <=> (~((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W)))))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(55,plain,
% 0.17/0.37 (((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))) | (~((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W))) | (~(tptp_fun_X_2(Z!1) = Z!1))))))) <=> ((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))) | (~((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W))))))))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[54])).
% 0.17/0.37 tff(56,plain,
% 0.17/0.37 (((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))) | (~((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W))) | (~(tptp_fun_X_2(Z!1) = Z!1))))))) <=> ((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))) | (~((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W))))))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[55, 53])).
% 0.17/0.37 tff(57,plain,
% 0.17/0.37 ((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))) | (~((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W))) | (~(tptp_fun_X_2(Z!1) = Z!1))))))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(58,plain,
% 0.17/0.37 ((~![Z: $i] : (~((~((tptp_fun_X_2(Z) = Z) | ![Y: $i] : (big_f(tptp_fun_X_2(Z), Y) <=> (Y = tptp_fun_W_3(Z))))) | (~(![W: $i] : (~(big_f(tptp_fun_X_2(Z), tptp_fun_Y_4(W, Z)) <=> (tptp_fun_Y_4(W, Z) = W))) | (~(tptp_fun_X_2(Z) = Z))))))) | (~((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W)))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.17/0.37 tff(59,plain,
% 0.17/0.37 (~((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W))))))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[58, 52])).
% 0.17/0.37 tff(60,plain,
% 0.17/0.37 (((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W)))))) | ((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W))))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(61,plain,
% 0.17/0.38 ((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W)))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.17/0.38 tff(62,plain,
% 0.17/0.38 ((~((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W))))) | (~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W)))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(63,plain,
% 0.17/0.38 ((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W)))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.17/0.38 tff(64,plain,
% 0.17/0.38 (![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W)))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[63, 1])).
% 0.17/0.38 tff(65,plain,
% 0.17/0.38 ((~![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W)))) | (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1)) <=> (tptp_fun_Y_4(W!0, Z!1) = W!0)))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(66,plain,
% 0.17/0.38 (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1)) <=> (tptp_fun_Y_4(W!0, Z!1) = W!0))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.17/0.38 tff(67,plain,
% 0.17/0.38 ((big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1)) <=> (tptp_fun_Y_4(W!0, Z!1) = W!0)) | big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1)) | (tptp_fun_Y_4(W!0, Z!1) = W!0)),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(68,plain,
% 0.17/0.38 (tptp_fun_Y_4(W!0, Z!1) = W!0),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[67, 6, 66])).
% 0.17/0.38 tff(69,plain,
% 0.17/0.38 ((~((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0)) | big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(70,plain,
% 0.17/0.38 (big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[69, 68, 38])).
% 0.17/0.38 tff(71,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[70, 7])).
% 0.17/0.38 tff(72,plain,(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1)) | (~(tptp_fun_X_2(Z!1) = Z!1))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.38 tff(73,plain,
% 0.17/0.38 (big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[72, 1])).
% 0.17/0.38 tff(74,plain,
% 0.17/0.38 (big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[73, 4])).
% 0.17/0.38 tff(75,plain,
% 0.17/0.38 ((big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1)) <=> (tptp_fun_Y_4(W!0, Z!1) = W!0)) | (~big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W!0, Z!1))) | (~(tptp_fun_Y_4(W!0, Z!1) = W!0))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(76,plain,
% 0.17/0.38 (~(tptp_fun_Y_4(W!0, Z!1) = W!0)),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[75, 73, 66])).
% 0.17/0.38 tff(77,plain,
% 0.17/0.38 ((~((tptp_fun_Y_4(W!0, Z!1) = W!0) <=> big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))) | (tptp_fun_Y_4(W!0, Z!1) = W!0) | (~big_f(Z!1, tptp_fun_Y_4(W!0, Z!1)))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(78,plain,
% 0.17/0.38 (~big_f(Z!1, tptp_fun_Y_4(W!0, Z!1))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[77, 76, 38])).
% 0.17/0.38 tff(79,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[78, 74])).
% 0.17/0.38 tff(80,plain,(~(tptp_fun_X_2(Z!1) = Z!1)), inference(lemma,lemma(discharge,[]))).
% 0.17/0.38 tff(81,plain,
% 0.17/0.38 (((~(tptp_fun_X_2(Z!1) = Z!1)) | (~(tptp_fun_W_3(Z!1) = W!0))) | (tptp_fun_X_2(Z!1) = Z!1)),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(82,plain,
% 0.17/0.38 ((~(tptp_fun_X_2(Z!1) = Z!1)) | (~(tptp_fun_W_3(Z!1) = W!0))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.17/0.38 tff(83,plain,
% 0.17/0.38 (((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (~((~(tptp_fun_X_2(Z!1) = Z!1)) | ![W: $i] : (~(big_f(tptp_fun_X_2(Z!1), tptp_fun_Y_4(W, Z!1)) <=> (tptp_fun_Y_4(W, Z!1) = W)))))) | ((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(84,plain,
% 0.17/0.38 ((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[83, 59])).
% 0.17/0.38 tff(85,plain,
% 0.17/0.38 ((~((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1))))) | (tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(86,plain,
% 0.17/0.38 ((tptp_fun_X_2(Z!1) = Z!1) | ![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.17/0.38 tff(87,plain,
% 0.17/0.38 (![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[86, 80])).
% 0.17/0.38 tff(88,plain,
% 0.17/0.38 (((~![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))) | big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1))) <=> ((~![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))) | big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(89,plain,
% 0.17/0.38 ((big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1)) <=> $true) <=> big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(90,plain,
% 0.17/0.38 ((tptp_fun_W_3(Z!1) = tptp_fun_W_3(Z!1)) <=> $true),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(91,plain,
% 0.17/0.38 ((big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1)) <=> (tptp_fun_W_3(Z!1) = tptp_fun_W_3(Z!1))) <=> (big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1)) <=> $true)),
% 0.17/0.38 inference(monotonicity,[status(thm)],[90])).
% 0.17/0.38 tff(92,plain,
% 0.17/0.38 ((big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1)) <=> (tptp_fun_W_3(Z!1) = tptp_fun_W_3(Z!1))) <=> big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1))),
% 0.17/0.38 inference(transitivity,[status(thm)],[91, 89])).
% 0.17/0.38 tff(93,plain,
% 0.17/0.38 (((~![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))) | (big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1)) <=> (tptp_fun_W_3(Z!1) = tptp_fun_W_3(Z!1)))) <=> ((~![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))) | big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1)))),
% 0.17/0.38 inference(monotonicity,[status(thm)],[92])).
% 0.17/0.38 tff(94,plain,
% 0.17/0.38 (((~![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))) | (big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1)) <=> (tptp_fun_W_3(Z!1) = tptp_fun_W_3(Z!1)))) <=> ((~![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))) | big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1)))),
% 0.17/0.38 inference(transitivity,[status(thm)],[93, 88])).
% 0.17/0.38 tff(95,plain,
% 0.17/0.38 ((~![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))) | (big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1)) <=> (tptp_fun_W_3(Z!1) = tptp_fun_W_3(Z!1)))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(96,plain,
% 0.17/0.38 ((~![Y: $i] : (big_f(tptp_fun_X_2(Z!1), Y) <=> (Y = tptp_fun_W_3(Z!1)))) | big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.17/0.38 tff(97,plain,
% 0.17/0.38 (big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[96, 87])).
% 0.17/0.38 tff(98,plain,
% 0.17/0.38 ((((~(tptp_fun_X_2(Z!1) = Z!1)) | (~(tptp_fun_W_3(Z!1) = W!0))) <=> big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1))) | (~((~(tptp_fun_X_2(Z!1) = Z!1)) | (~(tptp_fun_W_3(Z!1) = W!0)))) | (~big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1)))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(99,plain,
% 0.17/0.38 (((~(tptp_fun_X_2(Z!1) = Z!1)) | (~(tptp_fun_W_3(Z!1) = W!0))) <=> big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[98, 97, 82])).
% 0.17/0.38 tff(100,plain,
% 0.17/0.38 ((~![X: $i, Y: $i] : (~(((~(X = Z!1)) | (~(Y = W!0))) <=> big_f(X, Y)))) | (~(((~(tptp_fun_X_2(Z!1) = Z!1)) | (~(tptp_fun_W_3(Z!1) = W!0))) <=> big_f(tptp_fun_X_2(Z!1), tptp_fun_W_3(Z!1))))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(101,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[100, 17, 99])).
% 0.17/0.38 % SZS output end Proof
% 0.17/0.38 % E exiting
%------------------------------------------------------------------------------