%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM003+3 : 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 05:00:56 AM UTC 2025
% Result : Theorem 0.24s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.15 % Problem : COM003+3 : TPTP v9.0.0. Released v2.0.0.
% 0.05/0.15 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Jun 19 12:20:41 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.24/0.41 % SZS status Theorem
% 0.24/0.41 % SZS output start Proof
% 0.24/0.41 tff(decides_type, type, (
% 0.24/0.41 decides: ( $i * $i * $i ) > $o)).
% 0.24/0.41 tff(tptp_fun_Y_0_type, type, (
% 0.24/0.41 tptp_fun_Y_0: $i > $i)).
% 0.24/0.41 tff(tptp_fun_X1_6_type, type, (
% 0.24/0.41 tptp_fun_X1_6: $i)).
% 0.24/0.41 tff(program_type, type, (
% 0.24/0.41 program: $i > $o)).
% 0.24/0.41 tff(tptp_fun_Z_1_type, type, (
% 0.24/0.41 tptp_fun_Z_1: $i > $i)).
% 0.24/0.41 tff(algorithm_type, type, (
% 0.24/0.41 algorithm: $i > $o)).
% 0.24/0.41 tff(tptp_fun_W_2_type, type, (
% 0.24/0.41 tptp_fun_W_2: $i)).
% 0.24/0.41 tff(halts3_type, type, (
% 0.24/0.41 halts3: ( $i * $i * $i ) > $o)).
% 0.24/0.41 tff(tptp_fun_V_5_type, type, (
% 0.24/0.41 tptp_fun_V_5: $i > $i)).
% 0.24/0.41 tff(halts2_type, type, (
% 0.24/0.41 halts2: ( $i * $i ) > $o)).
% 0.24/0.41 tff(outputs_type, type, (
% 0.24/0.41 outputs: ( $i * $i ) > $o)).
% 0.24/0.41 tff(good_type, type, (
% 0.24/0.41 good: $i)).
% 0.24/0.41 tff(bad_type, type, (
% 0.24/0.41 bad: $i)).
% 0.24/0.41 tff(tptp_fun_Z_3_type, type, (
% 0.24/0.41 tptp_fun_Z_3: $i > $i)).
% 0.24/0.41 tff(tptp_fun_Y_4_type, type, (
% 0.24/0.41 tptp_fun_Y_4: $i > $i)).
% 0.24/0.41 tff(1,plain,
% 0.24/0.41 ((algorithm(X1!6) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!6, Y1, Z1))) <=> (algorithm(X1!6) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!6, Y1, Z1)))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(2,plain,
% 0.24/0.41 (?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1))) <=> ?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1)))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(3,plain,
% 0.24/0.41 ((~(~?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1))))) <=> ?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1)))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(4,plain,
% 0.24/0.41 ((~?[X1: $i] : (algorithm(X1) & ![Y1: $i] : (program(Y1) => ![Z1: $i] : decides(X1, Y1, Z1)))) <=> (~?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1))))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(5,plain,
% 0.24/0.41 ((~(~?[X1: $i] : (algorithm(X1) & ![Y1: $i] : (program(Y1) => ![Z1: $i] : decides(X1, Y1, Z1))))) <=> (~(~?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1)))))),
% 0.24/0.41 inference(monotonicity,[status(thm)],[4])).
% 0.24/0.41 tff(6,plain,
% 0.24/0.41 ((~(~?[X1: $i] : (algorithm(X1) & ![Y1: $i] : (program(Y1) => ![Z1: $i] : decides(X1, Y1, Z1))))) <=> ?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1)))),
% 0.24/0.41 inference(transitivity,[status(thm)],[5, 3])).
% 0.24/0.41 tff(7,axiom,(~(~?[X1: $i] : (algorithm(X1) & ![Y1: $i] : (program(Y1) => ![Z1: $i] : decides(X1, Y1, Z1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.24/0.41 tff(8,plain,
% 0.24/0.41 (?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.24/0.41 tff(9,plain,
% 0.24/0.41 (?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1)))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.24/0.41 tff(10,plain,
% 0.24/0.41 (algorithm(X1!6) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!6, Y1, Z1))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.24/0.41 tff(11,plain,
% 0.24/0.41 (algorithm(X1!6)),
% 0.24/0.41 inference(and_elim,[status(thm)],[10])).
% 0.24/0.41 tff(12,assumption,(~((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))))), introduced(assumption)).
% 0.24/0.41 tff(13,plain,
% 0.24/0.41 (((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))) | ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))),
% 0.24/0.41 inference(tautology,[status(thm)],[])).
% 0.24/0.41 tff(14,plain,
% 0.24/0.41 (![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.24/0.41 tff(15,assumption,(~((~program(tptp_fun_Y_0(W!2))) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2)))), introduced(assumption)).
% 0.24/0.41 tff(16,plain,
% 0.24/0.41 (((~program(tptp_fun_Y_0(W!2))) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2))) | program(tptp_fun_Y_0(W!2))),
% 0.24/0.41 inference(tautology,[status(thm)],[])).
% 0.24/0.41 tff(17,plain,
% 0.24/0.41 (program(tptp_fun_Y_0(W!2))),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.24/0.41 tff(18,assumption,(![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))), introduced(assumption)).
% 0.24/0.42 tff(19,plain,
% 0.24/0.42 (((~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))) | ((~program(tptp_fun_Y_0(W!2))) | ![Z: $i] : decides(W!2, tptp_fun_Y_0(W!2), Z))) <=> ((~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))) | (~program(tptp_fun_Y_0(W!2))) | ![Z: $i] : decides(W!2, tptp_fun_Y_0(W!2), Z))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(20,plain,
% 0.24/0.42 ((~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))) | ((~program(tptp_fun_Y_0(W!2))) | ![Z: $i] : decides(W!2, tptp_fun_Y_0(W!2), Z))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(21,plain,
% 0.24/0.42 ((~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))) | (~program(tptp_fun_Y_0(W!2))) | ![Z: $i] : decides(W!2, tptp_fun_Y_0(W!2), Z)),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.24/0.42 tff(22,plain,
% 0.24/0.42 (![Z: $i] : decides(W!2, tptp_fun_Y_0(W!2), Z)),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[21, 18, 17])).
% 0.24/0.42 tff(23,plain,
% 0.24/0.42 (((~program(tptp_fun_Y_0(W!2))) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2))) | (~decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2)))),
% 0.24/0.42 inference(tautology,[status(thm)],[])).
% 0.24/0.42 tff(24,plain,
% 0.24/0.42 (~decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[23, 15])).
% 0.24/0.42 tff(25,plain,
% 0.24/0.42 ((~![Z: $i] : decides(W!2, tptp_fun_Y_0(W!2), Z)) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(26,plain,
% 0.24/0.42 ($false),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[25, 24, 22])).
% 0.24/0.42 tff(27,plain,(((~program(tptp_fun_Y_0(W!2))) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2))) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.42 tff(28,plain,
% 0.24/0.42 ((~program(tptp_fun_Y_0(W!2))) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[27, 14])).
% 0.24/0.42 tff(29,plain,
% 0.24/0.42 (^[W: $i] : refl(((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))))))) <=> ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(30,plain,
% 0.24/0.42 (![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))))))) <=> ![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.24/0.42 tff(31,plain,
% 0.24/0.42 (^[W: $i] : rewrite(((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))))))) <=> ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(32,plain,
% 0.24/0.42 (![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))))))) <=> ![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[31])).
% 0.24/0.42 tff(33,plain,
% 0.24/0.42 (![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))))))) <=> ![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))),
% 0.24/0.42 inference(transitivity,[status(thm)],[32, 30])).
% 0.24/0.42 tff(34,plain,
% 0.24/0.42 (^[W: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((program(Y) & halts2(Y, Z)) <=> (~((~program(Y)) | (~halts2(Y, Z))))), ((~(program(Y) & halts2(Y, Z))) <=> (~(~((~program(Y)) | (~halts2(Y, Z))))))), rewrite((~(~((~program(Y)) | (~halts2(Y, Z))))) <=> ((~program(Y)) | (~halts2(Y, Z)))), ((~(program(Y) & halts2(Y, Z))) <=> ((~program(Y)) | (~halts2(Y, Z))))), rewrite((halts3(W, Y, Z) & outputs(W, good)) <=> (~((~halts3(W, Y, Z)) | (~outputs(W, good))))), (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) <=> (((~program(Y)) | (~halts2(Y, Z))) | (~((~halts3(W, Y, Z)) | (~outputs(W, good))))))), rewrite((((~program(Y)) | (~halts2(Y, Z))) | (~((~halts3(W, Y, Z)) | (~outputs(W, good))))) <=> ((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))), (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) <=> ((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good))))))), trans(monotonicity(trans(monotonicity(rewrite((program(Y) & (~halts2(Y, Z))) <=> (~((~program(Y)) | halts2(Y, Z)))), ((~(program(Y) & (~halts2(Y, Z)))) <=> (~(~((~program(Y)) | halts2(Y, Z)))))), rewrite((~(~((~program(Y)) | halts2(Y, Z)))) <=> ((~program(Y)) | halts2(Y, Z))), ((~(program(Y) & (~halts2(Y, Z)))) <=> ((~program(Y)) | halts2(Y, Z)))), rewrite((halts3(W, Y, Z) & outputs(W, bad)) <=> (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))), (((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad))) <=> (((~program(Y)) | halts2(Y, Z)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))))), rewrite((((~program(Y)) | halts2(Y, Z)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))) <=> (halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))), (((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad))) <=> (halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))))), ((((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))) <=> (((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good))))) & (halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))), rewrite((((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good))))) & (halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))) <=> (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))))))), ((((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))) <=> (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad))))))))))), (![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))) <=> ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))), rewrite((program(tptp_fun_Y_0(W)) & (~decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) <=> (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W))))), (((~program(W)) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))) | (program(tptp_fun_Y_0(W)) & (~decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W))))) <=> ((~program(W)) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W))))))), rewrite(((~program(W)) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W))))) <=> ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))), (((~program(W)) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))) | (program(tptp_fun_Y_0(W)) & (~decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W))))) <=> ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(35,plain,
% 0.24/0.42 (![W: $i] : ((~program(W)) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))) | (program(tptp_fun_Y_0(W)) & (~decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W))))) <=> ![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.24/0.42 tff(36,plain,
% 0.24/0.42 (^[W: $i] : rewrite((((~program(W)) | (program(tptp_fun_Y_0(W)) & (~decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W))))) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad))))) <=> ((~program(W)) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))) | (program(tptp_fun_Y_0(W)) & (~decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(37,plain,
% 0.24/0.42 (![W: $i] : (((~program(W)) | (program(tptp_fun_Y_0(W)) & (~decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W))))) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad))))) <=> ![W: $i] : ((~program(W)) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))) | (program(tptp_fun_Y_0(W)) & (~decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.24/0.42 tff(38,plain,
% 0.24/0.42 (![W: $i] : ((~(program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad))))) <=> ![W: $i] : ((~(program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(39,plain,
% 0.24/0.42 (^[W: $i] : trans(monotonicity(rewrite((program(W) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(W, Y, Z))) <=> (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))), quant_intro(proof_bind(^[Y: $i, Z: $i] : rewrite((((program(Y) & halts2(Y, Z)) => (halts3(W, Y, Z) & outputs(W, good))) & ((program(Y) & (~halts2(Y, Z))) => (halts3(W, Y, Z) & outputs(W, bad)))) <=> (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))), (![Y: $i, Z: $i] : (((program(Y) & halts2(Y, Z)) => (halts3(W, Y, Z) & outputs(W, good))) & ((program(Y) & (~halts2(Y, Z))) => (halts3(W, Y, Z) & outputs(W, bad)))) <=> ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))), (((program(W) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(W, Y, Z))) => ![Y: $i, Z: $i] : (((program(Y) & halts2(Y, Z)) => (halts3(W, Y, Z) & outputs(W, good))) & ((program(Y) & (~halts2(Y, Z))) => (halts3(W, Y, Z) & outputs(W, bad))))) <=> ((program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z))) => ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad))))))), rewrite(((program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z))) => ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad))))) <=> ((~(program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))), (((program(W) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(W, Y, Z))) => ![Y: $i, Z: $i] : (((program(Y) & halts2(Y, Z)) => (halts3(W, Y, Z) & outputs(W, good))) & ((program(Y) & (~halts2(Y, Z))) => (halts3(W, Y, Z) & outputs(W, bad))))) <=> ((~(program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(40,plain,
% 0.24/0.42 (![W: $i] : ((program(W) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(W, Y, Z))) => ![Y: $i, Z: $i] : (((program(Y) & halts2(Y, Z)) => (halts3(W, Y, Z) & outputs(W, good))) & ((program(Y) & (~halts2(Y, Z))) => (halts3(W, Y, Z) & outputs(W, bad))))) <=> ![W: $i] : ((~(program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.24/0.42 tff(41,axiom,(![W: $i] : ((program(W) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(W, Y, Z))) => ![Y: $i, Z: $i] : (((program(Y) & halts2(Y, Z)) => (halts3(W, Y, Z) & outputs(W, good))) & ((program(Y) & (~halts2(Y, Z))) => (halts3(W, Y, Z) & outputs(W, bad)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2')).
% 0.24/0.43 tff(42,plain,
% 0.24/0.43 (![W: $i] : ((~(program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.24/0.43 tff(43,plain,
% 0.24/0.43 (![W: $i] : ((~(program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.24/0.43 tff(44,plain,(
% 0.24/0.43 ![W: $i] : (((~program(W)) | (program(tptp_fun_Y_0(W)) & (~decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W))))) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))),
% 0.24/0.43 inference(skolemize,[status(sab)],[43])).
% 0.24/0.43 tff(45,plain,
% 0.24/0.43 (![W: $i] : ((~program(W)) | ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))) | (program(tptp_fun_Y_0(W)) & (~decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.24/0.43 tff(46,plain,
% 0.24/0.43 (![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.24/0.43 tff(47,plain,
% 0.24/0.43 (![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[46, 33])).
% 0.24/0.43 tff(48,plain,
% 0.24/0.43 (((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))) | program(W!2)),
% 0.24/0.43 inference(tautology,[status(thm)],[])).
% 0.24/0.43 tff(49,plain,
% 0.24/0.43 (program(W!2)),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[48, 12])).
% 0.24/0.43 tff(50,plain,
% 0.24/0.43 (((~![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))) | ((~program(W!2)) | (~((~program(tptp_fun_Y_0(W!2))) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad)))))))))) <=> ((~![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))) | (~program(W!2)) | (~((~program(tptp_fun_Y_0(W!2))) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad)))))))))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(51,plain,
% 0.24/0.43 ((~![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))) | ((~program(W!2)) | (~((~program(tptp_fun_Y_0(W!2))) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad)))))))))),
% 0.24/0.43 inference(quant_inst,[status(thm)],[])).
% 0.24/0.43 tff(52,plain,
% 0.24/0.43 ((~![W: $i] : ((~program(W)) | (~((~program(tptp_fun_Y_0(W))) | decides(W, tptp_fun_Y_0(W), tptp_fun_Z_1(W)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W, Y, Z)) | (~outputs(W, bad)))))))))) | (~program(W!2)) | (~((~program(tptp_fun_Y_0(W!2))) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.24/0.43 tff(53,plain,
% 0.24/0.43 ((~((~program(tptp_fun_Y_0(W!2))) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2)))) | ![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[52, 49, 47])).
% 0.24/0.43 tff(54,plain,
% 0.24/0.43 (![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[53, 28])).
% 0.24/0.43 tff(55,assumption,((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)))))))), introduced(assumption)).
% 0.24/0.43 tff(56,assumption,(![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))), introduced(assumption)).
% 0.24/0.43 tff(57,plain,
% 0.24/0.43 (((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)))))))))) <=> ((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))))))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(58,plain,
% 0.24/0.43 ((~((~((~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, bad)))))))) <=> (~((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)))))))))),
% 0.24/0.43 inference(rewrite,[status(thm)],[])).
% 0.24/0.43 tff(59,plain,
% 0.24/0.43 (((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, bad))))))))) <=> ((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))))))),
% 0.24/0.43 inference(monotonicity,[status(thm)],[58])).
% 0.24/0.43 tff(60,plain,
% 0.24/0.43 (((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, bad))))))))) <=> ((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))))))),
% 0.24/0.43 inference(transitivity,[status(thm)],[59, 57])).
% 0.24/0.43 tff(61,plain,
% 0.24/0.43 ((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, bad))))))))),
% 0.24/0.43 inference(quant_inst,[status(thm)],[])).
% 0.24/0.43 tff(62,plain,
% 0.24/0.43 ((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)))))))))),
% 0.24/0.43 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.24/0.43 tff(63,plain,
% 0.24/0.43 ($false),
% 0.24/0.43 inference(unit_resolution,[status(thm)],[62, 56, 55])).
% 0.24/0.43 tff(64,plain,((~((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))))) | (~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.44 tff(65,plain,
% 0.24/0.44 (~((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))))),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[64, 54])).
% 0.24/0.44 tff(66,plain,
% 0.24/0.44 (((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)))))))) | ((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))),
% 0.24/0.44 inference(tautology,[status(thm)],[])).
% 0.24/0.44 tff(67,plain,
% 0.24/0.44 ((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)))))),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.24/0.44 tff(68,plain,
% 0.24/0.44 (((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)))))))) | ((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))),
% 0.24/0.44 inference(tautology,[status(thm)],[])).
% 0.24/0.44 tff(69,plain,
% 0.24/0.44 ((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)))))),
% 0.24/0.44 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.24/0.44 tff(70,plain,
% 0.24/0.44 (^[W: $i] : refl(((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))))))) <=> ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))))))))),
% 0.24/0.44 inference(bind,[status(th)],[])).
% 0.24/0.44 tff(71,plain,
% 0.24/0.44 (![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))))))) <=> ![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))),
% 0.24/0.44 inference(quant_intro,[status(thm)],[70])).
% 0.24/0.44 tff(72,plain,
% 0.24/0.44 (^[W: $i] : rewrite(((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))))))) <=> ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))))))))),
% 0.24/0.44 inference(bind,[status(th)],[])).
% 0.24/0.44 tff(73,plain,
% 0.24/0.44 (![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))))))) <=> ![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))),
% 0.24/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.24/0.44 tff(74,plain,
% 0.24/0.44 (![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))))))) <=> ![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))),
% 0.24/0.44 inference(transitivity,[status(thm)],[73, 71])).
% 0.24/0.44 tff(75,plain,
% 0.24/0.44 (^[W: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) <=> (~((~program(tptp_fun_Y_4(W))) | (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))))), ((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) <=> (~(~((~program(tptp_fun_Y_4(W))) | (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))))))), rewrite((~(~((~program(tptp_fun_Y_4(W))) | (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))))) <=> ((~program(tptp_fun_Y_4(W))) | (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))), ((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) <=> ((~program(tptp_fun_Y_4(W))) | (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))))), rewrite((halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good)) <=> (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good))))), (((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) <=> (((~program(tptp_fun_Y_4(W))) | (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good))))))), rewrite((((~program(tptp_fun_Y_4(W))) | (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good))))) <=> ((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))), (((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) <=> ((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good))))))), trans(monotonicity(trans(monotonicity(rewrite((program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) <=> (~((~program(tptp_fun_Y_4(W))) | halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))), ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) <=> (~(~((~program(tptp_fun_Y_4(W))) | halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))))), rewrite((~(~((~program(tptp_fun_Y_4(W))) | halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) <=> ((~program(tptp_fun_Y_4(W))) | halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))), ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) <=> ((~program(tptp_fun_Y_4(W))) | halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))), rewrite((halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad)) <=> (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad))))), (((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad))) <=> (((~program(tptp_fun_Y_4(W))) | halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad))))))), rewrite((((~program(tptp_fun_Y_4(W))) | halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad))))) <=> (halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))), (((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad))) <=> (halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad))))))), ((((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad)))) <=> (((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good))))) & (halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))))), rewrite((((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good))))) & (halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) <=> (~((~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad))))))))), ((((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad)))) <=> (~((~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))))))), ((~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad))))) <=> (~(~((~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad))))))))))), rewrite((~(~((~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad))))))))) <=> ((~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))))), ((~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad))))) <=> ((~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad))))))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((program(Y) & halts3(W, Y, Y) & outputs(W, good)) <=> (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good))))), ((~(program(Y) & halts3(W, Y, Y) & outputs(W, good))) <=> (~(~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good))))))), rewrite((~(~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good))))) <=> ((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))), ((~(program(Y) & halts3(W, Y, Y) & outputs(W, good))) <=> ((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good))))), (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) <=> ((~halts2(tptp_fun_V_5(W), Y)) | ((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))))), rewrite(((~halts2(tptp_fun_V_5(W), Y)) | ((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) <=> ((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))), (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) <=> ((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good))))), trans(monotonicity(trans(monotonicity(rewrite((program(Y) & halts3(W, Y, Y) & outputs(W, bad)) <=> (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad))))), ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) <=> (~(~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad))))))), rewrite((~(~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad))))) <=> ((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)))), ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) <=> ((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad))))), rewrite((halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)) <=> (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))), (((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad))) <=> (((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad))) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))), rewrite((((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad))) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))) <=> ((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))), (((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad))) <=> ((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))), ((((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))) <=> (((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good))) & ((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))), rewrite((((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good))) & ((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))) <=> (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))), ((((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))) <=> (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))), (![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))) <=> ![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))))), ((program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad))))) <=> (program(tptp_fun_V_5(W)) & ![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))), rewrite((program(tptp_fun_V_5(W)) & ![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))) <=> (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))))))), ((program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad))))) <=> (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))), (((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))))) <=> ((~program(W)) | ((~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad))))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))))))))), rewrite(((~program(W)) | ((~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad))))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad)))))))))))) <=> ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))), (((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))))) <=> ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(76,plain,
% 0.24/0.45 (![W: $i] : ((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))))) <=> ![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[75])).
% 0.24/0.45 tff(77,plain,
% 0.24/0.45 (^[W: $i] : trans(monotonicity(rewrite((program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad))))) <=> (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))))), ((((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad)))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))))) <=> (((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad)))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))))))), rewrite((((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad)))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))))) <=> ((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad))))))), ((((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad)))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))))) <=> ((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad))))))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(78,plain,
% 0.24/0.45 (![W: $i] : (((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad)))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad)))))) <=> ![W: $i] : ((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad))))))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.24/0.45 tff(79,plain,
% 0.24/0.45 (![W: $i] : ((~(program(W) & ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))) | ?[V: $i] : (program(V) & ![Y: $i] : (((~halts2(V, Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(V, Y) & outputs(V, bad)))))) <=> ![W: $i] : ((~(program(W) & ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))) | ?[V: $i] : (program(V) & ![Y: $i] : (((~halts2(V, Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(V, Y) & outputs(V, bad))))))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(80,plain,
% 0.24/0.45 (^[W: $i] : trans(monotonicity(rewrite((program(W) & ![Y: $i, Z: $i] : (((program(Y) & halts2(Y, Z)) => (halts3(W, Y, Z) & outputs(W, good))) & ((program(Y) & (~halts2(Y, Z))) => (halts3(W, Y, Z) & outputs(W, bad))))) <=> (program(W) & ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))), quant_intro(proof_bind(^[V: $i] : rewrite((program(V) & ![Y: $i] : ((((program(Y) & halts3(W, Y, Y)) & outputs(W, good)) => (~halts2(V, Y))) & (((program(Y) & halts3(W, Y, Y)) & outputs(W, bad)) => (halts2(V, Y) & outputs(V, bad))))) <=> (program(V) & ![Y: $i] : (((~halts2(V, Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(V, Y) & outputs(V, bad))))))), (?[V: $i] : (program(V) & ![Y: $i] : ((((program(Y) & halts3(W, Y, Y)) & outputs(W, good)) => (~halts2(V, Y))) & (((program(Y) & halts3(W, Y, Y)) & outputs(W, bad)) => (halts2(V, Y) & outputs(V, bad))))) <=> ?[V: $i] : (program(V) & ![Y: $i] : (((~halts2(V, Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(V, Y) & outputs(V, bad))))))), (((program(W) & ![Y: $i, Z: $i] : (((program(Y) & halts2(Y, Z)) => (halts3(W, Y, Z) & outputs(W, good))) & ((program(Y) & (~halts2(Y, Z))) => (halts3(W, Y, Z) & outputs(W, bad))))) => ?[V: $i] : (program(V) & ![Y: $i] : ((((program(Y) & halts3(W, Y, Y)) & outputs(W, good)) => (~halts2(V, Y))) & (((program(Y) & halts3(W, Y, Y)) & outputs(W, bad)) => (halts2(V, Y) & outputs(V, bad)))))) <=> ((program(W) & ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad))))) => ?[V: $i] : (program(V) & ![Y: $i] : (((~halts2(V, Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(V, Y) & outputs(V, bad)))))))), rewrite(((program(W) & ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad))))) => ?[V: $i] : (program(V) & ![Y: $i] : (((~halts2(V, Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(V, Y) & outputs(V, bad)))))) <=> ((~(program(W) & ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))) | ?[V: $i] : (program(V) & ![Y: $i] : (((~halts2(V, Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(V, Y) & outputs(V, bad))))))), (((program(W) & ![Y: $i, Z: $i] : (((program(Y) & halts2(Y, Z)) => (halts3(W, Y, Z) & outputs(W, good))) & ((program(Y) & (~halts2(Y, Z))) => (halts3(W, Y, Z) & outputs(W, bad))))) => ?[V: $i] : (program(V) & ![Y: $i] : ((((program(Y) & halts3(W, Y, Y)) & outputs(W, good)) => (~halts2(V, Y))) & (((program(Y) & halts3(W, Y, Y)) & outputs(W, bad)) => (halts2(V, Y) & outputs(V, bad)))))) <=> ((~(program(W) & ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))) | ?[V: $i] : (program(V) & ![Y: $i] : (((~halts2(V, Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(V, Y) & outputs(V, bad))))))))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(81,plain,
% 0.24/0.45 (![W: $i] : ((program(W) & ![Y: $i, Z: $i] : (((program(Y) & halts2(Y, Z)) => (halts3(W, Y, Z) & outputs(W, good))) & ((program(Y) & (~halts2(Y, Z))) => (halts3(W, Y, Z) & outputs(W, bad))))) => ?[V: $i] : (program(V) & ![Y: $i] : ((((program(Y) & halts3(W, Y, Y)) & outputs(W, good)) => (~halts2(V, Y))) & (((program(Y) & halts3(W, Y, Y)) & outputs(W, bad)) => (halts2(V, Y) & outputs(V, bad)))))) <=> ![W: $i] : ((~(program(W) & ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))) | ?[V: $i] : (program(V) & ![Y: $i] : (((~halts2(V, Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(V, Y) & outputs(V, bad))))))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.24/0.45 tff(82,axiom,(![W: $i] : ((program(W) & ![Y: $i, Z: $i] : (((program(Y) & halts2(Y, Z)) => (halts3(W, Y, Z) & outputs(W, good))) & ((program(Y) & (~halts2(Y, Z))) => (halts3(W, Y, Z) & outputs(W, bad))))) => ?[V: $i] : (program(V) & ![Y: $i] : ((((program(Y) & halts3(W, Y, Y)) & outputs(W, good)) => (~halts2(V, Y))) & (((program(Y) & halts3(W, Y, Y)) & outputs(W, bad)) => (halts2(V, Y) & outputs(V, bad))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3')).
% 0.24/0.45 tff(83,plain,
% 0.24/0.45 (![W: $i] : ((~(program(W) & ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))) | ?[V: $i] : (program(V) & ![Y: $i] : (((~halts2(V, Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(V, Y) & outputs(V, bad))))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.24/0.45 tff(84,plain,
% 0.24/0.45 (![W: $i] : ((~(program(W) & ![Y: $i, Z: $i] : (((~(program(Y) & halts2(Y, Z))) | (halts3(W, Y, Z) & outputs(W, good))) & ((~(program(Y) & (~halts2(Y, Z)))) | (halts3(W, Y, Z) & outputs(W, bad)))))) | ?[V: $i] : (program(V) & ![Y: $i] : (((~halts2(V, Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(V, Y) & outputs(V, bad))))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.24/0.45 tff(85,plain,(
% 0.24/0.45 ![W: $i] : (((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad)))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad))))))),
% 0.24/0.45 inference(skolemize,[status(sab)],[84])).
% 0.24/0.45 tff(86,plain,
% 0.24/0.45 (![W: $i] : ((~program(W)) | (~(((~(program(tptp_fun_Y_4(W)) & halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, good))) & ((~(program(tptp_fun_Y_4(W)) & (~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))))) | (halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W)) & outputs(W, bad))))) | (program(tptp_fun_V_5(W)) & ![Y: $i] : (((~halts2(tptp_fun_V_5(W), Y)) | (~(program(Y) & halts3(W, Y, Y) & outputs(W, good)))) & ((~(program(Y) & halts3(W, Y, Y) & outputs(W, bad))) | (halts2(tptp_fun_V_5(W), Y) & outputs(tptp_fun_V_5(W), bad))))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.24/0.45 tff(87,plain,
% 0.24/0.45 (![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.24/0.45 tff(88,plain,
% 0.24/0.45 (![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[87, 74])).
% 0.24/0.45 tff(89,plain,
% 0.24/0.45 (((~![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))) | ((~program(W!2)) | (~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))))))) <=> ((~![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))) | (~program(W!2)) | (~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))))))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(90,plain,
% 0.24/0.45 (((~program(W!2)) | (~((~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, bad)))))) | (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)) | (~outputs(W!2, good)))) | (~((~program(Y)) | (~halts3(W!2, Y, Y)) | (~outputs(W!2, bad)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad)))))))))))) <=> ((~program(W!2)) | (~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))))))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(91,plain,
% 0.24/0.46 (((~![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))) | ((~program(W!2)) | (~((~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, bad)))))) | (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)) | (~outputs(W!2, good)))) | (~((~program(Y)) | (~halts3(W!2, Y, Y)) | (~outputs(W!2, bad)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))))))) <=> ((~![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))) | ((~program(W!2)) | (~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad)))))))))))))),
% 0.24/0.46 inference(monotonicity,[status(thm)],[90])).
% 0.24/0.46 tff(92,plain,
% 0.24/0.46 (((~![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))) | ((~program(W!2)) | (~((~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, bad)))))) | (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)) | (~outputs(W!2, good)))) | (~((~program(Y)) | (~halts3(W!2, Y, Y)) | (~outputs(W!2, bad)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))))))) <=> ((~![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))) | (~program(W!2)) | (~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))))))),
% 0.24/0.46 inference(transitivity,[status(thm)],[91, 89])).
% 0.24/0.46 tff(93,plain,
% 0.24/0.46 ((~![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))) | ((~program(W!2)) | (~((~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~program(tptp_fun_Y_4(W!2))) | (~((~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~outputs(W!2, bad)))))) | (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)) | (~outputs(W!2, good)))) | (~((~program(Y)) | (~halts3(W!2, Y, Y)) | (~outputs(W!2, bad)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))))))),
% 0.24/0.46 inference(quant_inst,[status(thm)],[])).
% 0.24/0.46 tff(94,plain,
% 0.24/0.46 ((~![W: $i] : ((~program(W)) | (~((~halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, good)))))) | (~(halts2(tptp_fun_Y_4(W), tptp_fun_Z_3(W)) | (~program(tptp_fun_Y_4(W))) | (~((~halts3(W, tptp_fun_Y_4(W), tptp_fun_Z_3(W))) | (~outputs(W, bad)))))) | (~((~program(tptp_fun_V_5(W))) | (~![Y: $i] : (~((~((~program(Y)) | (~halts2(tptp_fun_V_5(W), Y)) | (~halts3(W, Y, Y)) | (~outputs(W, good)))) | (~((~program(Y)) | (~halts3(W, Y, Y)) | (~outputs(W, bad)) | (~((~halts2(tptp_fun_V_5(W), Y)) | (~outputs(tptp_fun_V_5(W), bad))))))))))))) | (~program(W!2)) | (~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad)))))))))))),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.24/0.46 tff(95,plain,
% 0.24/0.46 ((~((~program(tptp_fun_Y_4(W!2))) | (~halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_Y_4(W!2))) | halts2(tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_4(W!2), tptp_fun_Z_3(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad)))))))))))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[94, 49, 88])).
% 0.24/0.46 tff(96,plain,
% 0.24/0.46 (~((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[95, 69, 67])).
% 0.24/0.46 tff(97,plain,
% 0.24/0.46 (((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad)))))))))) | ![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))),
% 0.24/0.46 inference(tautology,[status(thm)],[])).
% 0.24/0.46 tff(98,plain,
% 0.24/0.46 (![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.24/0.46 tff(99,plain,
% 0.24/0.46 (((~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))) | (~((~((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))))))) <=> ((~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))) | (~((~((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad)))))))))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(100,plain,
% 0.24/0.47 ((~((~((~program(tptp_fun_V_5(W!2))) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~program(tptp_fun_V_5(W!2))) | (~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad)))))))) <=> (~((~((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))))))),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(101,plain,
% 0.24/0.47 (((~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))) | (~((~((~program(tptp_fun_V_5(W!2))) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~program(tptp_fun_V_5(W!2))) | (~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))))))) <=> ((~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))) | (~((~((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad)))))))))),
% 0.24/0.47 inference(monotonicity,[status(thm)],[100])).
% 0.24/0.47 tff(102,plain,
% 0.24/0.47 (((~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))) | (~((~((~program(tptp_fun_V_5(W!2))) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~program(tptp_fun_V_5(W!2))) | (~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))))))) <=> ((~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))) | (~((~((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad)))))))))),
% 0.24/0.47 inference(transitivity,[status(thm)],[101, 99])).
% 0.24/0.47 tff(103,plain,
% 0.24/0.47 ((~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))) | (~((~((~program(tptp_fun_V_5(W!2))) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~program(tptp_fun_V_5(W!2))) | (~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))))))),
% 0.24/0.47 inference(quant_inst,[status(thm)],[])).
% 0.24/0.47 tff(104,plain,
% 0.24/0.47 ((~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad))))))))) | (~((~((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))))))),
% 0.24/0.47 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.24/0.47 tff(105,plain,
% 0.24/0.47 (~((~((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad)))))))),
% 0.24/0.47 inference(unit_resolution,[status(thm)],[104, 98])).
% 0.24/0.47 tff(106,plain,
% 0.24/0.47 (((~((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))))) | ((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))),
% 0.24/0.47 inference(tautology,[status(thm)],[])).
% 0.24/0.47 tff(107,plain,
% 0.24/0.47 ((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))),
% 0.24/0.47 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.24/0.47 tff(108,assumption,((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))))), introduced(assumption)).
% 0.24/0.47 tff(109,plain,
% 0.24/0.47 (((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))))))) <=> ((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))))))),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(110,plain,
% 0.24/0.47 ((~((~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~program(tptp_fun_V_5(W!2))) | (~((~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~program(tptp_fun_V_5(W!2))) | (~((~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(W!2, bad)))))))) <=> (~((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))))))),
% 0.24/0.47 inference(rewrite,[status(thm)],[])).
% 0.24/0.47 tff(111,plain,
% 0.24/0.47 (((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~program(tptp_fun_V_5(W!2))) | (~((~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~program(tptp_fun_V_5(W!2))) | (~((~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(W!2, bad))))))))) <=> ((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))))))),
% 0.24/0.47 inference(monotonicity,[status(thm)],[110])).
% 0.24/0.47 tff(112,plain,
% 0.24/0.47 (((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~program(tptp_fun_V_5(W!2))) | (~((~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~program(tptp_fun_V_5(W!2))) | (~((~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(W!2, bad))))))))) <=> ((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))))))),
% 0.24/0.47 inference(transitivity,[status(thm)],[111, 109])).
% 0.24/0.47 tff(113,plain,
% 0.24/0.47 ((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~program(tptp_fun_V_5(W!2))) | (~((~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(W!2, good)))))) | (~(halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~program(tptp_fun_V_5(W!2))) | (~((~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(W!2, bad))))))))),
% 0.24/0.47 inference(quant_inst,[status(thm)],[])).
% 0.24/0.47 tff(114,plain,
% 0.24/0.47 ((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad))))))))) | (~((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))))))),
% 0.24/0.47 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.24/0.47 tff(115,plain,
% 0.24/0.47 ($false),
% 0.24/0.47 inference(unit_resolution,[status(thm)],[114, 56, 108])).
% 0.24/0.47 tff(116,plain,((~((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))))) | (~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, good)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~halts3(W!2, Y, Z)) | (~outputs(W!2, bad)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.48 tff(117,plain,
% 0.24/0.48 (~((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[116, 54])).
% 0.24/0.48 tff(118,plain,
% 0.24/0.48 (((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))))) | ((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(119,plain,
% 0.24/0.48 ((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.24/0.48 tff(120,plain,
% 0.24/0.48 (((~program(tptp_fun_V_5(W!2))) | (~![Y: $i] : (~((~((~program(Y)) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), Y)) | (~halts3(W!2, Y, Y)))) | (~((~program(Y)) | (~outputs(W!2, bad)) | (~halts3(W!2, Y, Y)) | (~((~halts2(tptp_fun_V_5(W!2), Y)) | (~outputs(tptp_fun_V_5(W!2), bad)))))))))) | program(tptp_fun_V_5(W!2))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(121,plain,
% 0.24/0.48 (program(tptp_fun_V_5(W!2))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[120, 96])).
% 0.24/0.48 tff(122,plain,
% 0.24/0.48 (((~((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))))) | ((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad)))))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(123,plain,
% 0.24/0.48 ((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[122, 105])).
% 0.24/0.48 tff(124,assumption,(program(tptp_fun_V_5(W!2))), introduced(assumption)).
% 0.24/0.48 tff(125,assumption,((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))), introduced(assumption)).
% 0.24/0.48 tff(126,assumption,(~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))), introduced(assumption)).
% 0.24/0.48 tff(127,plain,
% 0.24/0.48 (((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(128,plain,
% 0.24/0.48 ((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.24/0.48 tff(129,assumption,((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))), introduced(assumption)).
% 0.24/0.48 tff(130,plain,
% 0.24/0.48 ((~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(131,plain,
% 0.24/0.48 ((~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[130, 124])).
% 0.24/0.48 tff(132,plain,
% 0.24/0.48 (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[131, 126, 129])).
% 0.24/0.48 tff(133,assumption,((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))), introduced(assumption)).
% 0.24/0.48 tff(134,assumption,(~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))), introduced(assumption)).
% 0.24/0.48 tff(135,plain,
% 0.24/0.48 (((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))) | outputs(W!2, bad)),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(136,plain,
% 0.24/0.48 (outputs(W!2, bad)),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.24/0.48 tff(137,plain,
% 0.24/0.48 (((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))) | halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(138,plain,
% 0.24/0.48 (halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[137, 134])).
% 0.24/0.48 tff(139,plain,
% 0.24/0.48 ((~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad)))))) | (~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(140,plain,
% 0.24/0.48 ((~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad)))))) | (~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[139, 124])).
% 0.24/0.48 tff(141,plain,
% 0.24/0.48 ($false),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[140, 138, 136, 133, 125])).
% 0.24/0.48 tff(142,plain,(((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad)))) | (~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad)))))) | (~program(tptp_fun_V_5(W!2)))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.48 tff(143,plain,
% 0.24/0.48 ($false),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[142, 132, 128, 125, 124])).
% 0.24/0.48 tff(144,plain,(halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~program(tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~outputs(tptp_fun_V_5(W!2), bad)))))) | (~program(tptp_fun_V_5(W!2))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.48 tff(145,plain,
% 0.24/0.48 (halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[144, 123, 121, 119])).
% 0.24/0.48 tff(146,plain,
% 0.24/0.48 (((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~((~program(tptp_fun_V_5(W!2))) | halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))))) | ((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(147,plain,
% 0.24/0.48 ((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[146, 117])).
% 0.24/0.48 tff(148,plain,
% 0.24/0.48 ((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(149,plain,
% 0.24/0.48 ((~((~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[148, 121])).
% 0.24/0.48 tff(150,plain,
% 0.24/0.48 (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[149, 145, 147])).
% 0.24/0.48 tff(151,plain,
% 0.24/0.48 (((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))) | outputs(W!2, good)),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(152,plain,
% 0.24/0.48 (outputs(W!2, good)),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.24/0.48 tff(153,plain,
% 0.24/0.48 (((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))) | halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(154,plain,
% 0.24/0.48 (halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[153, 150])).
% 0.24/0.48 tff(155,plain,
% 0.24/0.48 ((~((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))),
% 0.24/0.48 inference(tautology,[status(thm)],[])).
% 0.24/0.48 tff(156,plain,
% 0.24/0.48 ((~((~outputs(W!2, good)) | (~program(tptp_fun_V_5(W!2))) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))))) | (~outputs(W!2, good)) | (~halts2(tptp_fun_V_5(W!2), tptp_fun_V_5(W!2))) | (~halts3(W!2, tptp_fun_V_5(W!2), tptp_fun_V_5(W!2)))),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[155, 121])).
% 0.24/0.48 tff(157,plain,
% 0.24/0.48 ($false),
% 0.24/0.48 inference(unit_resolution,[status(thm)],[156, 154, 152, 145, 107])).
% 0.24/0.48 tff(158,plain,((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))), inference(lemma,lemma(discharge,[]))).
% 0.24/0.48 tff(159,plain,
% 0.24/0.48 ((![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (~((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))))) <=> (![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (~((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))))))),
% 0.24/0.48 inference(rewrite,[status(thm)],[])).
% 0.24/0.48 tff(160,plain,
% 0.24/0.48 ((![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (~((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))))) <=> (![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (~((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))))))),
% 0.24/0.48 inference(rewrite,[status(thm)],[])).
% 0.24/0.48 tff(161,plain,
% 0.24/0.48 ((program(W!2) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))) <=> (~((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))))),
% 0.24/0.48 inference(rewrite,[status(thm)],[])).
% 0.24/0.48 tff(162,plain,
% 0.24/0.48 (^[X: $i] : rewrite(((~algorithm(X)) | (program(tptp_fun_Y_0(X)) & (~decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) <=> ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))))),
% 0.24/0.48 inference(bind,[status(th)],[])).
% 0.24/0.48 tff(163,plain,
% 0.24/0.48 (![X: $i] : ((~algorithm(X)) | (program(tptp_fun_Y_0(X)) & (~decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) <=> ![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X)))))),
% 0.24/0.48 inference(quant_intro,[status(thm)],[162])).
% 0.24/0.48 tff(164,plain,
% 0.24/0.48 ((![X: $i] : ((~algorithm(X)) | (program(tptp_fun_Y_0(X)) & (~decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (program(W!2) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))) <=> (![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (~((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))))))),
% 0.24/0.48 inference(monotonicity,[status(thm)],[163, 161])).
% 0.24/0.48 tff(165,plain,
% 0.24/0.48 ((![X: $i] : ((~algorithm(X)) | (program(tptp_fun_Y_0(X)) & (~decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (program(W!2) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))) <=> (![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (~((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))))))),
% 0.24/0.48 inference(transitivity,[status(thm)],[164, 160])).
% 0.24/0.48 tff(166,plain,
% 0.24/0.48 ((![X: $i] : ((~algorithm(X)) | (program(tptp_fun_Y_0(X)) & (~decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (program(W!2) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))) <=> (![X: $i] : ((~algorithm(X)) | (program(tptp_fun_Y_0(X)) & (~decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (program(W!2) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))))),
% 0.24/0.48 inference(rewrite,[status(thm)],[])).
% 0.24/0.48 tff(167,plain,
% 0.24/0.48 ((program(W!2) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))) <=> (program(W!2) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))),
% 0.24/0.48 inference(rewrite,[status(thm)],[])).
% 0.24/0.48 tff(168,plain,
% 0.24/0.48 ((![X: $i] : ((~algorithm(X)) | (program(tptp_fun_Y_0(X)) & (~decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (program(W!2) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))) <=> (![X: $i] : ((~algorithm(X)) | (program(tptp_fun_Y_0(X)) & (~decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (program(W!2) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))))),
% 0.24/0.48 inference(monotonicity,[status(thm)],[167])).
% 0.24/0.48 tff(169,plain,
% 0.24/0.48 ((![X: $i] : ((~algorithm(X)) | (program(tptp_fun_Y_0(X)) & (~decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (program(W!2) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))) <=> (![X: $i] : ((~algorithm(X)) | (program(tptp_fun_Y_0(X)) & (~decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))) | (program(W!2) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))))),
% 0.24/0.48 inference(transitivity,[status(thm)],[168, 166])).
% 0.24/0.48 tff(170,plain,
% 0.24/0.48 (((~?[X: $i] : (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z)))) | ?[W: $i] : (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))) <=> ((~?[X: $i] : (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z)))) | ?[W: $i] : (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z))))),
% 0.24/0.48 inference(rewrite,[status(thm)],[])).
% 0.24/0.48 tff(171,plain,
% 0.24/0.48 ((?[X: $i] : (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z))) => ?[W: $i] : (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))) <=> ((~?[X: $i] : (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z)))) | ?[W: $i] : (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z))))),
% 0.24/0.48 inference(rewrite,[status(thm)],[])).
% 0.24/0.48 tff(172,plain,
% 0.24/0.48 (^[W: $i] : rewrite((program(W) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(W, Y, Z))) <=> (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z))))),
% 0.24/0.48 inference(bind,[status(th)],[])).
% 0.24/0.48 tff(173,plain,
% 0.24/0.48 (?[W: $i] : (program(W) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(W, Y, Z))) <=> ?[W: $i] : (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))),
% 0.24/0.48 inference(quant_intro,[status(thm)],[172])).
% 0.24/0.48 tff(174,plain,
% 0.24/0.48 (^[X: $i] : rewrite((algorithm(X) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(X, Y, Z))) <=> (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z))))),
% 0.24/0.48 inference(bind,[status(th)],[])).
% 0.24/0.48 tff(175,plain,
% 0.24/0.48 (?[X: $i] : (algorithm(X) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(X, Y, Z))) <=> ?[X: $i] : (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z)))),
% 0.24/0.48 inference(quant_intro,[status(thm)],[174])).
% 0.24/0.48 tff(176,plain,
% 0.24/0.48 ((?[X: $i] : (algorithm(X) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(X, Y, Z))) => ?[W: $i] : (program(W) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(W, Y, Z)))) <=> (?[X: $i] : (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z))) => ?[W: $i] : (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z))))),
% 0.24/0.48 inference(monotonicity,[status(thm)],[175, 173])).
% 0.24/0.48 tff(177,plain,
% 0.24/0.48 ((?[X: $i] : (algorithm(X) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(X, Y, Z))) => ?[W: $i] : (program(W) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(W, Y, Z)))) <=> ((~?[X: $i] : (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z)))) | ?[W: $i] : (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z))))),
% 0.24/0.48 inference(transitivity,[status(thm)],[176, 171])).
% 0.24/0.48 tff(178,axiom,(?[X: $i] : (algorithm(X) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(X, Y, Z))) => ?[W: $i] : (program(W) & ![Y: $i] : (program(Y) => ![Z: $i] : decides(W, Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p1')).
% 0.24/0.48 tff(179,plain,
% 0.24/0.48 ((~?[X: $i] : (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z)))) | ?[W: $i] : (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.24/0.48 tff(180,plain,
% 0.24/0.48 ((~?[X: $i] : (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z)))) | ?[W: $i] : (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[179, 170])).
% 0.24/0.48 tff(181,plain,
% 0.24/0.48 ((~?[X: $i] : (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z)))) | ?[W: $i] : (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[180, 170])).
% 0.24/0.48 tff(182,plain,
% 0.24/0.48 ((~?[X: $i] : (algorithm(X) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(X, Y, Z)))) | ?[W: $i] : (program(W) & ![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W, Y, Z)))),
% 0.24/0.48 inference(modus_ponens,[status(thm)],[181, 170])).
% 0.24/0.48 Proof display could not be completed: monotonicity rule is not handled
% 0.24/0.49 % E exiting
%------------------------------------------------------------------------------