%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM003+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 0.22s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM003+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 12:19:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 tff(decides_type, type, (
% 0.22/0.40 decides: ( $i * $i * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun_Z_1_type, type, (
% 0.22/0.40 tptp_fun_Z_1: $i > $i)).
% 0.22/0.40 tff(tptp_fun_X1_7_type, type, (
% 0.22/0.40 tptp_fun_X1_7: $i)).
% 0.22/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.22/0.40 tptp_fun_Y_0: $i > $i)).
% 0.22/0.40 tff(program_type, type, (
% 0.22/0.40 program: $i > $o)).
% 0.22/0.40 tff(algorithm_type, type, (
% 0.22/0.40 algorithm: $i > $o)).
% 0.22/0.40 tff(tptp_fun_W_2_type, type, (
% 0.22/0.40 tptp_fun_W_2: $i)).
% 0.22/0.40 tff(outputs_type, type, (
% 0.22/0.40 outputs: ( $i * $i ) > $o)).
% 0.22/0.40 tff(good_type, type, (
% 0.22/0.40 good: $i)).
% 0.22/0.40 tff(halts3_type, type, (
% 0.22/0.40 halts3: ( $i * $i * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.22/0.40 tptp_fun_Y_3: $i > $i)).
% 0.22/0.40 tff(halts2_type, type, (
% 0.22/0.40 halts2: ( $i * $i ) > $o)).
% 0.22/0.40 tff(bad_type, type, (
% 0.22/0.40 bad: $i)).
% 0.22/0.40 tff(tptp_fun_V_4_type, type, (
% 0.22/0.40 tptp_fun_V_4: $i)).
% 0.22/0.40 tff(tptp_fun_Y_5_type, type, (
% 0.22/0.40 tptp_fun_Y_5: $i > $i)).
% 0.22/0.40 tff(tptp_fun_U_6_type, type, (
% 0.22/0.40 tptp_fun_U_6: $i)).
% 0.22/0.40 tff(1,assumption,(~((~program(tptp_fun_Y_0(X1!7))) | decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7)))), introduced(assumption)).
% 0.22/0.40 tff(2,plain,
% 0.22/0.40 (((~program(tptp_fun_Y_0(X1!7))) | decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7))) | program(tptp_fun_Y_0(X1!7))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(3,plain,
% 0.22/0.40 (program(tptp_fun_Y_0(X1!7))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.22/0.40 tff(4,plain,
% 0.22/0.40 (^[Y1: $i] : refl(((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)) <=> ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 (![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)) <=> ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.22/0.40 tff(6,plain,
% 0.22/0.40 (^[Y1: $i] : rewrite(((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)) <=> ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(7,plain,
% 0.22/0.40 (![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)) <=> ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.40 tff(8,plain,
% 0.22/0.40 (![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)) <=> ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.22/0.40 inference(transitivity,[status(thm)],[7, 5])).
% 0.22/0.40 tff(9,plain,
% 0.22/0.40 ((algorithm(X1!7) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))) <=> (algorithm(X1!7) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(10,plain,
% 0.22/0.40 (?[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)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(11,plain,
% 0.22/0.40 ((~(~?[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)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(12,plain,
% 0.22/0.40 ((~?[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))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(13,plain,
% 0.22/0.40 ((~(~?[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)))))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[12])).
% 0.22/0.40 tff(14,plain,
% 0.22/0.40 ((~(~?[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)))),
% 0.22/0.40 inference(transitivity,[status(thm)],[13, 11])).
% 0.22/0.40 tff(15,axiom,(~(~?[X1: $i] : (algorithm(X1) & ![Y1: $i] : (program(Y1) => ![Z1: $i] : decides(X1, Y1, Z1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.22/0.40 tff(16,plain,
% 0.22/0.40 (?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.22/0.40 tff(17,plain,
% 0.22/0.40 (?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.22/0.40 tff(18,plain,
% 0.22/0.40 (algorithm(X1!7) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[17, 9])).
% 0.22/0.40 tff(19,plain,
% 0.22/0.40 (![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.22/0.40 inference(and_elim,[status(thm)],[18])).
% 0.22/0.40 tff(20,plain,
% 0.22/0.40 (![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[19, 8])).
% 0.22/0.40 tff(21,plain,
% 0.22/0.40 (((~![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))) | ((~program(tptp_fun_Y_0(X1!7))) | ![Z1: $i] : decides(X1!7, tptp_fun_Y_0(X1!7), Z1))) <=> ((~![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))) | (~program(tptp_fun_Y_0(X1!7))) | ![Z1: $i] : decides(X1!7, tptp_fun_Y_0(X1!7), Z1))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(22,plain,
% 0.22/0.40 ((~![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))) | ((~program(tptp_fun_Y_0(X1!7))) | ![Z1: $i] : decides(X1!7, tptp_fun_Y_0(X1!7), Z1))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(23,plain,
% 0.22/0.40 ((~![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))) | (~program(tptp_fun_Y_0(X1!7))) | ![Z1: $i] : decides(X1!7, tptp_fun_Y_0(X1!7), Z1)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.22/0.40 tff(24,plain,
% 0.22/0.40 (![Z1: $i] : decides(X1!7, tptp_fun_Y_0(X1!7), Z1)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[23, 20, 3])).
% 0.22/0.40 tff(25,plain,
% 0.22/0.40 (((~program(tptp_fun_Y_0(X1!7))) | decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7))) | (~decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7)))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(26,plain,
% 0.22/0.40 (~decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[25, 1])).
% 0.22/0.40 tff(27,plain,
% 0.22/0.40 ((~![Z1: $i] : decides(X1!7, tptp_fun_Y_0(X1!7), Z1)) | decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(28,plain,
% 0.22/0.40 ($false),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[27, 26, 24])).
% 0.22/0.40 tff(29,plain,((~program(tptp_fun_Y_0(X1!7))) | decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.40 tff(30,plain,
% 0.22/0.40 (algorithm(X1!7)),
% 0.22/0.40 inference(and_elim,[status(thm)],[18])).
% 0.22/0.40 tff(31,assumption,(~((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))))), introduced(assumption)).
% 0.22/0.40 tff(32,plain,
% 0.22/0.40 (((~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))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(33,plain,
% 0.22/0.40 (![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.22/0.40 tff(34,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)).
% 0.22/0.40 tff(35,plain,
% 0.22/0.40 (((~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))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(36,plain,
% 0.22/0.40 (program(tptp_fun_Y_0(W!2))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.22/0.40 tff(37,assumption,(![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z))), introduced(assumption)).
% 0.22/0.40 tff(38,plain,
% 0.22/0.40 (((~![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))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(39,plain,
% 0.22/0.40 ((~![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))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(40,plain,
% 0.22/0.40 ((~![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)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.22/0.40 tff(41,plain,
% 0.22/0.40 (![Z: $i] : decides(W!2, tptp_fun_Y_0(W!2), Z)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[40, 37, 36])).
% 0.22/0.40 tff(42,plain,
% 0.22/0.40 (((~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)))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(43,plain,
% 0.22/0.40 (~decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[42, 34])).
% 0.22/0.40 tff(44,plain,
% 0.22/0.40 ((~![Z: $i] : decides(W!2, tptp_fun_Y_0(W!2), Z)) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(45,plain,
% 0.22/0.40 ($false),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[44, 43, 41])).
% 0.22/0.40 tff(46,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,[]))).
% 0.22/0.40 tff(47,plain,
% 0.22/0.40 ((~program(tptp_fun_Y_0(W!2))) | decides(W!2, tptp_fun_Y_0(W!2), tptp_fun_Z_1(W!2))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[46, 33])).
% 0.22/0.40 tff(48,plain,
% 0.22/0.40 (^[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))))))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(49,plain,
% 0.22/0.40 (![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)))))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.22/0.40 tff(50,plain,
% 0.22/0.40 (^[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))))))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(51,plain,
% 0.22/0.40 (![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)))))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.22/0.40 tff(52,plain,
% 0.22/0.40 (![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)))))))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[51, 49])).
% 0.22/0.40 tff(53,plain,
% 0.22/0.40 (^[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)))))))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(54,plain,
% 0.22/0.41 (![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)))))))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.22/0.41 tff(55,plain,
% 0.22/0.41 (^[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))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(56,plain,
% 0.22/0.41 (![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)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.22/0.41 tff(57,plain,
% 0.22/0.41 (![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)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(58,plain,
% 0.22/0.41 (^[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)))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(59,plain,
% 0.22/0.41 (![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)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.22/0.41 tff(60,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/sandbox2/benchmark/theBenchmark.p','p2')).
% 0.22/0.41 tff(61,plain,
% 0.22/0.41 (![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)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.22/0.41 tff(62,plain,
% 0.22/0.41 (![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)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.22/0.41 tff(63,plain,(
% 0.22/0.41 ![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)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[62])).
% 0.22/0.41 tff(64,plain,
% 0.22/0.41 (![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)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.22/0.41 tff(65,plain,
% 0.22/0.41 (![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)))))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.22/0.41 tff(66,plain,
% 0.22/0.41 (![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)))))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[65, 52])).
% 0.22/0.41 tff(67,plain,
% 0.22/0.41 (((~program(W!2)) | (~![Y: $i] : ((~program(Y)) | ![Z: $i] : decides(W!2, Y, Z)))) | program(W!2)),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(68,plain,
% 0.22/0.41 (program(W!2)),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[67, 31])).
% 0.22/0.41 tff(69,plain,
% 0.22/0.41 (((~![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)) | (~((~outputs(W!2, good)) | (~halts3(W!2, Y, Z)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, Y, Z)))))))))) <=> ((~![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)) | (~((~outputs(W!2, good)) | (~halts3(W!2, Y, Z)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, Y, Z)))))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(70,plain,
% 0.22/0.41 (((~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))))))))) <=> ((~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)) | (~((~outputs(W!2, good)) | (~halts3(W!2, Y, Z)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, Y, Z)))))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(71,plain,
% 0.22/0.41 (((~![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)) | (~((~outputs(W!2, good)) | (~halts3(W!2, Y, Z)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, Y, Z))))))))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[70])).
% 0.22/0.42 tff(72,plain,
% 0.22/0.42 (((~![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)))))))))) | ((~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)) | (~((~outputs(W!2, good)) | (~halts3(W!2, Y, Z)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, Y, Z)))))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[71, 69])).
% 0.22/0.42 tff(73,plain,
% 0.22/0.42 ((~![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)))))))))) | ((~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)))))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(74,plain,
% 0.22/0.42 ((~![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)))))))))) | (~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)) | (~((~outputs(W!2, good)) | (~halts3(W!2, Y, Z)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, Y, Z))))))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.22/0.42 tff(75,plain,
% 0.22/0.42 ((~((~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)) | (~((~outputs(W!2, good)) | (~halts3(W!2, Y, Z)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, Y, Z))))))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[74, 68, 66])).
% 0.22/0.42 tff(76,plain,
% 0.22/0.42 (![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~outputs(W!2, good)) | (~halts3(W!2, Y, Z)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, Y, Z))))))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[75, 47])).
% 0.22/0.42 tff(77,assumption,(~((~((~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~outputs(W!2, bad)))) | halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2))))), introduced(assumption)).
% 0.22/0.42 tff(78,plain,
% 0.22/0.42 (((~((~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~outputs(W!2, bad)))) | halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2)))) | ((~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~outputs(W!2, bad)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(79,plain,
% 0.22/0.42 ((~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~outputs(W!2, bad))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.22/0.42 tff(80,assumption,(![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~outputs(W!2, good)) | (~halts3(W!2, Y, Z)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, Y, Z))))))))), introduced(assumption)).
% 0.22/0.42 tff(81,plain,
% 0.22/0.42 ((~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~outputs(W!2, good)) | (~halts3(W!2, Y, Z)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, Y, Z))))))))) | (~((~((~halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~program(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))))))) | (~(halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)))))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(82,plain,
% 0.22/0.42 (~((~((~halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~program(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))))))) | (~(halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))))))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.22/0.42 tff(83,plain,
% 0.22/0.42 (((~((~halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~program(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, good)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))))))) | (~(halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)))))))) | (halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))))))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(84,plain,
% 0.22/0.42 (halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.22/0.42 tff(85,plain,
% 0.22/0.42 (((~((~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~outputs(W!2, bad)))) | halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2)))) | program(tptp_fun_Y_3(W!2))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(86,plain,
% 0.22/0.42 (program(tptp_fun_Y_3(W!2))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[85, 77])).
% 0.22/0.42 tff(87,plain,
% 0.22/0.42 (((~((~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~outputs(W!2, bad)))) | halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2)))) | (~halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(88,plain,
% 0.22/0.42 (~halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[87, 77])).
% 0.22/0.42 tff(89,plain,
% 0.22/0.42 ((~(halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))))))) | halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)))))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(90,plain,
% 0.22/0.42 ((~(halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2))) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))))))) | (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[89, 88, 86])).
% 0.22/0.42 tff(91,plain,
% 0.22/0.42 (~((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[90, 84])).
% 0.22/0.42 tff(92,plain,
% 0.22/0.42 (((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)))) | outputs(W!2, bad)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(93,plain,
% 0.22/0.42 (outputs(W!2, bad)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.22/0.42 tff(94,plain,
% 0.22/0.42 (((~outputs(W!2, bad)) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)))) | halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(95,plain,
% 0.22/0.42 (halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[94, 91])).
% 0.22/0.42 tff(96,plain,
% 0.22/0.42 ((~((~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~outputs(W!2, bad)))) | (~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~outputs(W!2, bad))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(97,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[96, 95, 93, 79])).
% 0.22/0.42 tff(98,plain,(((~((~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~outputs(W!2, bad)))) | halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2)))) | (~![Y: $i, Z: $i] : (~((~((~halts2(Y, Z)) | (~program(Y)) | (~((~outputs(W!2, good)) | (~halts3(W!2, Y, Z)))))) | (~(halts2(Y, Z) | (~program(Y)) | (~((~outputs(W!2, bad)) | (~halts3(W!2, Y, Z)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.42 tff(99,plain,
% 0.22/0.42 ((~((~halts3(W!2, tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2))) | (~outputs(W!2, bad)))) | halts2(tptp_fun_Y_3(W!2), tptp_fun_Y_3(W!2)) | (~program(tptp_fun_Y_3(W!2)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[98, 76])).
% 0.22/0.42 tff(100,assumption,(~((~program(V!4)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))))), introduced(assumption)).
% 0.22/0.42 tff(101,plain,
% 0.22/0.42 (((~program(V!4)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad)))))))))) | ![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(102,plain,
% 0.22/0.42 (![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.22/0.42 tff(103,assumption,((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))) | (~((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))))), introduced(assumption)).
% 0.22/0.42 tff(104,assumption,(![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))), introduced(assumption)).
% 0.22/0.42 tff(105,plain,
% 0.22/0.42 (((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))) | (~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))) | (~((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))))))) <=> ((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))) | (~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))) | (~((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4)))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(106,plain,
% 0.22/0.43 ((~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~halts2(V!4, tptp_fun_Y_5(V!4))) | (~outputs(V!4, good)))))) | (~(halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4)) | (~program(tptp_fun_Y_5(V!4))) | (~((~halts2(V!4, tptp_fun_Y_5(V!4))) | (~outputs(V!4, bad)))))))) <=> (~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))) | (~((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(107,plain,
% 0.22/0.43 (((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))) | (~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~halts2(V!4, tptp_fun_Y_5(V!4))) | (~outputs(V!4, good)))))) | (~(halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4)) | (~program(tptp_fun_Y_5(V!4))) | (~((~halts2(V!4, tptp_fun_Y_5(V!4))) | (~outputs(V!4, bad))))))))) <=> ((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))) | (~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))) | (~((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4)))))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[106])).
% 0.22/0.43 tff(108,plain,
% 0.22/0.43 (((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))) | (~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~halts2(V!4, tptp_fun_Y_5(V!4))) | (~outputs(V!4, good)))))) | (~(halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4)) | (~program(tptp_fun_Y_5(V!4))) | (~((~halts2(V!4, tptp_fun_Y_5(V!4))) | (~outputs(V!4, bad))))))))) <=> ((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))) | (~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))) | (~((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4)))))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[107, 105])).
% 0.22/0.43 tff(109,plain,
% 0.22/0.43 ((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))) | (~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~halts2(V!4, tptp_fun_Y_5(V!4))) | (~outputs(V!4, good)))))) | (~(halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4)) | (~program(tptp_fun_Y_5(V!4))) | (~((~halts2(V!4, tptp_fun_Y_5(V!4))) | (~outputs(V!4, bad))))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(110,plain,
% 0.22/0.43 ((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad))))))))) | (~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))) | (~((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.22/0.43 tff(111,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[110, 104, 103])).
% 0.22/0.43 tff(112,plain,((~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))) | (~((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4)))))) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, good)))))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(V!4, Y)) | (~outputs(V!4, bad)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(113,plain,
% 0.22/0.43 (~((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))) | (~((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4)))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[112, 102])).
% 0.22/0.43 tff(114,plain,
% 0.22/0.43 (((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))) | (~((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))))) | ((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(115,plain,
% 0.22/0.43 ((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4)))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.22/0.43 tff(116,plain,
% 0.22/0.43 (((~((~halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))) | (~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, good)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))))) | (~((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))))) | ((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(117,plain,
% 0.22/0.43 ((~program(tptp_fun_Y_5(V!4))) | (~((~outputs(V!4, bad)) | (~halts2(V!4, tptp_fun_Y_5(V!4))))) | halts2(tptp_fun_Y_5(V!4), tptp_fun_Y_5(V!4))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.22/0.43 tff(118,assumption,(~((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))))), introduced(assumption)).
% 0.22/0.43 tff(119,plain,
% 0.22/0.43 (((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad)))))))))) | ![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(120,plain,
% 0.22/0.43 (![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.22/0.43 tff(121,plain,
% 0.22/0.43 (((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))) | (~((~((~program(U!6)) | (~halts2(U!6, U!6)))) | (~((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad))))))))) <=> ((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))) | (~((~((~program(U!6)) | (~halts2(U!6, U!6)))) | (~((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad)))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(122,plain,
% 0.22/0.43 ((~((~((~halts2(U!6, U!6)) | (~program(U!6)) | (~halts2(U!6, U!6)))) | (~(halts2(U!6, U!6) | (~program(U!6)) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad)))))))) <=> (~((~((~program(U!6)) | (~halts2(U!6, U!6)))) | (~((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(123,plain,
% 0.22/0.43 (((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))) | (~((~((~halts2(U!6, U!6)) | (~program(U!6)) | (~halts2(U!6, U!6)))) | (~(halts2(U!6, U!6) | (~program(U!6)) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad))))))))) <=> ((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))) | (~((~((~program(U!6)) | (~halts2(U!6, U!6)))) | (~((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad)))))))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[122])).
% 0.22/0.43 tff(124,plain,
% 0.22/0.43 (((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))) | (~((~((~halts2(U!6, U!6)) | (~program(U!6)) | (~halts2(U!6, U!6)))) | (~(halts2(U!6, U!6) | (~program(U!6)) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad))))))))) <=> ((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))) | (~((~((~program(U!6)) | (~halts2(U!6, U!6)))) | (~((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad)))))))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[123, 121])).
% 0.22/0.43 tff(125,plain,
% 0.22/0.43 ((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))) | (~((~((~halts2(U!6, U!6)) | (~program(U!6)) | (~halts2(U!6, U!6)))) | (~(halts2(U!6, U!6) | (~program(U!6)) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad))))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(126,plain,
% 0.22/0.43 ((~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))) | (~((~((~program(U!6)) | (~halts2(U!6, U!6)))) | (~((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad))))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.22/0.43 tff(127,plain,
% 0.22/0.43 (~((~((~program(U!6)) | (~halts2(U!6, U!6)))) | (~((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad)))))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[126, 120])).
% 0.22/0.43 tff(128,plain,
% 0.22/0.43 (((~((~program(U!6)) | (~halts2(U!6, U!6)))) | (~((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad))))))) | ((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad)))))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(129,plain,
% 0.22/0.43 ((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.22/0.43 tff(130,plain,
% 0.22/0.43 (((~((~program(U!6)) | (~halts2(U!6, U!6)))) | (~((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad))))))) | ((~program(U!6)) | (~halts2(U!6, U!6)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(131,plain,
% 0.22/0.43 ((~program(U!6)) | (~halts2(U!6, U!6))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[130, 127])).
% 0.22/0.43 tff(132,plain,
% 0.22/0.43 (((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad)))))))))) | program(U!6)),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(133,plain,
% 0.22/0.44 (program(U!6)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[132, 118])).
% 0.22/0.44 tff(134,plain,
% 0.22/0.44 ((~((~program(U!6)) | (~halts2(U!6, U!6)))) | (~program(U!6)) | (~halts2(U!6, U!6))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(135,plain,
% 0.22/0.44 ((~((~program(U!6)) | (~halts2(U!6, U!6)))) | (~halts2(U!6, U!6))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.22/0.44 tff(136,plain,
% 0.22/0.44 (~halts2(U!6, U!6)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[135, 131])).
% 0.22/0.44 tff(137,plain,
% 0.22/0.44 (((~halts2(U!6, U!6)) | (~outputs(U!6, bad))) | halts2(U!6, U!6)),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(138,plain,
% 0.22/0.44 ((~halts2(U!6, U!6)) | (~outputs(U!6, bad))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.22/0.44 tff(139,plain,
% 0.22/0.44 ((~((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad)))))) | (~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad))))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(140,plain,
% 0.22/0.44 ((~((~program(U!6)) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad)))))) | halts2(U!6, U!6) | (~((~halts2(U!6, U!6)) | (~outputs(U!6, bad))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[139, 133])).
% 0.22/0.44 tff(141,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[140, 138, 136, 129])).
% 0.22/0.44 tff(142,plain,((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(143,plain,
% 0.22/0.44 ((![V: $i] : ((~program(V)) | (~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))) | (~((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad)))))))))))) <=> (![V: $i] : ((~program(V)) | (~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))) | (~((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(144,plain,
% 0.22/0.44 ((![V: $i] : ((~program(V)) | (~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))) | (~((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad)))))))))))) <=> (![V: $i] : ((~program(V)) | (~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))) | (~((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(145,plain,
% 0.22/0.44 ((program(U!6) & ![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))) <=> (~((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad)))))))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(146,plain,
% 0.22/0.44 (^[Y: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((program(Y) & halts2(Y, Y)) <=> (~((~program(Y)) | (~halts2(Y, Y))))), ((~(program(Y) & halts2(Y, Y))) <=> (~(~((~program(Y)) | (~halts2(Y, Y))))))), rewrite((~(~((~program(Y)) | (~halts2(Y, Y))))) <=> ((~program(Y)) | (~halts2(Y, Y)))), ((~(program(Y) & halts2(Y, Y))) <=> ((~program(Y)) | (~halts2(Y, Y))))), (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) <=> ((~halts2(U!6, Y)) | ((~program(Y)) | (~halts2(Y, Y)))))), rewrite(((~halts2(U!6, Y)) | ((~program(Y)) | (~halts2(Y, Y)))) <=> ((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))), (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) <=> ((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y))))), trans(monotonicity(trans(monotonicity(rewrite((program(Y) & (~halts2(Y, Y))) <=> (~((~program(Y)) | halts2(Y, Y)))), ((~(program(Y) & (~halts2(Y, Y)))) <=> (~(~((~program(Y)) | halts2(Y, Y)))))), rewrite((~(~((~program(Y)) | halts2(Y, Y)))) <=> ((~program(Y)) | halts2(Y, Y))), ((~(program(Y) & (~halts2(Y, Y)))) <=> ((~program(Y)) | halts2(Y, Y)))), rewrite((halts2(U!6, Y) & outputs(U!6, bad)) <=> (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))), (((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad))) <=> (((~program(Y)) | halts2(Y, Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))), rewrite((((~program(Y)) | halts2(Y, Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))) <=> (halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad)))))), (((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad))) <=> (halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))), ((((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad)))) <=> (((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y))) & (halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad)))))))), rewrite((((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y))) & (halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad)))))) <=> (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))), ((((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad)))) <=> (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(147,plain,
% 0.22/0.44 (![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad)))) <=> ![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[146])).
% 0.22/0.44 tff(148,plain,
% 0.22/0.44 ((program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad))))) <=> (program(U!6) & ![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad)))))))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[147])).
% 0.22/0.44 tff(149,plain,
% 0.22/0.44 ((program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad))))) <=> (~((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad)))))))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[148, 145])).
% 0.22/0.44 tff(150,plain,
% 0.22/0.44 (^[V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) <=> (~((~program(tptp_fun_Y_5(V))) | (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))))), ((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) <=> (~(~((~program(tptp_fun_Y_5(V))) | (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))))))), rewrite((~(~((~program(tptp_fun_Y_5(V))) | (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))))) <=> ((~program(tptp_fun_Y_5(V))) | (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))), ((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) <=> ((~program(tptp_fun_Y_5(V))) | (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))))), rewrite((halts2(V, tptp_fun_Y_5(V)) & outputs(V, good)) <=> (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V)))))), (((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) <=> (((~program(tptp_fun_Y_5(V))) | (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V)))))))), rewrite((((~program(tptp_fun_Y_5(V))) | (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V)))))) <=> ((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))), (((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) <=> ((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V)))))))), trans(monotonicity(trans(monotonicity(rewrite((program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) <=> (~((~program(tptp_fun_Y_5(V))) | halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))), ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) <=> (~(~((~program(tptp_fun_Y_5(V))) | halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))))), rewrite((~(~((~program(tptp_fun_Y_5(V))) | halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) <=> ((~program(tptp_fun_Y_5(V))) | halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))), ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) <=> ((~program(tptp_fun_Y_5(V))) | halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))), rewrite((halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)) <=> (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))), (((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad))) <=> (((~program(tptp_fun_Y_5(V))) | halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))), rewrite((((~program(tptp_fun_Y_5(V))) | halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))) <=> (halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V))))))), (((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad))) <=> (halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))), ((((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))) <=> (((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V)))))) & (halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V))))))))), rewrite((((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V)))))) & (halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V))))))) <=> (~((~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))))), ((((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))) <=> (~((~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V))))))))))), ((~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad))))) <=> (~(~((~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))))))), rewrite((~(~((~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))))) <=> ((~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V))))))))), ((~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad))))) <=> ((~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))))), (((~program(V)) | (~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))))) <=> ((~program(V)) | ((~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V))))))))))), rewrite(((~program(V)) | ((~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V))))))))) <=> ((~program(V)) | (~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V))))))))), (((~program(V)) | (~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))))) <=> ((~program(V)) | (~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V))))))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(151,plain,
% 0.22/0.44 (![V: $i] : ((~program(V)) | (~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))))) <=> ![V: $i] : ((~program(V)) | (~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V))))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[150])).
% 0.22/0.44 tff(152,plain,
% 0.22/0.44 ((![V: $i] : ((~program(V)) | (~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))))) | (program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad)))))) <=> (![V: $i] : ((~program(V)) | (~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))) | (~((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[151, 149])).
% 0.22/0.44 tff(153,plain,
% 0.22/0.44 ((![V: $i] : ((~program(V)) | (~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))))) | (program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad)))))) <=> (![V: $i] : ((~program(V)) | (~((~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, good)) | (~halts2(V, tptp_fun_Y_5(V))))))) | (~(halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)) | (~program(tptp_fun_Y_5(V))) | (~((~outputs(V, bad)) | (~halts2(V, tptp_fun_Y_5(V)))))))) | (~((~program(U!6)) | (~![Y: $i] : (~((~((~halts2(Y, Y)) | (~program(Y)) | (~halts2(U!6, Y)))) | (~(halts2(Y, Y) | (~program(Y)) | (~((~halts2(U!6, Y)) | (~outputs(U!6, bad))))))))))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[152, 144])).
% 0.22/0.44 tff(154,plain,
% 0.22/0.44 ((![V: $i] : ((~program(V)) | (~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))))) | (program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad)))))) <=> (![V: $i] : ((~program(V)) | (~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))))) | (program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(155,plain,
% 0.22/0.44 ((program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad))))) <=> (program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad)))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(156,plain,
% 0.22/0.45 ((![V: $i] : ((~program(V)) | (~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))))) | (program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad)))))) <=> (![V: $i] : ((~program(V)) | (~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))))) | (program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad))))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[155])).
% 0.22/0.45 tff(157,plain,
% 0.22/0.45 ((![V: $i] : ((~program(V)) | (~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))))) | (program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad)))))) <=> (![V: $i] : ((~program(V)) | (~(((~(program(tptp_fun_Y_5(V)) & halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V)))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, good))) & ((~(program(tptp_fun_Y_5(V)) & (~halts2(tptp_fun_Y_5(V), tptp_fun_Y_5(V))))) | (halts2(V, tptp_fun_Y_5(V)) & outputs(V, bad)))))) | (program(U!6) & ![Y: $i] : (((~halts2(U!6, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U!6, Y) & outputs(U!6, bad))))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[156, 154])).
% 0.22/0.45 tff(158,plain,
% 0.22/0.45 (((~?[V: $i] : (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad)))))) | ?[U: $i] : (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad)))))) <=> ((~?[V: $i] : (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad)))))) | ?[U: $i] : (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(159,plain,
% 0.22/0.45 ((?[V: $i] : (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad))))) => ?[U: $i] : (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad)))))) <=> ((~?[V: $i] : (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad)))))) | ?[U: $i] : (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(160,plain,
% 0.22/0.45 (^[U: $i] : rewrite((program(U) & ![Y: $i] : (((program(Y) & halts2(Y, Y)) => (~halts2(U, Y))) & ((program(Y) & (~halts2(Y, Y))) => (halts2(U, Y) & outputs(U, bad))))) <=> (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(161,plain,
% 0.22/0.45 (?[U: $i] : (program(U) & ![Y: $i] : (((program(Y) & halts2(Y, Y)) => (~halts2(U, Y))) & ((program(Y) & (~halts2(Y, Y))) => (halts2(U, Y) & outputs(U, bad))))) <=> ?[U: $i] : (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad)))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[160])).
% 0.22/0.45 tff(162,plain,
% 0.22/0.45 (^[V: $i] : rewrite((program(V) & ![Y: $i] : (((program(Y) & halts2(Y, Y)) => (halts2(V, Y) & outputs(V, good))) & ((program(Y) & (~halts2(Y, Y))) => (halts2(V, Y) & outputs(V, bad))))) <=> (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(163,plain,
% 0.22/0.45 (?[V: $i] : (program(V) & ![Y: $i] : (((program(Y) & halts2(Y, Y)) => (halts2(V, Y) & outputs(V, good))) & ((program(Y) & (~halts2(Y, Y))) => (halts2(V, Y) & outputs(V, bad))))) <=> ?[V: $i] : (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad)))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[162])).
% 0.22/0.45 tff(164,plain,
% 0.22/0.45 ((?[V: $i] : (program(V) & ![Y: $i] : (((program(Y) & halts2(Y, Y)) => (halts2(V, Y) & outputs(V, good))) & ((program(Y) & (~halts2(Y, Y))) => (halts2(V, Y) & outputs(V, bad))))) => ?[U: $i] : (program(U) & ![Y: $i] : (((program(Y) & halts2(Y, Y)) => (~halts2(U, Y))) & ((program(Y) & (~halts2(Y, Y))) => (halts2(U, Y) & outputs(U, bad)))))) <=> (?[V: $i] : (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad))))) => ?[U: $i] : (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad))))))),
% 0.22/0.45 inference(monotonicity,[status(thm)],[163, 161])).
% 0.22/0.45 tff(165,plain,
% 0.22/0.45 ((?[V: $i] : (program(V) & ![Y: $i] : (((program(Y) & halts2(Y, Y)) => (halts2(V, Y) & outputs(V, good))) & ((program(Y) & (~halts2(Y, Y))) => (halts2(V, Y) & outputs(V, bad))))) => ?[U: $i] : (program(U) & ![Y: $i] : (((program(Y) & halts2(Y, Y)) => (~halts2(U, Y))) & ((program(Y) & (~halts2(Y, Y))) => (halts2(U, Y) & outputs(U, bad)))))) <=> ((~?[V: $i] : (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad)))))) | ?[U: $i] : (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad))))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[164, 159])).
% 0.22/0.45 tff(166,axiom,(?[V: $i] : (program(V) & ![Y: $i] : (((program(Y) & halts2(Y, Y)) => (halts2(V, Y) & outputs(V, good))) & ((program(Y) & (~halts2(Y, Y))) => (halts2(V, Y) & outputs(V, bad))))) => ?[U: $i] : (program(U) & ![Y: $i] : (((program(Y) & halts2(Y, Y)) => (~halts2(U, Y))) & ((program(Y) & (~halts2(Y, Y))) => (halts2(U, Y) & outputs(U, bad)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4')).
% 0.22/0.45 tff(167,plain,
% 0.22/0.45 ((~?[V: $i] : (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad)))))) | ?[U: $i] : (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.22/0.45 tff(168,plain,
% 0.22/0.45 ((~?[V: $i] : (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad)))))) | ?[U: $i] : (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[167, 158])).
% 0.22/0.45 tff(169,plain,
% 0.22/0.45 ((~?[V: $i] : (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad)))))) | ?[U: $i] : (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[168, 158])).
% 0.22/0.45 tff(170,plain,
% 0.22/0.45 ((~?[V: $i] : (program(V) & ![Y: $i] : (((~(program(Y) & halts2(Y, Y))) | (halts2(V, Y) & outputs(V, good))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(V, Y) & outputs(V, bad)))))) | ?[U: $i] : (program(U) & ![Y: $i] : (((~halts2(U, Y)) | (~(program(Y) & halts2(Y, Y)))) & ((~(program(Y) & (~halts2(Y, Y)))) | (halts2(U, Y) & outputs(U, bad)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[169, 158])).
% 0.22/0.45 Proof display could not be completed: monotonicity rule is not handled
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------