TSTP Solution File: COM003+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM003+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Tue Sep 6 18:05:42 EDT 2022
% Result : Theorem 0.21s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM003+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 13:33:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(halts3_type, type, (
% 0.21/0.40 halts3: ( $i * $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.21/0.40 tptp_fun_Y_3: $i > $i)).
% 0.21/0.40 tff(tptp_fun_W_2_type, type, (
% 0.21/0.40 tptp_fun_W_2: $i)).
% 0.21/0.40 tff(outputs_type, type, (
% 0.21/0.40 outputs: ( $i * $i ) > $o)).
% 0.21/0.40 tff(good_type, type, (
% 0.21/0.40 good: $i)).
% 0.21/0.40 tff(program_type, type, (
% 0.21/0.40 program: $i > $o)).
% 0.21/0.40 tff(halts2_type, type, (
% 0.21/0.40 halts2: ( $i * $i ) > $o)).
% 0.21/0.40 tff(bad_type, type, (
% 0.21/0.40 bad: $i)).
% 0.21/0.40 tff(decides_type, type, (
% 0.21/0.40 decides: ( $i * $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_Z_1_type, type, (
% 0.21/0.40 tptp_fun_Z_1: $i > $i)).
% 0.21/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.21/0.40 tptp_fun_Y_0: $i > $i)).
% 0.21/0.40 tff(algorithm_type, type, (
% 0.21/0.40 algorithm: $i > $o)).
% 0.21/0.40 tff(tptp_fun_X1_7_type, type, (
% 0.21/0.40 tptp_fun_X1_7: $i)).
% 0.21/0.40 tff(tptp_fun_V_4_type, type, (
% 0.21/0.40 tptp_fun_V_4: $i)).
% 0.21/0.40 tff(tptp_fun_Y_5_type, type, (
% 0.21/0.40 tptp_fun_Y_5: $i > $i)).
% 0.21/0.40 tff(tptp_fun_U_6_type, type, (
% 0.21/0.40 tptp_fun_U_6: $i)).
% 0.21/0.40 tff(1,assumption,((~((~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)))))))), introduced(assumption)).
% 0.21/0.40 tff(2,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)).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (((~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))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 (program(tptp_fun_Y_0(W!2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.21/0.40 tff(5,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)).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (((~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))),
% 0.21/0.40 inference(tautology,[status(thm)],[])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (program(tptp_fun_Y_0(X1!7))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (^[Y1: $i] : refl(((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)) <=> ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)) <=> ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (^[Y1: $i] : rewrite(((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)) <=> ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(11,plain,
% 0.21/0.40 (![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)) <=> ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1)) <=> ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.21/0.40 inference(transitivity,[status(thm)],[11, 9])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 ((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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (?[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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 ((~(~?[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)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 ((~?[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))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 ((~(~?[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)))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[16])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 ((~(~?[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)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.21/0.41 tff(19,axiom,(~(~?[X1: $i] : (algorithm(X1) & ![Y1: $i] : (program(Y1) => ![Z1: $i] : decides(X1, Y1, Z1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (?[X1: $i] : (algorithm(X1) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1, Y1, Z1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (algorithm(X1!7) & ![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.21/0.41 inference(and_elim,[status(thm)],[22])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![Y1: $i] : ((~program(Y1)) | ![Z1: $i] : decides(X1!7, Y1, Z1))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[23, 12])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (((~![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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 ((~![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))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 ((~![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)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (![Z1: $i] : decides(X1!7, tptp_fun_Y_0(X1!7), Z1)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[27, 24, 7])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (((~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)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (~decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[29, 5])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 ((~![Z1: $i] : decides(X1!7, tptp_fun_Y_0(X1!7), Z1)) | decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[31, 30, 28])).
% 0.21/0.41 tff(33,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,[]))).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (algorithm(X1!7)),
% 0.21/0.41 inference(and_elim,[status(thm)],[22])).
% 0.21/0.41 tff(35,assumption,(![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X)))))), introduced(assumption)).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (((~![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X)))))) | ((~algorithm(X1!7)) | (~((~program(tptp_fun_Y_0(X1!7))) | decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7)))))) <=> ((~![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X)))))) | (~algorithm(X1!7)) | (~((~program(tptp_fun_Y_0(X1!7))) | decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 ((~![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X)))))) | ((~algorithm(X1!7)) | (~((~program(tptp_fun_Y_0(X1!7))) | decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 ((~![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X)))))) | (~algorithm(X1!7)) | (~((~program(tptp_fun_Y_0(X1!7))) | decides(X1!7, tptp_fun_Y_0(X1!7), tptp_fun_Z_1(X1!7))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[38, 35, 34, 33])).
% 0.21/0.41 tff(40,plain,(~![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (((~((~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))))) | ![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (((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))))) | ![X: $i] : ((~algorithm(X)) | (~((~program(tptp_fun_Y_0(X))) | decides(X, tptp_fun_Y_0(X), tptp_fun_Z_1(X))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 ((![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)))) <=> ((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))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 ((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)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (^[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))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![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)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 ((![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))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[46, 44])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 ((![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)))) <=> ((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))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[47, 43])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (((~?[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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 ((?[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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (?[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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (^[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))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (?[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)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 ((?[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))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[54, 52])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 ((?[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))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[55, 50])).
% 0.21/0.41 tff(57,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/sandbox2/benchmark/theBenchmark.p','p1')).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 ((~?[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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 ((~?[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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[58, 49])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 ((~?[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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 ((~?[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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[60, 49])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 ((~?[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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[61, 49])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 ((~?[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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[62, 49])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 ((~?[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)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[63, 49])).
% 0.21/0.41 Proof display could not be completed: monotonicity rule is not handled
%------------------------------------------------------------------------------