TSTP Solution File: GRP555-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP555-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% 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 : 600s
% DateTime : Sat Jul 16 11:19:35 EDT 2022
% Result : Unsatisfiable 0.47s 1.01s
% Output : Refutation 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP555-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 07:20:24 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.47/1.01 ============================== Prover9 ===============================
% 0.47/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.01 Process 5586 was started by sandbox2 on n004.cluster.edu,
% 0.47/1.01 Tue Jun 14 07:20:24 2022
% 0.47/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5433_n004.cluster.edu".
% 0.47/1.01 ============================== end of head ===========================
% 0.47/1.01
% 0.47/1.01 ============================== INPUT =================================
% 0.47/1.01
% 0.47/1.01 % Reading from file /tmp/Prover9_5433_n004.cluster.edu
% 0.47/1.01
% 0.47/1.01 set(prolog_style_variables).
% 0.47/1.01 set(auto2).
% 0.47/1.01 % set(auto2) -> set(auto).
% 0.47/1.01 % set(auto) -> set(auto_inference).
% 0.47/1.01 % set(auto) -> set(auto_setup).
% 0.47/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.47/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.01 % set(auto) -> set(auto_limits).
% 0.47/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.01 % set(auto) -> set(auto_denials).
% 0.47/1.01 % set(auto) -> set(auto_process).
% 0.47/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.47/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.47/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.47/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.47/1.01 % set(auto2) -> assign(stats, some).
% 0.47/1.01 % set(auto2) -> clear(echo_input).
% 0.47/1.01 % set(auto2) -> set(quiet).
% 0.47/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.01 % set(auto2) -> clear(print_given).
% 0.47/1.01 assign(lrs_ticks,-1).
% 0.47/1.01 assign(sos_limit,10000).
% 0.47/1.01 assign(order,kbo).
% 0.47/1.01 set(lex_order_vars).
% 0.47/1.01 clear(print_given).
% 0.47/1.01
% 0.47/1.01 % formulas(sos). % not echoed (3 formulas)
% 0.47/1.01
% 0.47/1.01 ============================== end of input ==========================
% 0.47/1.01
% 0.47/1.01 % From the command line: assign(max_seconds, 300).
% 0.47/1.01
% 0.47/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.01
% 0.47/1.01 % Formulas that are not ordinary clauses:
% 0.47/1.01
% 0.47/1.01 ============================== end of process non-clausal formulas ===
% 0.47/1.01
% 0.47/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.47/1.01
% 0.47/1.01 ============================== PREDICATE ELIMINATION =================
% 0.47/1.01
% 0.47/1.01 ============================== end predicate elimination =============
% 0.47/1.01
% 0.47/1.01 Auto_denials:
% 0.47/1.01 % copying label prove_these_axioms_3 to answer in negative clause
% 0.47/1.01
% 0.47/1.01 Term ordering decisions:
% 0.47/1.01
% 0.47/1.01 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.47/1.01 Function symbol KB weights: a3=1. b3=1. c3=1. divide=1. multiply=1. inverse=0.
% 0.47/1.01
% 0.47/1.01 ============================== end of process initial clauses ========
% 0.47/1.01
% 0.47/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.47/1.01
% 0.47/1.01 ============================== end of clauses for search =============
% 0.47/1.01
% 0.47/1.01 ============================== SEARCH ================================
% 0.47/1.01
% 0.47/1.01 % Starting search at 0.01 seconds.
% 0.47/1.01
% 0.47/1.01 ============================== PROOF =================================
% 0.47/1.01 % SZS status Unsatisfiable
% 0.47/1.01 % SZS output start Refutation
% 0.47/1.01
% 0.47/1.01 % Proof 1 at 0.01 (+ 0.00) seconds: prove_these_axioms_3.
% 0.47/1.01 % Length of proof is 46.
% 0.47/1.01 % Level of proof is 20.
% 0.47/1.01 % Maximum clause weight is 36.000.
% 0.47/1.01 % Given clauses 29.
% 0.47/1.01
% 0.47/1.01 1 multiply(A,B) = divide(A,inverse(B)) # label(multiply) # label(axiom). [assumption].
% 0.47/1.01 2 divide(divide(A,inverse(divide(B,divide(A,C)))),C) = B # label(single_axiom) # label(axiom). [assumption].
% 0.47/1.01 3 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3). [assumption].
% 0.47/1.01 4 divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) # answer(prove_these_axioms_3). [copy(3),rewrite([1(3),1(6),1(11),1(13)])].
% 0.47/1.01 5 divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(divide(D,B))),C) = D. [para(2(a,1),2(a,1,1,2,1,2))].
% 0.47/1.01 6 divide(A,inverse(divide(B,divide(A,divide(C,D))))) = divide(divide(C,inverse(B)),D). [para(2(a,1),2(a,1,1,2,1)),flip(a)].
% 0.47/1.01 10 divide(A,inverse(divide(B,A))) = B. [para(2(a,1),5(a,1,1))].
% 0.47/1.01 11 divide(divide(divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(divide(D,B))),inverse(divide(E,D))),inverse(divide(F,E))),C) = F. [para(5(a,1),5(a,1,1,1,2,1,2))].
% 0.47/1.01 12 divide(divide(divide(A,inverse(divide(B,divide(A,C)))),inverse(D)),C) = divide(divide(E,inverse(divide(F,divide(E,B)))),inverse(divide(D,F))). [para(5(a,1),5(a,1,1,2,1))].
% 0.47/1.01 14 divide(A,inverse(divide(B,divide(A,C)))) = divide(C,inverse(B)). [para(2(a,1),10(a,1,2,1)),flip(a)].
% 0.47/1.01 17 divide(divide(A,inverse(B)),inverse(divide(C,B))) = divide(A,inverse(C)). [para(5(a,1),10(a,1,2,1)),rewrite([14(6)]),flip(a)].
% 0.47/1.01 18 divide(inverse(divide(A,B)),inverse(A)) = B. [para(10(a,1),10(a,1,2,1))].
% 0.47/1.01 19 divide(divide(divide(A,inverse(B)),inverse(C)),A) = divide(B,inverse(C)). [back_rewrite(12),rewrite([14(4),14(9),17(10)])].
% 0.47/1.01 20 divide(divide(A,inverse(B)),A) = B. [back_rewrite(11),rewrite([14(4),17(5),17(5),17(5)])].
% 0.47/1.01 21 divide(divide(A,inverse(B)),C) = divide(divide(A,C),inverse(B)). [back_rewrite(6),rewrite([14(5)]),flip(a)].
% 0.47/1.01 22 divide(A,divide(inverse(B),inverse(A))) = B. [para(20(a,1),20(a,1,1))].
% 0.47/1.01 23 inverse(divide(A,B)) = divide(inverse(A),inverse(B)). [para(18(a,1),10(a,1,2,1)),flip(a)].
% 0.47/1.01 29 divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(b3),inverse(inverse(c3)))) # answer(prove_these_axioms_3). [back_rewrite(4),rewrite([23(13)])].
% 0.47/1.01 31 divide(divide(A,inverse(B)),divide(inverse(C),inverse(A))) = divide(C,inverse(B)). [para(20(a,1),19(a,1,1,1))].
% 0.47/1.01 34 divide(A,inverse(B)) = divide(B,inverse(A)). [para(19(a,1),19(a,1,1)),rewrite([31(6)])].
% 0.47/1.01 35 divide(divide(A,divide(inverse(B),divide(inverse(inverse(C)),divide(inverse(inverse(inverse(D))),inverse(inverse(inverse(inverse(inverse(A))))))))),B) = divide(D,inverse(C)). [para(19(a,1),19(a,2)),rewrite([34(3),34(5),23(4),23(7),23(7),34(12),23(11),23(11),23(11)])].
% 0.47/1.01 40 divide(c3,divide(inverse(a3),inverse(inverse(b3)))) != divide(a3,divide(inverse(b3),inverse(inverse(c3)))) # answer(prove_these_axioms_3). [back_rewrite(29),rewrite([34(7),23(6)])].
% 0.47/1.01 46 inverse(divide(A,B)) = divide(B,inverse(inverse(A))). [back_rewrite(23),rewrite([34(5)])].
% 0.47/1.01 47 divide(A,divide(A,inverse(inverse(B)))) = B. [back_rewrite(22),rewrite([34(3)])].
% 0.47/1.01 48 divide(divide(A,inverse(B)),C) = divide(B,divide(C,inverse(inverse(A)))). [back_rewrite(21),rewrite([34(6),46(5)])].
% 0.47/1.01 49 divide(divide(A,divide(inverse(B),inverse(inverse(C)))),B) = divide(C,inverse(A)). [back_rewrite(19),rewrite([34(4),46(3),34(4)])].
% 0.47/1.01 52 divide(A,divide(B,inverse(inverse(B)))) = A. [back_rewrite(20),rewrite([48(3)])].
% 0.47/1.01 57 divide(A,inverse(inverse(A))) = divide(B,inverse(inverse(B))). [para(47(a,1),35(a,1,1,2,2)),rewrite([49(7),34(3)])].
% 0.47/1.01 58 divide(A,divide(inverse(inverse(B)),divide(divide(inverse(inverse(C)),divide(inverse(inverse(inverse(D))),inverse(inverse(inverse(inverse(inverse(A))))))),inverse(inverse(inverse(B)))))) = divide(D,inverse(C)). [para(35(a,1),52(a,1)),rewrite([46(6),34(7),48(20)]),flip(a)].
% 0.47/1.01 61 divide(divide(A,divide(inverse(B),divide(inverse(inverse(C)),divide(inverse(inverse(inverse(inverse(A)))),divide(inverse(inverse(inverse(D))),inverse(inverse(inverse(inverse(inverse(E)))))))))),B) = divide(E,divide(D,inverse(inverse(C)))). [para(46(a,1),35(a,1,1,2,2,1,1)),rewrite([46(5),34(6),48(16),48(16),46(23)])].
% 0.47/1.01 65 divide(A,inverse(inverse(A))) = c_0. [new_symbol(57)].
% 0.47/1.01 66 divide(A,c_0) = A. [back_rewrite(52),rewrite([65(3)])].
% 0.47/1.01 69 inverse(c_0) = c_0. [para(65(a,1),46(a,1,1)),rewrite([34(7),65(7)])].
% 0.47/1.01 72 divide(A,A) = c_0. [para(69(a,1),47(a,1,2,2,1)),rewrite([69(2),66(2)])].
% 0.47/1.01 73 divide(divide(A,divide(inverse(B),divide(c_0,divide(inverse(inverse(inverse(C))),inverse(inverse(inverse(inverse(inverse(A))))))))),B) = C. [para(69(a,1),35(a,1,1,2,2,1,1)),rewrite([69(3),69(17),66(17)])].
% 0.47/1.01 75 inverse(inverse(A)) = A. [para(72(a,1),47(a,1,2)),rewrite([66(4)])].
% 0.47/1.01 76 divide(divide(A,divide(inverse(B),C)),B) = divide(A,inverse(C)). [para(72(a,1),35(a,1,1,2,2,2)),rewrite([75(3),66(3),75(6)])].
% 0.47/1.01 79 divide(A,divide(A,B)) = B. [back_rewrite(73),rewrite([75(4),75(5),75(5),34(5),75(4),76(7),46(4),69(3),69(3),66(3)])].
% 0.47/1.01 85 divide(A,divide(divide(A,divide(B,C)),D)) = divide(B,divide(C,D)). [back_rewrite(61),rewrite([75(3),75(3),75(3),75(3),75(4),75(4),34(4),75(3),76(7),46(4),75(4),75(6)])].
% 0.47/1.01 88 divide(A,divide(divide(A,B),C)) = divide(C,inverse(B)). [back_rewrite(58),rewrite([75(2),75(2),75(2),75(3),75(3),34(3),75(2),75(4),34(4),46(3),75(3),79(4),34(5)])].
% 0.47/1.01 94 inverse(divide(A,B)) = divide(B,A). [back_rewrite(46),rewrite([75(4)])].
% 0.47/1.01 96 divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(inverse(b3),c3)) # answer(prove_these_axioms_3). [back_rewrite(40),rewrite([75(6),75(12)])].
% 0.47/1.01 98 divide(A,divide(B,C)) = divide(C,divide(B,A)). [back_rewrite(85),rewrite([88(4),94(2)])].
% 0.47/1.01 100 divide(b3,divide(inverse(a3),c3)) != divide(a3,divide(inverse(b3),c3)) # answer(prove_these_axioms_3). [back_rewrite(96),rewrite([98(6)])].
% 0.47/1.01 105 divide(inverse(A),B) = divide(inverse(B),A). [para(34(a,1),94(a,1,1)),rewrite([94(3)])].
% 0.47/1.01 116 $F # answer(prove_these_axioms_3). [para(98(a,1),100(a,2)),rewrite([105(11),98(12)]),xx(a)].
% 0.47/1.01
% 0.47/1.01 % SZS output end Refutation
% 0.47/1.01 ============================== end of proof ==========================
% 0.47/1.01
% 0.47/1.01 ============================== STATISTICS ============================
% 0.47/1.01
% 0.47/1.01 Given=29. Generated=376. Kept=114. proofs=1.
% 0.47/1.01 Usable=13. Sos=4. Demods=16. Limbo=0, Disabled=100. Hints=0.
% 0.47/1.01 Megabytes=0.13.
% 0.47/1.01 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.47/1.01
% 0.47/1.01 ============================== end of statistics =====================
% 0.47/1.01
% 0.47/1.01 ============================== end of search =========================
% 0.47/1.01
% 0.47/1.01 THEOREM PROVED
% 0.47/1.01 % SZS status Unsatisfiable
% 0.47/1.01
% 0.47/1.01 Exiting with 1 proof.
% 0.47/1.01
% 0.47/1.01 Process 5586 exit (max_proofs) Tue Jun 14 07:20:24 2022
% 0.47/1.01 Prover9 interrupted
%------------------------------------------------------------------------------