TSTP Solution File: GRP409-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP409-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 11:18:58 EDT 2022
% Result : Unsatisfiable 1.11s 1.43s
% Output : Refutation 1.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP409-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 13:44:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.11/1.43 ============================== Prover9 ===============================
% 1.11/1.43 Prover9 (32) version 2009-11A, November 2009.
% 1.11/1.43 Process 22702 was started by sandbox on n008.cluster.edu,
% 1.11/1.43 Mon Jun 13 13:44:23 2022
% 1.11/1.43 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22548_n008.cluster.edu".
% 1.11/1.43 ============================== end of head ===========================
% 1.11/1.43
% 1.11/1.43 ============================== INPUT =================================
% 1.11/1.43
% 1.11/1.43 % Reading from file /tmp/Prover9_22548_n008.cluster.edu
% 1.11/1.43
% 1.11/1.43 set(prolog_style_variables).
% 1.11/1.43 set(auto2).
% 1.11/1.43 % set(auto2) -> set(auto).
% 1.11/1.43 % set(auto) -> set(auto_inference).
% 1.11/1.43 % set(auto) -> set(auto_setup).
% 1.11/1.43 % set(auto_setup) -> set(predicate_elim).
% 1.11/1.43 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.11/1.43 % set(auto) -> set(auto_limits).
% 1.11/1.43 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.11/1.43 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.11/1.43 % set(auto) -> set(auto_denials).
% 1.11/1.43 % set(auto) -> set(auto_process).
% 1.11/1.43 % set(auto2) -> assign(new_constants, 1).
% 1.11/1.43 % set(auto2) -> assign(fold_denial_max, 3).
% 1.11/1.43 % set(auto2) -> assign(max_weight, "200.000").
% 1.11/1.43 % set(auto2) -> assign(max_hours, 1).
% 1.11/1.43 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.11/1.43 % set(auto2) -> assign(max_seconds, 0).
% 1.11/1.43 % set(auto2) -> assign(max_minutes, 5).
% 1.11/1.43 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.11/1.43 % set(auto2) -> set(sort_initial_sos).
% 1.11/1.43 % set(auto2) -> assign(sos_limit, -1).
% 1.11/1.43 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.11/1.43 % set(auto2) -> assign(max_megs, 400).
% 1.11/1.43 % set(auto2) -> assign(stats, some).
% 1.11/1.43 % set(auto2) -> clear(echo_input).
% 1.11/1.43 % set(auto2) -> set(quiet).
% 1.11/1.43 % set(auto2) -> clear(print_initial_clauses).
% 1.11/1.43 % set(auto2) -> clear(print_given).
% 1.11/1.43 assign(lrs_ticks,-1).
% 1.11/1.43 assign(sos_limit,10000).
% 1.11/1.43 assign(order,kbo).
% 1.11/1.43 set(lex_order_vars).
% 1.11/1.43 clear(print_given).
% 1.11/1.43
% 1.11/1.43 % formulas(sos). % not echoed (2 formulas)
% 1.11/1.43
% 1.11/1.43 ============================== end of input ==========================
% 1.11/1.43
% 1.11/1.43 % From the command line: assign(max_seconds, 300).
% 1.11/1.43
% 1.11/1.43 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.11/1.43
% 1.11/1.43 % Formulas that are not ordinary clauses:
% 1.11/1.43
% 1.11/1.43 ============================== end of process non-clausal formulas ===
% 1.11/1.43
% 1.11/1.43 ============================== PROCESS INITIAL CLAUSES ===============
% 1.11/1.43
% 1.11/1.43 ============================== PREDICATE ELIMINATION =================
% 1.11/1.43
% 1.11/1.43 ============================== end predicate elimination =============
% 1.11/1.43
% 1.11/1.43 Auto_denials:
% 1.11/1.43 % copying label prove_these_axioms_1 to answer in negative clause
% 1.11/1.43
% 1.11/1.43 Term ordering decisions:
% 1.11/1.43
% 1.11/1.43 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.11/1.43 Function symbol KB weights: a1=1. b1=1. multiply=1. inverse=0.
% 1.11/1.43
% 1.11/1.43 ============================== end of process initial clauses ========
% 1.11/1.43
% 1.11/1.43 ============================== CLAUSES FOR SEARCH ====================
% 1.11/1.43
% 1.11/1.43 ============================== end of clauses for search =============
% 1.11/1.43
% 1.11/1.43 ============================== SEARCH ================================
% 1.11/1.43
% 1.11/1.43 % Starting search at 0.01 seconds.
% 1.11/1.43
% 1.11/1.43 ============================== PROOF =================================
% 1.11/1.43 % SZS status Unsatisfiable
% 1.11/1.43 % SZS output start Refutation
% 1.11/1.43
% 1.11/1.43 % Proof 1 at 0.45 (+ 0.01) seconds: prove_these_axioms_1.
% 1.11/1.43 % Length of proof is 24.
% 1.11/1.43 % Level of proof is 13.
% 1.11/1.43 % Maximum clause weight is 56.000.
% 1.11/1.43 % Given clauses 34.
% 1.11/1.43
% 1.11/1.43 1 multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))) = B # label(single_axiom) # label(axiom). [assumption].
% 1.11/1.43 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1). [assumption].
% 1.11/1.43 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) # answer(prove_these_axioms_1). [copy(2),flip(a)].
% 1.11/1.43 4 multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))). [para(1(a,1),1(a,1,1,1,1,2,1)),flip(a)].
% 1.11/1.43 5 multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))),inverse(multiply(inverse(C),C))) = inverse(C). [para(1(a,1),1(a,1,1,1,1))].
% 1.11/1.43 8 multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(C),C))) = B. [para(4(a,1),1(a,1,1))].
% 1.11/1.43 10 multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))),multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = inverse(inverse(multiply(inverse(C),C))). [para(4(a,2),1(a,1,1,1,1))].
% 1.11/1.43 12 multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C)))),multiply(A,inverse(C))) = B. [para(4(a,2),1(a,1))].
% 1.11/1.43 22 multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(multiply(B,C)))),multiply(D,inverse(C))). [para(4(a,2),4(a,2))].
% 1.11/1.43 23 multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))),inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(D))))) = inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(D),D))),D)))). [para(12(a,1),1(a,1,1,1,1,2,1))].
% 1.11/1.43 24 multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(multiply(D,inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C)))),multiply(inverse(C),C))))),B) = D. [para(1(a,1),12(a,1,2))].
% 1.11/1.43 35 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(multiply(E,inverse(B))),multiply(E,inverse(multiply(C,inverse(D))))). [para(12(a,1),22(a,1,1,1,2,1)),rewrite([12(19)])].
% 1.11/1.43 57 inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C)))) = B. [para(35(a,1),1(a,1,1)),rewrite([23(19)])].
% 1.11/1.43 60 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))). [para(1(a,1),35(a,1,2,2,1)),rewrite([1(20)])].
% 1.11/1.43 138 multiply(inverse(multiply(A,B)),multiply(A,inverse(C))) = multiply(inverse(multiply(D,B)),multiply(D,inverse(C))). [para(57(a,1),60(a,1,1,1,2)),rewrite([57(16)])].
% 1.11/1.43 152 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(57(a,1),138(a,1,2,2)),rewrite([57(17)])].
% 1.11/1.43 808 inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,B)))) = inverse(inverse(multiply(inverse(multiply(C,B)),multiply(C,B)))). [para(152(a,1),10(a,2,1,1)),rewrite([10(43)])].
% 1.11/1.43 896 inverse(inverse(multiply(inverse(multiply(A,multiply(B,inverse(C)))),multiply(A,multiply(B,inverse(C)))))) = inverse(inverse(multiply(inverse(D),D))). [para(12(a,1),808(a,1,1,1,1,1)),rewrite([12(12)]),flip(a)].
% 1.11/1.43 975 inverse(multiply(inverse(multiply(A,multiply(B,inverse(C)))),multiply(A,multiply(B,inverse(C))))) = inverse(multiply(inverse(D),D)). [para(896(a,1),8(a,1,1,1,1,1,2)),rewrite([8(26)]),flip(a)].
% 1.11/1.43 1557 inverse(multiply(inverse(A),A)) = inverse(multiply(inverse(B),B)). [para(12(a,1),975(a,1,1,1,1)),rewrite([12(12)])].
% 1.11/1.43 1647 multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C))))),B) = multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,multiply(inverse(C),C))))),multiply(E,inverse(multiply(inverse(C),C)))),inverse(multiply(inverse(C),C)))). [para(5(a,1),24(a,1,1,1,2,1,1))].
% 1.11/1.43 1730 multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(D),D))) = B. [para(1557(a,1),1(a,1,2))].
% 1.11/1.43 1774 multiply(inverse(A),A) = multiply(inverse(B),B). [back_rewrite(1647),rewrite([1730(15),1730(18)])].
% 1.11/1.43 1775 $F # answer(prove_these_axioms_1). [resolve(1774,a,3,a)].
% 1.11/1.43
% 1.11/1.43 % SZS output end Refutation
% 1.11/1.43 ============================== end of proof ==========================
% 1.11/1.43
% 1.11/1.43 ============================== STATISTICS ============================
% 1.11/1.43
% 1.11/1.43 Given=34. Generated=3638. Kept=1773. proofs=1.
% 1.11/1.43 Usable=18. Sos=988. Demods=434. Limbo=44, Disabled=724. Hints=0.
% 1.11/1.43 Megabytes=5.07.
% 1.11/1.43 User_CPU=0.45, System_CPU=0.01, Wall_clock=0.
% 1.11/1.43
% 1.11/1.43 ============================== end of statistics =====================
% 1.11/1.43
% 1.11/1.43 ============================== end of search =========================
% 1.11/1.43
% 1.11/1.43 THEOREM PROVED
% 1.11/1.43 % SZS status Unsatisfiable
% 1.11/1.43
% 1.11/1.43 Exiting with 1 proof.
% 1.11/1.43
% 1.11/1.43 Process 22702 exit (max_proofs) Mon Jun 13 13:44:23 2022
% 1.11/1.43 Prover9 interrupted
%------------------------------------------------------------------------------