TSTP Solution File: GRP412-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP412-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 11:18:59 EDT 2022
% Result : Unsatisfiable 2.91s 3.19s
% Output : Refutation 2.91s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP412-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 06:25:20 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.91/3.19 ============================== Prover9 ===============================
% 2.91/3.19 Prover9 (32) version 2009-11A, November 2009.
% 2.91/3.19 Process 31939 was started by sandbox on n020.cluster.edu,
% 2.91/3.19 Tue Jun 14 06:25:20 2022
% 2.91/3.19 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31785_n020.cluster.edu".
% 2.91/3.19 ============================== end of head ===========================
% 2.91/3.19
% 2.91/3.19 ============================== INPUT =================================
% 2.91/3.19
% 2.91/3.19 % Reading from file /tmp/Prover9_31785_n020.cluster.edu
% 2.91/3.19
% 2.91/3.19 set(prolog_style_variables).
% 2.91/3.19 set(auto2).
% 2.91/3.19 % set(auto2) -> set(auto).
% 2.91/3.19 % set(auto) -> set(auto_inference).
% 2.91/3.19 % set(auto) -> set(auto_setup).
% 2.91/3.19 % set(auto_setup) -> set(predicate_elim).
% 2.91/3.19 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.91/3.19 % set(auto) -> set(auto_limits).
% 2.91/3.19 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.91/3.19 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.91/3.19 % set(auto) -> set(auto_denials).
% 2.91/3.19 % set(auto) -> set(auto_process).
% 2.91/3.19 % set(auto2) -> assign(new_constants, 1).
% 2.91/3.19 % set(auto2) -> assign(fold_denial_max, 3).
% 2.91/3.19 % set(auto2) -> assign(max_weight, "200.000").
% 2.91/3.19 % set(auto2) -> assign(max_hours, 1).
% 2.91/3.19 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.91/3.19 % set(auto2) -> assign(max_seconds, 0).
% 2.91/3.19 % set(auto2) -> assign(max_minutes, 5).
% 2.91/3.19 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.91/3.19 % set(auto2) -> set(sort_initial_sos).
% 2.91/3.19 % set(auto2) -> assign(sos_limit, -1).
% 2.91/3.19 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.91/3.19 % set(auto2) -> assign(max_megs, 400).
% 2.91/3.19 % set(auto2) -> assign(stats, some).
% 2.91/3.19 % set(auto2) -> clear(echo_input).
% 2.91/3.19 % set(auto2) -> set(quiet).
% 2.91/3.19 % set(auto2) -> clear(print_initial_clauses).
% 2.91/3.19 % set(auto2) -> clear(print_given).
% 2.91/3.19 assign(lrs_ticks,-1).
% 2.91/3.19 assign(sos_limit,10000).
% 2.91/3.19 assign(order,kbo).
% 2.91/3.19 set(lex_order_vars).
% 2.91/3.19 clear(print_given).
% 2.91/3.19
% 2.91/3.19 % formulas(sos). % not echoed (2 formulas)
% 2.91/3.19
% 2.91/3.19 ============================== end of input ==========================
% 2.91/3.19
% 2.91/3.19 % From the command line: assign(max_seconds, 300).
% 2.91/3.19
% 2.91/3.19 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.91/3.19
% 2.91/3.19 % Formulas that are not ordinary clauses:
% 2.91/3.19
% 2.91/3.19 ============================== end of process non-clausal formulas ===
% 2.91/3.19
% 2.91/3.19 ============================== PROCESS INITIAL CLAUSES ===============
% 2.91/3.19
% 2.91/3.19 ============================== PREDICATE ELIMINATION =================
% 2.91/3.19
% 2.91/3.19 ============================== end predicate elimination =============
% 2.91/3.19
% 2.91/3.19 Auto_denials:
% 2.91/3.19 % copying label prove_these_axioms_1 to answer in negative clause
% 2.91/3.19
% 2.91/3.19 Term ordering decisions:
% 2.91/3.19
% 2.91/3.19 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 2.91/3.19 Function symbol KB weights: a1=1. b1=1. multiply=1. inverse=0.
% 2.91/3.19
% 2.91/3.19 ============================== end of process initial clauses ========
% 2.91/3.19
% 2.91/3.19 ============================== CLAUSES FOR SEARCH ====================
% 2.91/3.19
% 2.91/3.19 ============================== end of clauses for search =============
% 2.91/3.19
% 2.91/3.19 ============================== SEARCH ================================
% 2.91/3.19
% 2.91/3.19 % Starting search at 0.01 seconds.
% 2.91/3.19
% 2.91/3.19 ============================== PROOF =================================
% 2.91/3.19 % SZS status Unsatisfiable
% 2.91/3.19 % SZS output start Refutation
% 2.91/3.19
% 2.91/3.19 % Proof 1 at 2.21 (+ 0.02) seconds: prove_these_axioms_1.
% 2.91/3.19 % Length of proof is 21.
% 2.91/3.19 % Level of proof is 14.
% 2.91/3.19 % Maximum clause weight is 59.000.
% 2.91/3.19 % Given clauses 56.
% 2.91/3.19
% 2.91/3.19 1 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C # label(single_axiom) # label(axiom). [assumption].
% 2.91/3.19 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1). [assumption].
% 2.91/3.19 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) # answer(prove_these_axioms_1). [copy(2),flip(a)].
% 2.91/3.19 4 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))) = D. [para(1(a,1),1(a,1,2,1,1,2,1,1,1))].
% 2.91/3.19 5 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))) = inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)). [para(1(a,1),1(a,1,2,1,1,2,1))].
% 2.91/3.19 21 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B)))) = C. [para(5(a,2),1(a,1,2))].
% 2.91/3.19 22 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(multiply(inverse(C),C),inverse(D))),E))),D)))),A)) = multiply(B,inverse(multiply(E,C))). [para(1(a,1),5(a,1,2,1,1)),flip(a)].
% 2.91/3.19 36 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),multiply(inverse(B),C)))),A)) = C. [para(5(a,1),4(a,1)),rewrite([1(13)])].
% 2.91/3.19 102 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),A)) = C. [para(36(a,1),36(a,1,1,1,2,1,1,1,1)),rewrite([36(18)])].
% 2.91/3.19 127 multiply(inverse(multiply(A,inverse(B))),multiply(A,C)) = multiply(inverse(multiply(D,inverse(B))),multiply(D,C)). [para(102(a,1),21(a,1,2,2))].
% 2.91/3.19 157 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(102(a,1),127(a,1,1,1,2)),rewrite([102(15)])].
% 2.91/3.19 189 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(D,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(E,inverse(B))),multiply(E,D)))),C)). [para(102(a,1),157(a,1,1)),flip(a)].
% 2.91/3.19 4753 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,C)),multiply(B,C)))),A)) = inverse(A). [para(189(a,2),22(a,1,1,1,2,1)),rewrite([1(22)])].
% 2.91/3.19 4879 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),A)) = inverse(A). [para(1(a,1),4753(a,1,1,1,2,1,1,1)),rewrite([1(14)])].
% 2.91/3.19 5022 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),A) = A. [para(4879(a,1),21(a,1,2,2,1,1,2)),rewrite([21(11)]),flip(a)].
% 2.91/3.19 5023 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(B))) = multiply(inverse(C),C). [para(4879(a,1),21(a,1,2,2))].
% 2.91/3.19 5131 multiply(inverse(multiply(A,B)),multiply(A,B)) = multiply(inverse(B),B). [para(5022(a,1),189(a,2,2))].
% 2.91/3.19 5210 multiply(inverse(inverse(A)),inverse(A)) = multiply(inverse(B),B). [back_rewrite(5023),rewrite([5131(6)])].
% 2.91/3.19 6490 multiply(inverse(inverse(A)),inverse(A)) = c_0. [new_symbol(5210)].
% 2.91/3.19 6695 multiply(inverse(A),A) = c_0. [back_rewrite(5210),rewrite([6490(4)]),flip(a)].
% 2.91/3.19 8571 $F # answer(prove_these_axioms_1). [back_rewrite(3),rewrite([6695(4),6695(5)]),xx(a)].
% 2.91/3.19
% 2.91/3.19 % SZS output end Refutation
% 2.91/3.19 ============================== end of proof ==========================
% 2.91/3.19
% 2.91/3.19 ============================== STATISTICS ============================
% 2.91/3.19
% 2.91/3.19 Given=56. Generated=19263. Kept=8569. proofs=1.
% 2.91/3.19 Usable=20. Sos=1129. Demods=1431. Limbo=1876, Disabled=5546. Hints=0.
% 2.91/3.19 Megabytes=22.07.
% 2.91/3.19 User_CPU=2.21, System_CPU=0.02, Wall_clock=2.
% 2.91/3.19
% 2.91/3.19 ============================== end of statistics =====================
% 2.91/3.19
% 2.91/3.19 ============================== end of search =========================
% 2.91/3.19
% 2.91/3.19 THEOREM PROVED
% 2.91/3.19 % SZS status Unsatisfiable
% 2.91/3.19
% 2.91/3.19 Exiting with 1 proof.
% 2.91/3.19
% 2.91/3.19 Process 31939 exit (max_proofs) Tue Jun 14 06:25:22 2022
% 2.91/3.19 Prover9 interrupted
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