TSTP Solution File: GRP511-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP511-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 11:19:24 EDT 2022
% Result : Unsatisfiable 0.82s 1.09s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP511-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 01:30:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.82/1.09 ============================== Prover9 ===============================
% 0.82/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.09 Process 22599 was started by sandbox on n011.cluster.edu,
% 0.82/1.09 Tue Jun 14 01:30:19 2022
% 0.82/1.09 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22446_n011.cluster.edu".
% 0.82/1.09 ============================== end of head ===========================
% 0.82/1.09
% 0.82/1.09 ============================== INPUT =================================
% 0.82/1.09
% 0.82/1.09 % Reading from file /tmp/Prover9_22446_n011.cluster.edu
% 0.82/1.09
% 0.82/1.09 set(prolog_style_variables).
% 0.82/1.09 set(auto2).
% 0.82/1.09 % set(auto2) -> set(auto).
% 0.82/1.09 % set(auto) -> set(auto_inference).
% 0.82/1.09 % set(auto) -> set(auto_setup).
% 0.82/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.09 % set(auto) -> set(auto_limits).
% 0.82/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.09 % set(auto) -> set(auto_denials).
% 0.82/1.09 % set(auto) -> set(auto_process).
% 0.82/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.09 % set(auto2) -> assign(stats, some).
% 0.82/1.09 % set(auto2) -> clear(echo_input).
% 0.82/1.09 % set(auto2) -> set(quiet).
% 0.82/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.09 % set(auto2) -> clear(print_given).
% 0.82/1.09 assign(lrs_ticks,-1).
% 0.82/1.09 assign(sos_limit,10000).
% 0.82/1.09 assign(order,kbo).
% 0.82/1.09 set(lex_order_vars).
% 0.82/1.09 clear(print_given).
% 0.82/1.09
% 0.82/1.09 % formulas(sos). % not echoed (2 formulas)
% 0.82/1.09
% 0.82/1.09 ============================== end of input ==========================
% 0.82/1.09
% 0.82/1.09 % From the command line: assign(max_seconds, 300).
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.09
% 0.82/1.09 % Formulas that are not ordinary clauses:
% 0.82/1.09
% 0.82/1.09 ============================== end of process non-clausal formulas ===
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.09
% 0.82/1.09 ============================== PREDICATE ELIMINATION =================
% 0.82/1.09
% 0.82/1.09 ============================== end predicate elimination =============
% 0.82/1.09
% 0.82/1.09 Auto_denials:
% 0.82/1.09 % copying label prove_these_axioms_3 to answer in negative clause
% 0.82/1.09
% 0.82/1.09 Term ordering decisions:
% 0.82/1.09
% 0.82/1.09 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.82/1.09 Function symbol KB weights: a3=1. b3=1. c3=1. multiply=1. inverse=0.
% 0.82/1.09
% 0.82/1.09 ============================== end of process initial clauses ========
% 0.82/1.09
% 0.82/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.09
% 0.82/1.09 ============================== end of clauses for search =============
% 0.82/1.09
% 0.82/1.09 ============================== SEARCH ================================
% 0.82/1.09
% 0.82/1.09 % Starting search at 0.01 seconds.
% 0.82/1.09
% 0.82/1.09 ============================== PROOF =================================
% 0.82/1.09 % SZS status Unsatisfiable
% 0.82/1.09 % SZS output start Refutation
% 0.82/1.09
% 0.82/1.09 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms_3.
% 0.82/1.09 % Length of proof is 35.
% 0.82/1.09 % Level of proof is 16.
% 0.82/1.09 % Maximum clause weight is 23.000.
% 0.82/1.09 % Given clauses 18.
% 0.82/1.09
% 0.82/1.09 1 multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.82/1.09 2 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3). [assumption].
% 0.82/1.09 3 multiply(multiply(A,B),inverse(multiply(multiply(multiply(C,A),D),B))) = inverse(multiply(C,D)). [para(1(a,1),1(a,1,1,1))].
% 0.82/1.09 4 multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) = C. [para(1(a,1),1(a,1,1))].
% 0.82/1.09 10 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(multiply(C,D),inverse(multiply(B,D))). [para(1(a,1),3(a,1,2,1,1)),flip(a)].
% 0.82/1.09 11 multiply(multiply(A,inverse(multiply(B,C))),inverse(A)) = inverse(multiply(B,C)). [para(1(a,1),3(a,1,2,1))].
% 0.82/1.09 19 inverse(multiply(A,inverse(multiply(multiply(B,multiply(A,C)),inverse(multiply(B,D)))))) = multiply(multiply(C,E),inverse(multiply(D,E))). [para(4(a,1),3(a,1,2,1,1)),flip(a)].
% 0.82/1.09 21 inverse(multiply(A,multiply(B,inverse(multiply(multiply(A,B),C))))) = C. [para(4(a,1),3(a,1)),flip(a)].
% 0.82/1.09 24 multiply(inverse(multiply(multiply(A,B),inverse(multiply(A,C)))),inverse(multiply(C,inverse(multiply(B,D))))) = D. [para(4(a,1),4(a,1,2,1,1))].
% 0.82/1.09 25 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))). [para(4(a,1),4(a,1,2,1,2,1)),flip(a)].
% 0.82/1.09 26 multiply(multiply(multiply(A,B),multiply(C,inverse(multiply(multiply(A,C),D)))),D) = B. [para(21(a,1),1(a,1,2))].
% 0.82/1.09 27 inverse(multiply(multiply(multiply(A,B),C),multiply(inverse(multiply(A,C)),inverse(multiply(B,D))))) = D. [para(1(a,1),21(a,1,1,2,2,1,1))].
% 0.82/1.09 28 inverse(multiply(multiply(A,B),multiply(C,inverse(B)))) = inverse(multiply(A,C)). [para(1(a,1),21(a,1,1,2,2,1))].
% 0.82/1.09 31 inverse(multiply(multiply(multiply(A,B),C),D)) = inverse(multiply(B,multiply(D,inverse(inverse(multiply(A,C)))))). [para(3(a,1),21(a,1,1,2,2,1)),flip(a)].
% 0.82/1.09 35 inverse(multiply(multiply(A,multiply(B,C)),inverse(multiply(A,D)))) = inverse(multiply(B,multiply(C,inverse(D)))). [para(4(a,1),21(a,1,1,2,2,1)),flip(a)].
% 0.82/1.09 39 inverse(multiply(A,inverse(multiply(A,B)))) = B. [back_rewrite(27),rewrite([31(9),11(9)])].
% 0.82/1.09 49 multiply(multiply(A,B),inverse(multiply(C,B))) = multiply(A,inverse(C)). [back_rewrite(19),rewrite([35(6),39(6)]),flip(a)].
% 0.82/1.09 52 inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(C,inverse(B)). [back_rewrite(10),rewrite([49(9)])].
% 0.82/1.09 53 multiply(multiply(A,B),inverse(A)) = B. [back_rewrite(1),rewrite([49(5)])].
% 0.82/1.09 60 inverse(multiply(A,multiply(B,inverse(C)))) = multiply(C,inverse(multiply(A,B))). [back_rewrite(35),rewrite([52(6)]),flip(a)].
% 0.82/1.09 61 multiply(A,inverse(multiply(multiply(B,A),inverse(C)))) = multiply(C,inverse(B)). [back_rewrite(25),rewrite([52(5)]),flip(a)].
% 0.82/1.09 62 multiply(multiply(A,inverse(B)),inverse(multiply(A,inverse(multiply(B,C))))) = C. [back_rewrite(24),rewrite([52(5)])].
% 0.82/1.09 64 multiply(A,inverse(multiply(multiply(B,A),C))) = inverse(multiply(B,C)). [back_rewrite(28),rewrite([60(5)])].
% 0.82/1.09 65 inverse(multiply(A,inverse(B))) = multiply(B,inverse(A)). [back_rewrite(61),rewrite([64(5)])].
% 0.82/1.09 67 multiply(multiply(multiply(A,B),inverse(multiply(A,C))),C) = B. [back_rewrite(26),rewrite([64(5)])].
% 0.82/1.09 68 multiply(multiply(A,inverse(B)),multiply(multiply(B,C),inverse(A))) = C. [back_rewrite(62),rewrite([65(6)])].
% 0.82/1.09 69 multiply(multiply(A,B),inverse(multiply(A,C))) = multiply(B,inverse(C)). [back_rewrite(52),rewrite([65(5)])].
% 0.82/1.09 70 multiply(multiply(A,inverse(B)),B) = A. [back_rewrite(67),rewrite([69(4)])].
% 0.82/1.09 99 inverse(inverse(A)) = A. [para(70(a,1),53(a,1)),flip(a)].
% 0.82/1.09 100 multiply(A,B) = multiply(B,A). [para(53(a,1),70(a,1,1))].
% 0.82/1.09 114 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(53),rewrite([100(3)])].
% 0.82/1.09 115 multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms_3). [back_rewrite(2),rewrite([100(5)])].
% 0.82/1.09 122 multiply(multiply(A,B),multiply(C,inverse(A))) = multiply(B,C). [para(114(a,1),68(a,1,2,1)),rewrite([99(2)])].
% 0.82/1.09 139 multiply(A,multiply(B,C)) = multiply(B,multiply(A,C)). [para(114(a,1),122(a,1,1)),rewrite([99(2),100(3),100(4)])].
% 0.82/1.09 144 $F # answer(prove_these_axioms_3). [back_rewrite(115),rewrite([139(5),100(4)]),xx(a)].
% 0.82/1.09
% 0.82/1.09 % SZS output end Refutation
% 0.82/1.09 ============================== end of proof ==========================
% 0.82/1.09
% 0.82/1.09 ============================== STATISTICS ============================
% 0.82/1.09
% 0.82/1.09 Given=18. Generated=308. Kept=143. proofs=1.
% 0.82/1.09 Usable=6. Sos=10. Demods=21. Limbo=5, Disabled=124. Hints=0.
% 0.82/1.09 Megabytes=0.14.
% 0.82/1.09 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.82/1.09
% 0.82/1.09 ============================== end of statistics =====================
% 0.82/1.09
% 0.82/1.09 ============================== end of search =========================
% 0.82/1.09
% 0.82/1.09 THEOREM PROVED
% 0.82/1.09 % SZS status Unsatisfiable
% 0.82/1.09
% 0.82/1.09 Exiting with 1 proof.
% 0.82/1.09
% 0.82/1.09 Process 22599 exit (max_proofs) Tue Jun 14 01:30:19 2022
% 0.82/1.09 Prover9 interrupted
%------------------------------------------------------------------------------