TSTP Solution File: GRP419-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP419-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 11:19:01 EDT 2022
% Result : Unsatisfiable 1.75s 2.04s
% Output : Refutation 1.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP419-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 23:31:41 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.75/2.04 ============================== Prover9 ===============================
% 1.75/2.04 Prover9 (32) version 2009-11A, November 2009.
% 1.75/2.04 Process 16730 was started by sandbox2 on n006.cluster.edu,
% 1.75/2.04 Mon Jun 13 23:31:42 2022
% 1.75/2.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16577_n006.cluster.edu".
% 1.75/2.04 ============================== end of head ===========================
% 1.75/2.04
% 1.75/2.04 ============================== INPUT =================================
% 1.75/2.04
% 1.75/2.04 % Reading from file /tmp/Prover9_16577_n006.cluster.edu
% 1.75/2.04
% 1.75/2.04 set(prolog_style_variables).
% 1.75/2.04 set(auto2).
% 1.75/2.04 % set(auto2) -> set(auto).
% 1.75/2.04 % set(auto) -> set(auto_inference).
% 1.75/2.04 % set(auto) -> set(auto_setup).
% 1.75/2.04 % set(auto_setup) -> set(predicate_elim).
% 1.75/2.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.75/2.04 % set(auto) -> set(auto_limits).
% 1.75/2.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.75/2.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.75/2.04 % set(auto) -> set(auto_denials).
% 1.75/2.04 % set(auto) -> set(auto_process).
% 1.75/2.04 % set(auto2) -> assign(new_constants, 1).
% 1.75/2.04 % set(auto2) -> assign(fold_denial_max, 3).
% 1.75/2.04 % set(auto2) -> assign(max_weight, "200.000").
% 1.75/2.04 % set(auto2) -> assign(max_hours, 1).
% 1.75/2.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.75/2.04 % set(auto2) -> assign(max_seconds, 0).
% 1.75/2.04 % set(auto2) -> assign(max_minutes, 5).
% 1.75/2.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.75/2.04 % set(auto2) -> set(sort_initial_sos).
% 1.75/2.04 % set(auto2) -> assign(sos_limit, -1).
% 1.75/2.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.75/2.04 % set(auto2) -> assign(max_megs, 400).
% 1.75/2.04 % set(auto2) -> assign(stats, some).
% 1.75/2.04 % set(auto2) -> clear(echo_input).
% 1.75/2.04 % set(auto2) -> set(quiet).
% 1.75/2.04 % set(auto2) -> clear(print_initial_clauses).
% 1.75/2.04 % set(auto2) -> clear(print_given).
% 1.75/2.04 assign(lrs_ticks,-1).
% 1.75/2.04 assign(sos_limit,10000).
% 1.75/2.04 assign(order,kbo).
% 1.75/2.04 set(lex_order_vars).
% 1.75/2.04 clear(print_given).
% 1.75/2.04
% 1.75/2.04 % formulas(sos). % not echoed (2 formulas)
% 1.75/2.04
% 1.75/2.04 ============================== end of input ==========================
% 1.75/2.04
% 1.75/2.04 % From the command line: assign(max_seconds, 300).
% 1.75/2.04
% 1.75/2.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.75/2.04
% 1.75/2.04 % Formulas that are not ordinary clauses:
% 1.75/2.04
% 1.75/2.04 ============================== end of process non-clausal formulas ===
% 1.75/2.04
% 1.75/2.04 ============================== PROCESS INITIAL CLAUSES ===============
% 1.75/2.04
% 1.75/2.04 ============================== PREDICATE ELIMINATION =================
% 1.75/2.04
% 1.75/2.04 ============================== end predicate elimination =============
% 1.75/2.04
% 1.75/2.04 Auto_denials:
% 1.75/2.04 % copying label prove_these_axioms_2 to answer in negative clause
% 1.75/2.04
% 1.75/2.04 Term ordering decisions:
% 1.75/2.04
% 1.75/2.04 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.75/2.04 Function symbol KB weights: a2=1. b2=1. multiply=1. inverse=0.
% 1.75/2.04
% 1.75/2.04 ============================== end of process initial clauses ========
% 1.75/2.04
% 1.75/2.04 ============================== CLAUSES FOR SEARCH ====================
% 1.75/2.04
% 1.75/2.04 ============================== end of clauses for search =============
% 1.75/2.04
% 1.75/2.04 ============================== SEARCH ================================
% 1.75/2.04
% 1.75/2.04 % Starting search at 0.01 seconds.
% 1.75/2.04
% 1.75/2.04 ============================== PROOF =================================
% 1.75/2.04 % SZS status Unsatisfiable
% 1.75/2.04 % SZS output start Refutation
% 1.75/2.04
% 1.75/2.04 % Proof 1 at 1.01 (+ 0.01) seconds: prove_these_axioms_2.
% 1.75/2.04 % Length of proof is 33.
% 1.75/2.04 % Level of proof is 18.
% 1.75/2.04 % Maximum clause weight is 52.000.
% 1.75/2.04 % Given clauses 42.
% 1.75/2.04
% 1.75/2.04 1 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))) = B # label(single_axiom) # label(axiom). [assumption].
% 1.75/2.04 2 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 1.75/2.04 3 multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(B,inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(D,E))). [para(1(a,1),1(a,1,1,1,1,2,1,1)),flip(a)].
% 1.75/2.04 9 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = B. [para(3(a,2),1(a,1))].
% 1.75/2.04 27 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),B)) = D. [para(9(a,1),1(a,1,1,2))].
% 1.75/2.04 87 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,inverse(multiply(inverse(B),B)))))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C)))))))) = inverse(multiply(inverse(multiply(E,D)),multiply(E,B))). [para(27(a,1),1(a,1,1,1,1,2)),flip(a)].
% 1.75/2.04 210 multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)))),inverse(multiply(C,inverse(multiply(inverse(C),C))))) = B. [para(87(a,1),9(a,1,1,1)),rewrite([9(25)])].
% 1.75/2.04 271 inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,C))). [para(87(a,1),87(a,1))].
% 1.75/2.04 344 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(271(a,1),1(a,1,1,1,1,2,1,1)),rewrite([1(17)])].
% 1.75/2.04 404 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D)) = multiply(E,multiply(inverse(multiply(B,inverse(multiply(inverse(E),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),D)). [para(1(a,1),344(a,1,1)),flip(a)].
% 1.75/2.04 1722 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))) = multiply(inverse(D),D). [para(9(a,1),404(a,2,2))].
% 1.75/2.04 2188 multiply(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))),a2) != a2 # answer(prove_these_axioms_2). [para(1722(a,2),2(a,1,1))].
% 1.75/2.04 2194 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,multiply(C,D))),multiply(B,multiply(C,D)))))),multiply(A,E)) = multiply(E,inverse(multiply(inverse(E),E))). [para(1722(a,2),3(a,1,1,1,2,1)),rewrite([1(28)])].
% 1.75/2.04 2212 multiply(inverse(A),A) = multiply(inverse(B),B). [para(9(a,1),1722(a,1,1,1)),rewrite([9(14)])].
% 1.75/2.04 2233 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C)))),multiply(inverse(D),E)) = multiply(inverse(multiply(F,D)),multiply(F,E)). [para(1722(a,2),344(a,1,1,1))].
% 1.75/2.04 2234 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E)))) = multiply(inverse(multiply(F,B)),multiply(F,A)). [para(1722(a,2),344(a,1,2))].
% 1.75/2.04 2275 multiply(inverse(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))))),inverse(multiply(inverse(D),inverse(multiply(inverse(inverse(D)),inverse(D)))))) = D. [para(1722(a,2),210(a,1,1,1,1))].
% 1.75/2.04 2418 multiply(inverse(A),A) = c_0. [new_symbol(2212)].
% 1.75/2.04 2492 multiply(inverse(inverse(c_0)),inverse(multiply(inverse(A),inverse(c_0)))) = A. [back_rewrite(2275),rewrite([2418(6),2418(8)])].
% 1.75/2.04 2514 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(C),B)),c_0). [back_rewrite(2234),rewrite([2418(9)]),flip(a)].
% 1.75/2.04 2515 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(inverse(c_0),multiply(inverse(B),A)). [back_rewrite(2233),rewrite([2418(6),2514(9)]),flip(a)].
% 1.75/2.04 2527 multiply(inverse(c_0),multiply(inverse(inverse(c_0)),A)) = multiply(A,inverse(c_0)). [back_rewrite(2194),rewrite([2418(6),2514(6),2515(7),2418(9)])].
% 1.75/2.04 2528 multiply(c_0,a2) != a2 # answer(prove_these_axioms_2). [back_rewrite(2188),rewrite([2418(6)])].
% 1.75/2.04 3125 inverse(c_0) = c_0. [para(2418(a,1),2492(a,1,2,1)),rewrite([2418(6)]),flip(a)].
% 1.75/2.04 3339 multiply(c_0,multiply(c_0,A)) = multiply(A,c_0). [back_rewrite(2527),rewrite([3125(2),3125(3),3125(3),3125(6)])].
% 1.75/2.04 3346 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(c_0,multiply(inverse(B),A)). [back_rewrite(2515),rewrite([3125(7)])].
% 1.75/2.04 3350 multiply(c_0,inverse(multiply(inverse(A),c_0))) = A. [back_rewrite(2492),rewrite([3125(2),3125(2),3125(4)])].
% 1.75/2.04 3413 multiply(c_0,A) = multiply(A,c_0). [para(3350(a,1),3339(a,1,2)),rewrite([3346(8),3125(5),3339(6)])].
% 1.75/2.04 3472 multiply(c_0,inverse(multiply(inverse(A),B))) = multiply(c_0,multiply(inverse(B),A)). [back_rewrite(3346),rewrite([3413(5,R)])].
% 1.75/2.04 3473 multiply(c_0,multiply(A,c_0)) = multiply(A,c_0). [back_rewrite(3339),rewrite([3413(3)])].
% 1.75/2.04 3558 multiply(a2,c_0) != a2 # answer(prove_these_axioms_2). [back_rewrite(2528),rewrite([3413(3)])].
% 1.75/2.04 3559 multiply(A,c_0) = A. [back_rewrite(3350),rewrite([3472(6),3125(3),3413(3),3473(4)])].
% 1.75/2.04 3560 $F # answer(prove_these_axioms_2). [resolve(3559,a,3558,a)].
% 1.75/2.04
% 1.75/2.04 % SZS output end Refutation
% 1.75/2.04 ============================== end of proof ==========================
% 1.75/2.04
% 1.75/2.04 ============================== STATISTICS ============================
% 1.75/2.04
% 1.75/2.04 Given=42. Generated=8199. Kept=3559. proofs=1.
% 1.75/2.04 Usable=4. Sos=139. Demods=132. Limbo=87, Disabled=3330. Hints=0.
% 1.75/2.04 Megabytes=10.49.
% 1.75/2.04 User_CPU=1.01, System_CPU=0.01, Wall_clock=1.
% 1.75/2.04
% 1.75/2.04 ============================== end of statistics =====================
% 1.75/2.04
% 1.75/2.04 ============================== end of search =========================
% 1.75/2.04
% 1.75/2.04 THEOREM PROVED
% 1.75/2.04 % SZS status Unsatisfiable
% 1.75/2.04
% 1.75/2.04 Exiting with 1 proof.
% 1.75/2.04
% 1.75/2.04 Process 16730 exit (max_proofs) Mon Jun 13 23:31:43 2022
% 1.75/2.04 Prover9 interrupted
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