TSTP Solution File: GRP617-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP617-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 11:19:52 EDT 2022
% Result : Unsatisfiable 1.95s 2.27s
% Output : Refutation 1.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP617-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n026.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 05:52:35 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.95/2.27 ============================== Prover9 ===============================
% 1.95/2.27 Prover9 (32) version 2009-11A, November 2009.
% 1.95/2.27 Process 12423 was started by sandbox on n026.cluster.edu,
% 1.95/2.27 Mon Jun 13 05:52:36 2022
% 1.95/2.27 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12260_n026.cluster.edu".
% 1.95/2.27 ============================== end of head ===========================
% 1.95/2.27
% 1.95/2.27 ============================== INPUT =================================
% 1.95/2.27
% 1.95/2.27 % Reading from file /tmp/Prover9_12260_n026.cluster.edu
% 1.95/2.27
% 1.95/2.27 set(prolog_style_variables).
% 1.95/2.27 set(auto2).
% 1.95/2.27 % set(auto2) -> set(auto).
% 1.95/2.27 % set(auto) -> set(auto_inference).
% 1.95/2.27 % set(auto) -> set(auto_setup).
% 1.95/2.27 % set(auto_setup) -> set(predicate_elim).
% 1.95/2.27 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.95/2.27 % set(auto) -> set(auto_limits).
% 1.95/2.27 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.95/2.27 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.95/2.27 % set(auto) -> set(auto_denials).
% 1.95/2.27 % set(auto) -> set(auto_process).
% 1.95/2.27 % set(auto2) -> assign(new_constants, 1).
% 1.95/2.27 % set(auto2) -> assign(fold_denial_max, 3).
% 1.95/2.27 % set(auto2) -> assign(max_weight, "200.000").
% 1.95/2.27 % set(auto2) -> assign(max_hours, 1).
% 1.95/2.27 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.95/2.27 % set(auto2) -> assign(max_seconds, 0).
% 1.95/2.27 % set(auto2) -> assign(max_minutes, 5).
% 1.95/2.27 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.95/2.27 % set(auto2) -> set(sort_initial_sos).
% 1.95/2.27 % set(auto2) -> assign(sos_limit, -1).
% 1.95/2.27 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.95/2.27 % set(auto2) -> assign(max_megs, 400).
% 1.95/2.27 % set(auto2) -> assign(stats, some).
% 1.95/2.27 % set(auto2) -> clear(echo_input).
% 1.95/2.27 % set(auto2) -> set(quiet).
% 1.95/2.27 % set(auto2) -> clear(print_initial_clauses).
% 1.95/2.27 % set(auto2) -> clear(print_given).
% 1.95/2.27 assign(lrs_ticks,-1).
% 1.95/2.27 assign(sos_limit,10000).
% 1.95/2.27 assign(order,kbo).
% 1.95/2.27 set(lex_order_vars).
% 1.95/2.27 clear(print_given).
% 1.95/2.27
% 1.95/2.27 % formulas(sos). % not echoed (18 formulas)
% 1.95/2.27
% 1.95/2.27 ============================== end of input ==========================
% 1.95/2.27
% 1.95/2.27 % From the command line: assign(max_seconds, 300).
% 1.95/2.27
% 1.95/2.27 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.95/2.27
% 1.95/2.27 % Formulas that are not ordinary clauses:
% 1.95/2.27
% 1.95/2.27 ============================== end of process non-clausal formulas ===
% 1.95/2.27
% 1.95/2.27 ============================== PROCESS INITIAL CLAUSES ===============
% 1.95/2.27
% 1.95/2.27 ============================== PREDICATE ELIMINATION =================
% 1.95/2.27
% 1.95/2.27 ============================== end predicate elimination =============
% 1.95/2.27
% 1.95/2.27 Auto_denials:
% 1.95/2.27 % copying label prove_vu_equals_uv to answer in negative clause
% 1.95/2.27
% 1.95/2.27 Term ordering decisions:
% 1.95/2.27
% 1.95/2.27 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 1.95/2.27 Function symbol KB weights: identity=1. u=1. v=1. multiply=1. inverse=0.
% 1.95/2.27
% 1.95/2.27 ============================== end of process initial clauses ========
% 1.95/2.27
% 1.95/2.27 ============================== CLAUSES FOR SEARCH ====================
% 1.95/2.27
% 1.95/2.27 ============================== end of clauses for search =============
% 1.95/2.27
% 1.95/2.27 ============================== SEARCH ================================
% 1.95/2.27
% 1.95/2.27 % Starting search at 0.01 seconds.
% 1.95/2.27
% 1.95/2.27 Low Water (keep): wt=15.000, iters=3814
% 1.95/2.27
% 1.95/2.27 Low Water (keep): wt=14.000, iters=3348
% 1.95/2.27
% 1.95/2.27 Low Water (keep): wt=13.000, iters=3337
% 1.95/2.27
% 1.95/2.27 ============================== PROOF =================================
% 1.95/2.27 % SZS status Unsatisfiable
% 1.95/2.27 % SZS output start Refutation
% 1.95/2.27
% 1.95/2.27 % Proof 1 at 1.11 (+ 0.04) seconds: prove_vu_equals_uv.
% 1.95/2.27 % Length of proof is 52.
% 1.95/2.27 % Level of proof is 11.
% 1.95/2.27 % Maximum clause weight is 16.000.
% 1.95/2.27 % Given clauses 216.
% 1.95/2.27
% 1.95/2.27 1 subgroup1_member(v) # label(v_in_G1) # label(hypothesis). [assumption].
% 1.95/2.27 2 subgroup2_member(u) # label(u_in_G2) # label(hypothesis). [assumption].
% 1.95/2.27 3 product(identity,A,A) # label(left_identity) # label(axiom). [assumption].
% 1.95/2.27 4 product(A,identity,A) # label(right_identity) # label(axiom). [assumption].
% 1.95/2.27 5 product(inverse(A),A,identity) # label(left_inverse) # label(axiom). [assumption].
% 1.95/2.27 6 product(A,inverse(A),identity) # label(right_inverse) # label(axiom). [assumption].
% 1.95/2.27 7 product(A,B,multiply(A,B)) # label(total_function1) # label(axiom). [assumption].
% 1.95/2.27 8 multiply(v,u) != multiply(u,v) # label(prove_vu_equals_uv) # label(negated_conjecture) # answer(prove_vu_equals_uv). [assumption].
% 1.95/2.27 9 -subgroup1_member(A) | subgroup1_member(inverse(A)) # label(closure_of_inverse1) # label(axiom). [assumption].
% 1.95/2.27 10 -subgroup2_member(A) | subgroup2_member(inverse(A)) # label(closure_of_inverse2) # label(axiom). [assumption].
% 1.95/2.27 11 -subgroup1_member(A) | -subgroup2_member(A) | A = identity # label(trivial_intersection) # label(hypothesis). [assumption].
% 1.95/2.27 12 -subgroup1_member(A) | -subgroup2_member(A) | identity = A. [copy(11),flip(c)].
% 1.95/2.27 13 -subgroup1_member(A) | subgroup1_member(multiply(B,multiply(A,inverse(B)))) # label(normality1) # label(hypothesis). [assumption].
% 1.95/2.27 14 -subgroup2_member(A) | subgroup2_member(multiply(B,multiply(A,inverse(B)))) # label(normality2) # label(hypothesis). [assumption].
% 1.95/2.27 15 -subgroup1_member(A) | -subgroup1_member(B) | -product(A,B,C) | subgroup1_member(C) # label(closure_of_product1) # label(axiom). [assumption].
% 1.95/2.27 16 -subgroup2_member(A) | -subgroup2_member(B) | -product(A,B,C) | subgroup2_member(C) # label(closure_of_product2) # label(axiom). [assumption].
% 1.95/2.27 17 -product(A,B,C) | -product(A,B,D) | C = D # label(total_function2) # label(axiom). [assumption].
% 1.95/2.27 18 -product(A,B,C) | -product(B,D,E) | -product(C,D,F) | product(A,E,F) # label(associativity1) # label(axiom). [assumption].
% 1.95/2.27 19 -product(A,B,C) | -product(B,D,E) | -product(A,E,F) | product(C,D,F) # label(associativity2) # label(axiom). [assumption].
% 1.95/2.27 20 multiply(v,u) = c_0. [new_symbol(8)].
% 1.95/2.27 21 multiply(u,v) != c_0 # answer(prove_vu_equals_uv). [back_rewrite(8),rewrite([20(3)]),flip(a)].
% 1.95/2.27 22 subgroup1_member(inverse(v)). [hyper(9,a,1,a)].
% 1.95/2.27 23 subgroup2_member(inverse(u)). [hyper(10,a,2,a)].
% 1.95/2.27 30 multiply(A,identity) = A. [hyper(17,a,7,a,b,4,a)].
% 1.95/2.27 31 multiply(identity,A) = A. [hyper(17,a,7,a,b,3,a)].
% 1.95/2.27 37 product(A,multiply(inverse(A),B),B). [hyper(18,a,6,a,b,7,a,c,7,a),rewrite([31(4)])].
% 1.95/2.27 38 product(A,identity,inverse(inverse(A))). [hyper(18,a,6,a,b,6,a,c,7,a),rewrite([31(5)])].
% 1.95/2.27 39 product(inverse(A),multiply(A,B),B). [hyper(18,a,5,a,b,7,a,c,7,a),rewrite([31(4)])].
% 1.95/2.27 41 product(multiply(A,B),C,multiply(A,multiply(B,C))). [hyper(19,a,7,a,b,7,a,c,7,a)].
% 1.95/2.27 49 product(v,u,c_0). [para(20(a,1),7(a,3))].
% 1.95/2.27 52 -product(u,v,c_0) # answer(prove_vu_equals_uv). [ur(17,a,7,a,c,21,a)].
% 1.95/2.27 57 subgroup1_member(multiply(A,multiply(inverse(v),inverse(A)))). [hyper(13,a,22,a)].
% 1.95/2.27 59 -product(c_0,inverse(v),u) # answer(prove_vu_equals_uv). [ur(19,b,5,a,c,4,a,d,52,a)].
% 1.95/2.27 64 -product(multiply(c_0,inverse(v)),identity,u) # answer(prove_vu_equals_uv). [ur(18,a,7,a,b,4,a,d,59,a)].
% 1.95/2.27 76 subgroup2_member(multiply(A,multiply(inverse(u),inverse(A)))). [hyper(14,a,23,a)].
% 1.95/2.27 120 product(c_0,inverse(u),v). [hyper(19,a,49,a,b,6,a,c,7,a),rewrite([30(6)])].
% 1.95/2.27 122 product(inverse(v),c_0,u). [hyper(18,a,5,a,b,49,a,c,7,a),rewrite([31(6)])].
% 1.95/2.27 223 product(inverse(c_0),v,inverse(u)). [hyper(18,a,5,a,b,120,a,c,7,a),rewrite([31(7)])].
% 1.95/2.27 249 multiply(inverse(v),c_0) = u. [hyper(17,a,7,a,b,122,a)].
% 1.95/2.27 342 inverse(inverse(A)) = A. [hyper(17,a,7,a,b,38,a),rewrite([30(2)]),flip(a)].
% 1.95/2.27 488 product(inverse(u),inverse(v),inverse(c_0)). [hyper(19,a,223,a,b,6,a,c,7,a),rewrite([30(8)])].
% 1.95/2.27 712 -product(inverse(v),identity,multiply(inverse(c_0),u)) # answer(prove_vu_equals_uv). [ur(19,a,7,a,c,37,a,d,64,a)].
% 1.95/2.27 2426 subgroup1_member(multiply(inverse(A),multiply(inverse(v),A))). [para(342(a,1),57(a,1,2,2))].
% 1.95/2.27 2633 multiply(inverse(u),inverse(v)) = inverse(c_0). [hyper(17,a,7,a,b,488,a)].
% 1.95/2.27 7569 -product(identity,identity,multiply(v,multiply(inverse(c_0),u))) # answer(prove_vu_equals_uv). [ur(19,a,4,a,c,39,a,d,712,a)].
% 1.95/2.27 7698 subgroup1_member(multiply(inverse(c_0),u)). [para(249(a,1),2426(a,1,2))].
% 1.95/2.27 7726 subgroup1_member(multiply(v,multiply(inverse(c_0),u))). [hyper(15,a,1,a,b,7698,a,c,7,a)].
% 1.95/2.27 8081 subgroup2_member(multiply(v,inverse(c_0))). [para(2633(a,1),76(a,1,2))].
% 1.95/2.27 8121 subgroup2_member(multiply(v,multiply(inverse(c_0),u))). [hyper(16,a,8081,a,b,2,a,c,41,a)].
% 1.95/2.27 8375 multiply(v,multiply(inverse(c_0),u)) = identity. [hyper(12,a,7726,a,b,8121,a),flip(a)].
% 1.95/2.27 8376 -product(identity,identity,identity) # answer(prove_vu_equals_uv). [back_rewrite(7569),rewrite([8375(8)])].
% 1.95/2.27 8377 $F # answer(prove_vu_equals_uv). [resolve(8376,a,4,a)].
% 1.95/2.27
% 1.95/2.27 % SZS output end Refutation
% 1.95/2.27 ============================== end of proof ==========================
% 1.95/2.27
% 1.95/2.27 ============================== STATISTICS ============================
% 1.95/2.27
% 1.95/2.27 Given=216. Generated=40767. Kept=8375. proofs=1.
% 1.95/2.27 Usable=199. Sos=6406. Demods=21. Limbo=1, Disabled=1786. Hints=0.
% 1.95/2.27 Megabytes=5.88.
% 1.95/2.27 User_CPU=1.11, System_CPU=0.04, Wall_clock=1.
% 1.95/2.27
% 1.95/2.27 ============================== end of statistics =====================
% 1.95/2.27
% 1.95/2.27 ============================== end of search =========================
% 1.95/2.27
% 1.95/2.27 THEOREM PROVED
% 1.95/2.27 % SZS status Unsatisfiable
% 1.95/2.27
% 1.95/2.27 Exiting with 1 proof.
% 1.95/2.27
% 1.95/2.27 Process 12423 exit (max_proofs) Mon Jun 13 05:52:37 2022
% 1.95/2.27 Prover9 interrupted
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