TSTP Solution File: GRP039-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP039-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 11:16:52 EDT 2022
% Result : Unsatisfiable 1.23s 1.51s
% Output : Refutation 1.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP039-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n024.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 12:42:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.23/1.51 ============================== Prover9 ===============================
% 1.23/1.51 Prover9 (32) version 2009-11A, November 2009.
% 1.23/1.51 Process 27123 was started by sandbox on n024.cluster.edu,
% 1.23/1.51 Mon Jun 13 12:42:04 2022
% 1.23/1.51 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26970_n024.cluster.edu".
% 1.23/1.51 ============================== end of head ===========================
% 1.23/1.51
% 1.23/1.51 ============================== INPUT =================================
% 1.23/1.51
% 1.23/1.51 % Reading from file /tmp/Prover9_26970_n024.cluster.edu
% 1.23/1.51
% 1.23/1.51 set(prolog_style_variables).
% 1.23/1.51 set(auto2).
% 1.23/1.51 % set(auto2) -> set(auto).
% 1.23/1.51 % set(auto) -> set(auto_inference).
% 1.23/1.51 % set(auto) -> set(auto_setup).
% 1.23/1.51 % set(auto_setup) -> set(predicate_elim).
% 1.23/1.51 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.23/1.51 % set(auto) -> set(auto_limits).
% 1.23/1.51 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.23/1.51 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.23/1.51 % set(auto) -> set(auto_denials).
% 1.23/1.51 % set(auto) -> set(auto_process).
% 1.23/1.51 % set(auto2) -> assign(new_constants, 1).
% 1.23/1.51 % set(auto2) -> assign(fold_denial_max, 3).
% 1.23/1.51 % set(auto2) -> assign(max_weight, "200.000").
% 1.23/1.51 % set(auto2) -> assign(max_hours, 1).
% 1.23/1.51 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.23/1.51 % set(auto2) -> assign(max_seconds, 0).
% 1.23/1.51 % set(auto2) -> assign(max_minutes, 5).
% 1.23/1.51 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.23/1.51 % set(auto2) -> set(sort_initial_sos).
% 1.23/1.51 % set(auto2) -> assign(sos_limit, -1).
% 1.23/1.51 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.23/1.51 % set(auto2) -> assign(max_megs, 400).
% 1.23/1.51 % set(auto2) -> assign(stats, some).
% 1.23/1.51 % set(auto2) -> clear(echo_input).
% 1.23/1.51 % set(auto2) -> set(quiet).
% 1.23/1.51 % set(auto2) -> clear(print_initial_clauses).
% 1.23/1.51 % set(auto2) -> clear(print_given).
% 1.23/1.51 assign(lrs_ticks,-1).
% 1.23/1.51 assign(sos_limit,10000).
% 1.23/1.51 assign(order,kbo).
% 1.23/1.51 set(lex_order_vars).
% 1.23/1.51 clear(print_given).
% 1.23/1.51
% 1.23/1.51 % formulas(sos). % not echoed (16 formulas)
% 1.23/1.51
% 1.23/1.51 ============================== end of input ==========================
% 1.23/1.51
% 1.23/1.51 % From the command line: assign(max_seconds, 300).
% 1.23/1.51
% 1.23/1.51 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.23/1.51
% 1.23/1.51 % Formulas that are not ordinary clauses:
% 1.23/1.51
% 1.23/1.51 ============================== end of process non-clausal formulas ===
% 1.23/1.51
% 1.23/1.51 ============================== PROCESS INITIAL CLAUSES ===============
% 1.23/1.51
% 1.23/1.51 ============================== PREDICATE ELIMINATION =================
% 1.23/1.51
% 1.23/1.51 ============================== end predicate elimination =============
% 1.23/1.51
% 1.23/1.51 Auto_denials: (non-Horn, no changes).
% 1.23/1.51
% 1.23/1.51 Term ordering decisions:
% 1.23/1.51
% 1.23/1.51 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 1.23/1.51 Function symbol KB weights: identity=1. a=1. b=1. c=1. d=1. element_in_O2=1. multiply=1. inverse=0.
% 1.23/1.51
% 1.23/1.51 ============================== end of process initial clauses ========
% 1.23/1.51
% 1.23/1.51 ============================== CLAUSES FOR SEARCH ====================
% 1.23/1.51
% 1.23/1.51 ============================== end of clauses for search =============
% 1.23/1.51
% 1.23/1.51 ============================== SEARCH ================================
% 1.23/1.51
% 1.23/1.51 % Starting search at 0.01 seconds.
% 1.23/1.51
% 1.23/1.51 Low Water (keep): wt=16.000, iters=3443
% 1.23/1.51
% 1.23/1.51 Low Water (keep): wt=15.000, iters=3368
% 1.23/1.51
% 1.23/1.51 ============================== PROOF =================================
% 1.23/1.51 % SZS status Unsatisfiable
% 1.23/1.51 % SZS output start Refutation
% 1.23/1.51
% 1.23/1.51 % Proof 1 at 0.54 (+ 0.02) seconds.
% 1.23/1.51 % Length of proof is 48.
% 1.23/1.51 % Level of proof is 13.
% 1.23/1.51 % Maximum clause weight is 16.000.
% 1.23/1.51 % Given clauses 446.
% 1.23/1.51
% 1.23/1.51 1 subgroup_member(b) # label(b_is_in_subgroup) # label(negated_conjecture). [assumption].
% 1.23/1.51 2 product(identity,A,A) # label(left_identity) # label(axiom). [assumption].
% 1.23/1.51 3 product(A,identity,A) # label(right_identity) # label(axiom). [assumption].
% 1.23/1.51 4 product(a,c,d) # label(a_times_c_is_d) # label(negated_conjecture). [assumption].
% 1.23/1.51 5 product(inverse(A),A,identity) # label(left_inverse) # label(axiom). [assumption].
% 1.23/1.51 6 product(A,inverse(A),identity) # label(right_inverse) # label(axiom). [assumption].
% 1.23/1.51 7 product(b,inverse(a),c) # label(b_times_a_inverse_is_c) # label(negated_conjecture). [assumption].
% 1.23/1.51 8 product(A,B,multiply(A,B)) # label(total_function1) # label(axiom). [assumption].
% 1.23/1.51 9 subgroup_member(element_in_O2(A,B)) | subgroup_member(B) | subgroup_member(A) # label(an_element_in_O2) # label(axiom). [assumption].
% 1.23/1.51 10 product(A,element_in_O2(A,B),B) | subgroup_member(B) | subgroup_member(A) # label(property_of_O2) # label(axiom). [assumption].
% 1.23/1.51 11 -subgroup_member(d) # label(prove_d_is_in_subgroup) # label(negated_conjecture). [assumption].
% 1.23/1.51 12 -subgroup_member(A) | subgroup_member(inverse(A)) # label(closure_of_inverse) # label(axiom). [assumption].
% 1.23/1.51 13 -subgroup_member(A) | -subgroup_member(B) | -product(A,B,C) | subgroup_member(C) # label(closure_of_product) # label(axiom). [assumption].
% 1.23/1.51 14 -product(A,B,C) | -product(A,B,D) | C = D # label(total_function2) # label(axiom). [assumption].
% 1.23/1.51 15 -product(A,B,C) | -product(B,D,E) | -product(C,D,F) | product(A,E,F) # label(associativity1) # label(axiom). [assumption].
% 1.23/1.51 16 -product(A,B,C) | -product(B,D,E) | -product(A,E,F) | product(C,D,F) # label(associativity2) # label(axiom). [assumption].
% 1.23/1.51 29 -subgroup_member(A) | -subgroup_member(B) | subgroup_member(multiply(A,B)). [resolve(13,c,8,a)].
% 1.23/1.51 30 -subgroup_member(inverse(a)) | subgroup_member(c). [resolve(13,c,7,a),unit_del(a,1)].
% 1.23/1.51 31 -subgroup_member(A) | -subgroup_member(inverse(A)) | subgroup_member(identity). [resolve(13,c,6,a)].
% 1.23/1.51 32 -subgroup_member(a) | -subgroup_member(c). [resolve(13,c,4,a),unit_del(c,11)].
% 1.23/1.51 34 -subgroup_member(A) | subgroup_member(multiply(A,A)). [factor(29,a,b)].
% 1.23/1.51 44 -product(A,identity,B) | B = A. [resolve(14,b,3,a)].
% 1.23/1.51 50 -product(inverse(a),A,B) | -product(c,A,C) | product(b,B,C). [resolve(15,a,7,a)].
% 1.23/1.51 61 -product(A,a,B) | -product(B,c,C) | product(A,d,C). [resolve(15,b,4,a)].
% 1.23/1.51 71 -product(A,B,identity) | -product(B,C,D) | product(A,D,C). [resolve(15,c,2,a)].
% 1.23/1.51 86 -product(A,B,C) | -product(inverse(A),C,D) | product(identity,B,D). [resolve(16,a,5,a)].
% 1.23/1.51 235 subgroup_member(multiply(b,b)). [resolve(34,a,1,a)].
% 1.23/1.51 237 subgroup_member(inverse(multiply(b,b))). [resolve(235,a,12,a)].
% 1.23/1.51 248 subgroup_member(inverse(inverse(multiply(b,b)))). [resolve(237,a,12,a)].
% 1.23/1.51 429 subgroup_member(identity). [resolve(31,b,248,a),unit_del(a,237)].
% 1.23/1.51 1918 -product(c,a,A) | product(b,identity,A). [resolve(50,a,5,a)].
% 1.23/1.51 5190 -product(A,a,identity) | product(A,d,c). [resolve(61,b,2,a)].
% 1.23/1.51 5220 product(b,identity,multiply(c,a)). [resolve(1918,a,8,a)].
% 1.23/1.51 5230 multiply(c,a) = b. [resolve(5220,a,44,a)].
% 1.23/1.51 5259 product(c,a,b). [para(5230(a,1),8(a,3))].
% 1.23/1.51 5633 product(inverse(a),d,c). [resolve(5190,a,5,a)].
% 1.23/1.51 5992 -product(A,c,identity) | product(A,b,a). [resolve(71,b,5259,a)].
% 1.23/1.51 6121 product(inverse(c),b,a). [resolve(5992,a,5,a)].
% 1.23/1.51 6156 -subgroup_member(inverse(c)) | subgroup_member(a). [resolve(6121,a,13,c),unit_del(b,1)].
% 1.23/1.51 6934 -product(a,A,d) | product(identity,A,c). [resolve(86,b,5633,a)].
% 1.23/1.51 6970 product(identity,element_in_O2(a,d),c) | subgroup_member(a). [resolve(6934,a,10,a),unit_del(b,11)].
% 1.23/1.51 7005 subgroup_member(a) | -subgroup_member(element_in_O2(a,d)) | subgroup_member(c). [resolve(6970,a,13,c),unit_del(b,429)].
% 1.23/1.51 7118 subgroup_member(a) | subgroup_member(c). [resolve(7005,b,9,a),merge(d),unit_del(c,11)].
% 1.23/1.51 7134 subgroup_member(a) | subgroup_member(inverse(c)). [resolve(7118,b,12,a)].
% 1.23/1.51 7171 subgroup_member(a). [resolve(7134,b,6156,a),merge(b)].
% 1.23/1.51 7172 -subgroup_member(c). [back_unit_del(32),unit_del(a,7171)].
% 1.23/1.51 7183 -subgroup_member(inverse(a)). [back_unit_del(30),unit_del(b,7172)].
% 1.23/1.51 7204 $F. [resolve(7171,a,12,a),unit_del(a,7183)].
% 1.23/1.51
% 1.23/1.51 % SZS output end Refutation
% 1.23/1.51 ============================== end of proof ==========================
% 1.23/1.51
% 1.23/1.51 ============================== STATISTICS ============================
% 1.23/1.51
% 1.23/1.51 Given=446. Generated=25251. Kept=7203. proofs=1.
% 1.23/1.51 Usable=403. Sos=5886. Demods=17. Limbo=15, Disabled=915. Hints=0.
% 1.23/1.51 Megabytes=4.53.
% 1.23/1.51 User_CPU=0.54, System_CPU=0.02, Wall_clock=0.
% 1.23/1.51
% 1.23/1.51 ============================== end of statistics =====================
% 1.23/1.51
% 1.23/1.51 ============================== end of search =========================
% 1.23/1.51
% 1.23/1.51 THEOREM PROVED
% 1.23/1.51 % SZS status Unsatisfiable
% 1.23/1.51
% 1.23/1.51 Exiting with 1 proof.
% 1.23/1.51
% 1.23/1.51 Process 27123 exit (max_proofs) Mon Jun 13 12:42:04 2022
% 1.23/1.51 Prover9 interrupted
%------------------------------------------------------------------------------