TSTP Solution File: GRP039-6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP039-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 11:16:53 EDT 2022
% Result : Unsatisfiable 2.99s 3.25s
% Output : Refutation 2.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP039-6 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 14 07:59:54 EDT 2022
% 0.15/0.36 % CPUTime :
% 2.99/3.25 ============================== Prover9 ===============================
% 2.99/3.25 Prover9 (32) version 2009-11A, November 2009.
% 2.99/3.25 Process 28158 was started by sandbox on n025.cluster.edu,
% 2.99/3.25 Tue Jun 14 07:59:55 2022
% 2.99/3.25 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28005_n025.cluster.edu".
% 2.99/3.25 ============================== end of head ===========================
% 2.99/3.25
% 2.99/3.25 ============================== INPUT =================================
% 2.99/3.25
% 2.99/3.25 % Reading from file /tmp/Prover9_28005_n025.cluster.edu
% 2.99/3.25
% 2.99/3.25 set(prolog_style_variables).
% 2.99/3.25 set(auto2).
% 2.99/3.25 % set(auto2) -> set(auto).
% 2.99/3.25 % set(auto) -> set(auto_inference).
% 2.99/3.25 % set(auto) -> set(auto_setup).
% 2.99/3.25 % set(auto_setup) -> set(predicate_elim).
% 2.99/3.25 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.99/3.25 % set(auto) -> set(auto_limits).
% 2.99/3.25 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.99/3.25 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.99/3.25 % set(auto) -> set(auto_denials).
% 2.99/3.25 % set(auto) -> set(auto_process).
% 2.99/3.25 % set(auto2) -> assign(new_constants, 1).
% 2.99/3.25 % set(auto2) -> assign(fold_denial_max, 3).
% 2.99/3.25 % set(auto2) -> assign(max_weight, "200.000").
% 2.99/3.25 % set(auto2) -> assign(max_hours, 1).
% 2.99/3.25 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.99/3.25 % set(auto2) -> assign(max_seconds, 0).
% 2.99/3.25 % set(auto2) -> assign(max_minutes, 5).
% 2.99/3.25 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.99/3.25 % set(auto2) -> set(sort_initial_sos).
% 2.99/3.25 % set(auto2) -> assign(sos_limit, -1).
% 2.99/3.25 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.99/3.25 % set(auto2) -> assign(max_megs, 400).
% 2.99/3.25 % set(auto2) -> assign(stats, some).
% 2.99/3.25 % set(auto2) -> clear(echo_input).
% 2.99/3.25 % set(auto2) -> set(quiet).
% 2.99/3.25 % set(auto2) -> clear(print_initial_clauses).
% 2.99/3.25 % set(auto2) -> clear(print_given).
% 2.99/3.25 assign(lrs_ticks,-1).
% 2.99/3.25 assign(sos_limit,10000).
% 2.99/3.25 assign(order,kbo).
% 2.99/3.25 set(lex_order_vars).
% 2.99/3.25 clear(print_given).
% 2.99/3.25
% 2.99/3.25 % formulas(sos). % not echoed (22 formulas)
% 2.99/3.25
% 2.99/3.25 ============================== end of input ==========================
% 2.99/3.25
% 2.99/3.25 % From the command line: assign(max_seconds, 300).
% 2.99/3.25
% 2.99/3.25 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.99/3.25
% 2.99/3.25 % Formulas that are not ordinary clauses:
% 2.99/3.25
% 2.99/3.25 ============================== end of process non-clausal formulas ===
% 2.99/3.25
% 2.99/3.25 ============================== PROCESS INITIAL CLAUSES ===============
% 2.99/3.25
% 2.99/3.25 ============================== PREDICATE ELIMINATION =================
% 2.99/3.25
% 2.99/3.25 ============================== end predicate elimination =============
% 2.99/3.25
% 2.99/3.25 Auto_denials: (non-Horn, no changes).
% 2.99/3.25
% 2.99/3.25 Term ordering decisions:
% 2.99/3.25
% 2.99/3.25 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 2.99/3.25 Function symbol KB weights: identity=1. a=1. b=1. c=1. d=1. element_in_O2=1. inverse=0.
% 2.99/3.25
% 2.99/3.25 ============================== end of process initial clauses ========
% 2.99/3.25
% 2.99/3.25 ============================== CLAUSES FOR SEARCH ====================
% 2.99/3.25
% 2.99/3.25 ============================== end of clauses for search =============
% 2.99/3.25
% 2.99/3.25 ============================== SEARCH ================================
% 2.99/3.25
% 2.99/3.25 % Starting search at 0.01 seconds.
% 2.99/3.25
% 2.99/3.25 Low Water (keep): wt=16.000, iters=3426
% 2.99/3.25
% 2.99/3.25 Low Water (keep): wt=15.000, iters=3363
% 2.99/3.25
% 2.99/3.25 Low Water (keep): wt=14.000, iters=3357
% 2.99/3.25
% 2.99/3.25 Low Water (keep): wt=13.000, iters=3352
% 2.99/3.25
% 2.99/3.25 Low Water (keep): wt=12.000, iters=3360
% 2.99/3.25
% 2.99/3.25 Low Water (keep): wt=11.000, iters=3429
% 2.99/3.25
% 2.99/3.25 ============================== PROOF =================================
% 2.99/3.25 % SZS status Unsatisfiable
% 2.99/3.25 % SZS output start Refutation
% 2.99/3.25
% 2.99/3.25 % Proof 1 at 2.09 (+ 0.12) seconds.
% 2.99/3.25 % Length of proof is 44.
% 2.99/3.25 % Level of proof is 10.
% 2.99/3.25 % Maximum clause weight is 16.000.
% 2.99/3.25 % Given clauses 626.
% 2.99/3.25
% 2.99/3.25 2 subgroup_member(b) # label(b_is_in_subgroup) # label(negated_conjecture). [assumption].
% 2.99/3.25 3 product(identity,A,A) # label(left_identity) # label(axiom). [assumption].
% 2.99/3.25 4 product(A,identity,A) # label(right_identity) # label(axiom). [assumption].
% 2.99/3.25 5 product(a,c,d) # label(a_times_c_is_d) # label(negated_conjecture). [assumption].
% 2.99/3.25 6 product(inverse(A),A,identity) # label(left_inverse) # label(axiom). [assumption].
% 2.99/3.25 7 product(A,inverse(A),identity) # label(right_inverse) # label(axiom). [assumption].
% 2.99/3.25 8 product(b,inverse(a),c) # label(b_times_a_inverse_is_c) # label(negated_conjecture). [assumption].
% 2.99/3.25 9 subgroup_member(element_in_O2(A,B)) | subgroup_member(B) | subgroup_member(A) # label(an_element_in_O2) # label(axiom). [assumption].
% 2.99/3.25 10 product(A,element_in_O2(A,B),B) | subgroup_member(B) | subgroup_member(A) # label(property_of_O2) # label(axiom). [assumption].
% 2.99/3.25 11 -subgroup_member(d) # label(prove_d_is_in_subgroup) # label(negated_conjecture). [assumption].
% 2.99/3.25 12 -subgroup_member(A) | subgroup_member(inverse(A)) # label(closure_of_inverse) # label(axiom). [assumption].
% 2.99/3.25 13 -equalish(A,B) | -subgroup_member(A) | subgroup_member(B) # label(subgroup_member_substitution) # label(axiom). [assumption].
% 2.99/3.25 16 -subgroup_member(A) | -subgroup_member(B) | -product(A,B,C) | subgroup_member(C) # label(closure_of_product) # label(axiom). [assumption].
% 2.99/3.25 17 -equalish(A,B) | -product(C,D,A) | product(C,D,B) # label(product_substitution3) # label(axiom). [assumption].
% 2.99/3.25 19 -product(A,B,C) | -product(A,D,C) | equalish(D,B) # label(product_right_cancellation) # label(axiom). [assumption].
% 2.99/3.25 21 -product(A,B,C) | -product(B,D,E) | -product(C,D,F) | product(A,E,F) # label(associativity1) # label(axiom). [assumption].
% 2.99/3.25 22 -product(A,B,C) | -product(B,D,E) | -product(A,E,F) | product(C,D,F) # label(associativity2) # label(axiom). [assumption].
% 2.99/3.25 48 -equalish(c,A) | product(b,inverse(a),A). [resolve(17,b,8,a)].
% 2.99/3.25 52 -equalish(A,B) | product(A,identity,B). [resolve(17,b,4,a)].
% 2.99/3.25 73 -product(A,B,identity) | equalish(B,inverse(A)). [resolve(19,a,7,a)].
% 2.99/3.25 75 -product(a,A,d) | equalish(A,c). [resolve(19,a,5,a)].
% 2.99/3.25 103 -product(c,A,B) | -product(d,A,C) | product(a,B,C). [resolve(21,a,5,a)].
% 2.99/3.25 119 -product(A,B,identity) | -product(B,C,D) | product(A,D,C). [resolve(21,c,3,a)].
% 2.99/3.25 129 -product(inverse(a),A,B) | -product(b,B,C) | product(c,A,C). [resolve(22,a,8,a)].
% 2.99/3.25 548 equalish(element_in_O2(a,d),c) | subgroup_member(a). [resolve(75,a,10,a),unit_del(b,11)].
% 2.99/3.25 814 subgroup_member(a) | -subgroup_member(element_in_O2(a,d)) | subgroup_member(c). [resolve(548,a,13,a)].
% 2.99/3.25 1162 equalish(A,inverse(inverse(A))). [resolve(73,a,6,a)].
% 2.99/3.25 1165 product(A,identity,inverse(inverse(A))). [resolve(1162,a,52,a)].
% 2.99/3.25 1167 product(b,inverse(a),inverse(inverse(c))). [resolve(1162,a,48,a)].
% 2.99/3.25 1924 -subgroup_member(inverse(a)) | subgroup_member(inverse(inverse(c))). [resolve(1167,a,16,c),unit_del(a,2)].
% 2.99/3.25 3066 -product(c,identity,A) | product(a,A,d). [resolve(103,b,4,a)].
% 2.99/3.25 3611 subgroup_member(a) | subgroup_member(c). [resolve(814,b,9,a),merge(d),unit_del(c,11)].
% 2.99/3.25 3613 subgroup_member(a) | subgroup_member(inverse(c)). [resolve(3611,b,12,a)].
% 2.99/3.25 4801 product(a,inverse(inverse(c)),d). [resolve(3066,a,1165,a)].
% 2.99/3.25 4827 -subgroup_member(a) | -subgroup_member(inverse(inverse(c))). [resolve(4801,a,16,c),unit_del(c,11)].
% 2.99/3.25 7203 -product(b,identity,A) | product(c,a,A). [resolve(129,a,6,a)].
% 2.99/3.25 8459 product(c,a,b). [resolve(7203,a,4,a)].
% 2.99/3.25 8468 -product(A,c,identity) | product(A,b,a). [resolve(8459,a,119,b)].
% 2.99/3.25 9457 product(inverse(c),b,a). [resolve(8468,a,6,a)].
% 2.99/3.25 9500 -subgroup_member(inverse(c)) | subgroup_member(a). [resolve(9457,a,16,c),unit_del(b,2)].
% 2.99/3.25 9502 subgroup_member(a). [resolve(9500,a,3613,b),merge(b)].
% 2.99/3.25 9503 -subgroup_member(inverse(inverse(c))). [back_unit_del(4827),unit_del(a,9502)].
% 2.99/3.25 9512 -subgroup_member(inverse(a)). [back_unit_del(1924),unit_del(b,9503)].
% 2.99/3.25 9564 $F. [resolve(9502,a,12,a),unit_del(a,9512)].
% 2.99/3.25
% 2.99/3.25 % SZS output end Refutation
% 2.99/3.25 ============================== end of proof ==========================
% 2.99/3.25
% 2.99/3.25 ============================== STATISTICS ============================
% 2.99/3.25
% 2.99/3.25 Given=626. Generated=218346. Kept=9563. proofs=1.
% 2.99/3.25 Usable=578. Sos=7952. Demods=0. Limbo=1, Disabled=1054. Hints=0.
% 2.99/3.25 Megabytes=5.23.
% 2.99/3.25 User_CPU=2.09, System_CPU=0.12, Wall_clock=2.
% 2.99/3.25
% 2.99/3.25 ============================== end of statistics =====================
% 2.99/3.25
% 2.99/3.25 ============================== end of search =========================
% 2.99/3.25
% 2.99/3.25 THEOREM PROVED
% 2.99/3.25 % SZS status Unsatisfiable
% 2.99/3.25
% 2.99/3.25 Exiting with 1 proof.
% 2.99/3.25
% 2.99/3.25 Process 28158 exit (max_proofs) Tue Jun 14 07:59:57 2022
% 2.99/3.25 Prover9 interrupted
%------------------------------------------------------------------------------