TSTP Solution File: GRP039-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP039-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 1.22s 1.47s
% Output : Refutation 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP039-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n013.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 : Mon Jun 13 18:52:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.22/1.47 ============================== Prover9 ===============================
% 1.22/1.47 Prover9 (32) version 2009-11A, November 2009.
% 1.22/1.47 Process 19574 was started by sandbox on n013.cluster.edu,
% 1.22/1.47 Mon Jun 13 18:52:29 2022
% 1.22/1.47 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19421_n013.cluster.edu".
% 1.22/1.47 ============================== end of head ===========================
% 1.22/1.47
% 1.22/1.47 ============================== INPUT =================================
% 1.22/1.47
% 1.22/1.47 % Reading from file /tmp/Prover9_19421_n013.cluster.edu
% 1.22/1.47
% 1.22/1.47 set(prolog_style_variables).
% 1.22/1.47 set(auto2).
% 1.22/1.47 % set(auto2) -> set(auto).
% 1.22/1.47 % set(auto) -> set(auto_inference).
% 1.22/1.47 % set(auto) -> set(auto_setup).
% 1.22/1.47 % set(auto_setup) -> set(predicate_elim).
% 1.22/1.47 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.22/1.47 % set(auto) -> set(auto_limits).
% 1.22/1.47 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.22/1.47 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.22/1.47 % set(auto) -> set(auto_denials).
% 1.22/1.47 % set(auto) -> set(auto_process).
% 1.22/1.47 % set(auto2) -> assign(new_constants, 1).
% 1.22/1.47 % set(auto2) -> assign(fold_denial_max, 3).
% 1.22/1.47 % set(auto2) -> assign(max_weight, "200.000").
% 1.22/1.47 % set(auto2) -> assign(max_hours, 1).
% 1.22/1.47 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.22/1.47 % set(auto2) -> assign(max_seconds, 0).
% 1.22/1.47 % set(auto2) -> assign(max_minutes, 5).
% 1.22/1.47 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.22/1.47 % set(auto2) -> set(sort_initial_sos).
% 1.22/1.47 % set(auto2) -> assign(sos_limit, -1).
% 1.22/1.47 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.22/1.47 % set(auto2) -> assign(max_megs, 400).
% 1.22/1.47 % set(auto2) -> assign(stats, some).
% 1.22/1.47 % set(auto2) -> clear(echo_input).
% 1.22/1.47 % set(auto2) -> set(quiet).
% 1.22/1.47 % set(auto2) -> clear(print_initial_clauses).
% 1.22/1.47 % set(auto2) -> clear(print_given).
% 1.22/1.47 assign(lrs_ticks,-1).
% 1.22/1.47 assign(sos_limit,10000).
% 1.22/1.47 assign(order,kbo).
% 1.22/1.47 set(lex_order_vars).
% 1.22/1.47 clear(print_given).
% 1.22/1.47
% 1.22/1.47 % formulas(sos). % not echoed (20 formulas)
% 1.22/1.47
% 1.22/1.47 ============================== end of input ==========================
% 1.22/1.47
% 1.22/1.47 % From the command line: assign(max_seconds, 300).
% 1.22/1.47
% 1.22/1.47 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.22/1.47
% 1.22/1.47 % Formulas that are not ordinary clauses:
% 1.22/1.47
% 1.22/1.47 ============================== end of process non-clausal formulas ===
% 1.22/1.47
% 1.22/1.47 ============================== PROCESS INITIAL CLAUSES ===============
% 1.22/1.47
% 1.22/1.47 ============================== PREDICATE ELIMINATION =================
% 1.22/1.47
% 1.22/1.47 ============================== end predicate elimination =============
% 1.22/1.47
% 1.22/1.47 Auto_denials: (non-Horn, no changes).
% 1.22/1.47
% 1.22/1.47 Term ordering decisions:
% 1.22/1.47
% 1.22/1.47 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 1.22/1.47 Function symbol KB weights: identity=1. a=1. b=1. c=1. d=1. element_in_O2=1. multiply=1. inverse=0.
% 1.22/1.47
% 1.22/1.47 ============================== end of process initial clauses ========
% 1.22/1.47
% 1.22/1.47 ============================== CLAUSES FOR SEARCH ====================
% 1.22/1.47
% 1.22/1.47 ============================== end of clauses for search =============
% 1.22/1.47
% 1.22/1.47 ============================== SEARCH ================================
% 1.22/1.47
% 1.22/1.47 % Starting search at 0.01 seconds.
% 1.22/1.47
% 1.22/1.47 ============================== PROOF =================================
% 1.22/1.47 % SZS status Unsatisfiable
% 1.22/1.47 % SZS output start Refutation
% 1.22/1.47
% 1.22/1.47 % Proof 1 at 0.41 (+ 0.02) seconds.
% 1.22/1.47 % Length of proof is 51.
% 1.22/1.47 % Level of proof is 12.
% 1.22/1.47 % Maximum clause weight is 16.000.
% 1.22/1.47 % Given clauses 443.
% 1.22/1.47
% 1.22/1.47 2 subgroup_member(b) # label(b_is_in_subgroup) # label(negated_conjecture). [assumption].
% 1.22/1.47 3 product(identity,A,A) # label(left_identity) # label(axiom). [assumption].
% 1.22/1.47 4 product(A,identity,A) # label(right_identity) # label(axiom). [assumption].
% 1.22/1.47 5 product(a,c,d) # label(a_times_c_is_d) # label(negated_conjecture). [assumption].
% 1.22/1.47 6 product(inverse(A),A,identity) # label(left_inverse) # label(axiom). [assumption].
% 1.22/1.47 7 product(A,inverse(A),identity) # label(right_inverse) # label(axiom). [assumption].
% 1.22/1.47 8 inverse(inverse(A)) = A # label(inverse_is_self_cancelling) # label(axiom). [assumption].
% 1.22/1.47 9 product(b,inverse(a),c) # label(b_times_a_inverse_is_c) # label(negated_conjecture). [assumption].
% 1.22/1.47 10 product(A,B,multiply(A,B)) # label(total_function1) # label(axiom). [assumption].
% 1.22/1.47 11 subgroup_member(element_in_O2(A,B)) | subgroup_member(B) | subgroup_member(A) # label(an_element_in_O2) # label(axiom). [assumption].
% 1.22/1.47 12 product(A,element_in_O2(A,B),B) | subgroup_member(B) | subgroup_member(A) # label(property_of_O2) # label(axiom). [assumption].
% 1.22/1.47 13 -subgroup_member(d) # label(prove_d_is_in_subgroup) # label(negated_conjecture). [assumption].
% 1.22/1.47 14 -subgroup_member(A) | subgroup_member(inverse(A)) # label(subgroup_member_inverse_are_in_subgroup) # label(axiom). [assumption].
% 1.22/1.47 15 -product(A,B,C) | -product(A,B,D) | C = D # label(total_function2) # label(axiom). [assumption].
% 1.22/1.47 16 -subgroup_member(A) | -subgroup_member(B) | -product(A,inverse(B),C) | subgroup_member(C) # label(closure_of_product_and_inverse) # label(axiom). [assumption].
% 1.22/1.47 17 -product(A,B,C) | -product(A,D,C) | D = B # label(product_right_cancellation) # label(axiom). [assumption].
% 1.22/1.47 19 -product(A,B,C) | -product(B,D,E) | -product(C,D,F) | product(A,E,F) # label(associativity1) # label(axiom). [assumption].
% 1.22/1.47 30 subgroup_member(inverse(element_in_O2(A,B))) | subgroup_member(B) | subgroup_member(A). [resolve(14,a,11,a)].
% 1.22/1.47 31 subgroup_member(inverse(b)). [resolve(14,a,2,a)].
% 1.22/1.47 35 -product(A,B,C) | multiply(A,B) = C. [resolve(15,a,10,a)].
% 1.22/1.47 39 -product(a,c,A) | d = A. [resolve(15,a,5,a)].
% 1.22/1.47 43 -product(A,identity,B) | B = A. [resolve(15,b,4,a)].
% 1.22/1.47 47 -subgroup_member(A) | -subgroup_member(B) | subgroup_member(multiply(A,inverse(B))). [resolve(16,c,10,a)].
% 1.22/1.47 48 -subgroup_member(a) | subgroup_member(c). [resolve(16,c,9,a),unit_del(a,2)].
% 1.22/1.47 53 -subgroup_member(A) | -subgroup_member(inverse(B)) | -product(A,B,C) | subgroup_member(C). [para(8(a,1),16(c,2))].
% 1.22/1.47 61 -product(a,A,d) | c = A. [resolve(17,a,5,a),flip(b)].
% 1.22/1.47 80 -product(inverse(a),A,B) | -product(c,A,C) | product(b,B,C). [resolve(19,a,9,a)].
% 1.22/1.47 101 -product(A,B,identity) | -product(B,C,D) | product(A,D,C). [resolve(19,c,3,a)].
% 1.22/1.47 280 multiply(a,c) = d. [resolve(39,a,10,a),flip(a)].
% 1.22/1.47 359 element_in_O2(a,d) = c | subgroup_member(a). [resolve(61,a,12,a),flip(a),unit_del(b,13)].
% 1.22/1.47 388 element_in_O2(a,d) = c | subgroup_member(c). [resolve(359,b,48,a)].
% 1.22/1.47 415 element_in_O2(a,d) = c | subgroup_member(inverse(c)). [resolve(388,b,14,a)].
% 1.22/1.47 459 -subgroup_member(A) | subgroup_member(multiply(A,b)). [resolve(47,b,31,a),rewrite([8(4)])].
% 1.22/1.47 518 -subgroup_member(a) | -subgroup_member(inverse(c)). [resolve(53,c,5,a),unit_del(c,13)].
% 1.22/1.47 1166 -subgroup_member(a) | element_in_O2(a,d) = c. [resolve(518,b,415,b)].
% 1.22/1.47 1170 element_in_O2(a,d) = c. [resolve(1166,a,359,b),merge(b)].
% 1.22/1.47 1172 subgroup_member(inverse(c)) | subgroup_member(a). [para(1170(a,1),30(a,1,1)),unit_del(b,13)].
% 1.22/1.47 1193 subgroup_member(a) | subgroup_member(multiply(inverse(c),b)). [resolve(1172,a,459,a)].
% 1.22/1.47 1196 subgroup_member(a) | -subgroup_member(A) | subgroup_member(multiply(A,c)). [resolve(1172,a,47,b),rewrite([8(6)])].
% 1.22/1.47 2398 -product(c,a,A) | product(b,identity,A). [resolve(80,a,7,a),rewrite([8(4)])].
% 1.22/1.47 2711 subgroup_member(a) | subgroup_member(multiply(multiply(inverse(c),b),c)). [resolve(1196,b,1193,b),merge(c)].
% 1.22/1.47 2981 product(b,identity,multiply(c,a)). [resolve(2398,a,10,a)].
% 1.22/1.47 2986 multiply(c,a) = b. [resolve(2981,a,43,a)].
% 1.22/1.47 3013 product(c,a,b). [para(2986(a,1),10(a,3))].
% 1.22/1.47 4569 -product(A,c,identity) | product(A,b,a). [resolve(101,b,3013,a)].
% 1.22/1.47 4599 product(inverse(c),b,a). [resolve(4569,a,6,a)].
% 1.22/1.47 4622 multiply(inverse(c),b) = a. [resolve(4599,a,35,a)].
% 1.22/1.47 4697 subgroup_member(a). [back_rewrite(2711),rewrite([4622(6),280(5)]),unit_del(b,13)].
% 1.22/1.47 4701 -subgroup_member(inverse(c)). [back_unit_del(518),unit_del(a,4697)].
% 1.22/1.47 4702 subgroup_member(c). [back_unit_del(48),unit_del(a,4697)].
% 1.22/1.47 4851 $F. [resolve(4702,a,14,a),unit_del(a,4701)].
% 1.22/1.47
% 1.22/1.47 % SZS output end Refutation
% 1.22/1.47 ============================== end of proof ==========================
% 1.22/1.47
% 1.22/1.47 ============================== STATISTICS ============================
% 1.22/1.47
% 1.22/1.47 Given=443. Generated=19579. Kept=4850. proofs=1.
% 1.22/1.47 Usable=378. Sos=3730. Demods=19. Limbo=10, Disabled=752. Hints=0.
% 1.22/1.47 Megabytes=3.11.
% 1.22/1.47 User_CPU=0.41, System_CPU=0.02, Wall_clock=1.
% 1.22/1.47
% 1.22/1.47 ============================== end of statistics =====================
% 1.22/1.47
% 1.22/1.47 ============================== end of search =========================
% 1.22/1.47
% 1.22/1.47 THEOREM PROVED
% 1.22/1.47 % SZS status Unsatisfiable
% 1.22/1.47
% 1.22/1.47 Exiting with 1 proof.
% 1.22/1.47
% 1.22/1.47 Process 19574 exit (max_proofs) Mon Jun 13 18:52:30 2022
% 1.22/1.47 Prover9 interrupted
%------------------------------------------------------------------------------