TSTP Solution File: GRP123-3.003 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP123-3.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 11:17:16 EDT 2022
% Result : Unsatisfiable 0.43s 1.00s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP123-3.003 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n012.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 16:42:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 2034 was started by sandbox2 on n012.cluster.edu,
% 0.43/0.99 Mon Jun 13 16:42:56 2022
% 0.43/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1879_n012.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_1879_n012.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (32 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99
% 0.43/0.99 ============================== end of process non-clausal formulas ===
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/0.99
% 0.43/0.99 ============================== PREDICATE ELIMINATION =================
% 0.43/0.99 1 -cycle(A,B) | -cycle(A,C) | equalish(B,C) # label(cycle1) # label(axiom). [assumption].
% 0.43/0.99 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.43/0.99 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.43/0.99 4 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.43/0.99 5 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.43/0.99 6 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.43/0.99 7 -equalish(e_3,e_2) # label(e_3_is_not_e_2) # label(axiom). [assumption].
% 0.43/0.99 Derived: -cycle(A,e_1) | -cycle(A,e_2). [resolve(1,c,2,a)].
% 0.43/0.99 Derived: -cycle(A,e_1) | -cycle(A,e_3). [resolve(1,c,3,a)].
% 0.43/0.99 Derived: -cycle(A,e_2) | -cycle(A,e_3). [resolve(1,c,5,a)].
% 0.43/0.99 8 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.43/0.99 Derived: -product(A,B,e_1) | -product(A,B,e_2). [resolve(8,c,2,a)].
% 0.43/0.99 Derived: -product(A,B,e_1) | -product(A,B,e_3). [resolve(8,c,3,a)].
% 0.43/0.99 Derived: -product(A,B,e_2) | -product(A,B,e_3). [resolve(8,c,5,a)].
% 0.43/0.99 9 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.43/0.99 Derived: -product(A,e_1,B) | -product(A,e_2,B). [resolve(9,c,2,a)].
% 0.43/0.99 Derived: -product(A,e_1,B) | -product(A,e_3,B). [resolve(9,c,3,a)].
% 0.43/0.99 Derived: -product(A,e_2,B) | -product(A,e_3,B). [resolve(9,c,5,a)].
% 0.43/0.99 10 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.43/0.99 Derived: -product(e_1,A,B) | -product(e_2,A,B). [resolve(10,c,2,a)].
% 0.43/0.99 Derived: -product(e_1,A,B) | -product(e_3,A,B). [resolve(10,c,3,a)].
% 0.43/0.99 Derived: -product(e_2,A,B) | -product(e_3,A,B). [resolve(10,c,5,a)].
% 0.43/0.99 11 -cycle(A,B) | -product(A,e_1,C) | -greater(B,e_0) | -next(A,D) | equalish(C,D) # label(cycle7) # label(axiom). [assumption].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_1) | -greater(B,e_0) | -next(A,e_2). [resolve(11,e,2,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_1) | -greater(B,e_0) | -next(A,e_3). [resolve(11,e,3,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_2) | -greater(B,e_0) | -next(A,e_1). [resolve(11,e,4,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_2) | -greater(B,e_0) | -next(A,e_3). [resolve(11,e,5,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_3) | -greater(B,e_0) | -next(A,e_1). [resolve(11,e,6,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_3) | -greater(B,e_0) | -next(A,e_2). [resolve(11,e,7,a)].
% 0.43/1.00 12 -cycle(A,B) | -cycle(C,D) | -next(A,C) | -greater(B,e_0) | -next(D,E) | equalish(B,E) # label(cycle4) # label(axiom). [assumption].
% 0.43/1.00 Derived: -cycle(A,e_1) | -cycle(B,C) | -next(A,B) | -greater(e_1,e_0) | -next(C,e_2). [resolve(12,f,2,a)].
% 0.43/1.00 Derived: -cycle(A,e_1) | -cycle(B,C) | -next(A,B) | -greater(e_1,e_0) | -next(C,e_3). [resolve(12,f,3,a)].
% 0.43/1.00 Derived: -cycle(A,e_2) | -cycle(B,C) | -next(A,B) | -greater(e_2,e_0) | -next(C,e_1). [resolve(12,f,4,a)].
% 0.43/1.00 Derived: -cycle(A,e_2) | -cycle(B,C) | -next(A,B) | -greater(e_2,e_0) | -next(C,e_3). [resolve(12,f,5,a)].
% 0.43/1.00 Derived: -cycle(A,e_3) | -cycle(B,C) | -next(A,B) | -greater(e_3,e_0) | -next(C,e_1). [resolve(12,f,6,a)].
% 0.43/1.00 Derived: -cycle(A,e_3) | -cycle(B,C) | -next(A,B) | -greater(e_3,e_0) | -next(C,e_2). [resolve(12,f,7,a)].
% 0.43/1.00 13 -product(A,B,C) | -product(D,E,C) | -product(F,B,A) | -product(F,E,D) | equalish(A,D) # label(qg1_1) # label(negated_conjecture). [assumption].
% 0.43/1.00 Derived: -product(e_1,A,B) | -product(e_2,C,B) | -product(D,A,e_1) | -product(D,C,e_2). [resolve(13,e,2,a)].
% 0.43/1.00 Derived: -product(e_1,A,B) | -product(e_3,C,B) | -product(D,A,e_1) | -product(D,C,e_3). [resolve(13,e,3,a)].
% 0.43/1.00 Derived: -product(e_2,A,B) | -product(e_3,C,B) | -product(D,A,e_2) | -product(D,C,e_3). [resolve(13,e,5,a)].
% 0.43/1.00 14 -product(A,B,C) | -product(D,E,C) | -product(F,B,A) | -product(F,E,D) | equalish(B,E) # label(qg1_2) # label(negated_conjecture). [assumption].
% 0.43/1.00 Derived: -product(A,e_1,B) | -product(C,e_2,B) | -product(D,e_1,A) | -product(D,e_2,C). [resolve(14,e,2,a)].
% 0.43/1.00 Derived: -product(A,e_1,B) | -product(C,e_3,B) | -product(D,e_1,A) | -product(D,e_3,C). [resolve(14,e,3,a)].
% 0.43/1.00 Derived: -product(A,e_2,B) | -product(C,e_3,B) | -product(D,e_2,A) | -product(D,e_3,C). [resolve(14,e,5,a)].
% 0.43/1.00
% 0.43/1.00 ============================== end predicate elimination =============
% 0.43/1.00
% 0.43/1.00 Auto_denials: (non-Horn, no changes).
% 0.43/1.00
% 0.43/1.00 Term ordering decisions:
% 0.43/1.00 Function symbol KB weights: e_1=1. e_2=1. e_3=1. e_0=1.
% 0.43/1.00
% 0.43/1.00 ============================== end of process initial clauses ========
% 0.43/1.00
% 0.43/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.43/1.00
% 0.43/1.00 ============================== end of clauses for search =============
% 0.43/1.00
% 0.43/1.00 ============================== SEARCH ================================
% 0.43/1.00
% 0.43/1.00 % Starting search at 0.02 seconds.
% 0.43/1.00
% 0.43/1.00 ============================== PROOF =================================
% 0.43/1.00 % SZS status Unsatisfiable
% 0.43/1.00 % SZS output start Refutation
% 0.43/1.00
% 0.43/1.00 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.43/1.00 % Length of proof is 25.
% 0.43/1.00 % Level of proof is 5.
% 0.43/1.00 % Maximum clause weight is 16.000.
% 0.43/1.00 % Given clauses 94.
% 0.43/1.00
% 0.43/1.00 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.43/1.00 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.43/1.00 9 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.43/1.00 10 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.43/1.00 14 -product(A,B,C) | -product(D,E,C) | -product(F,B,A) | -product(F,E,D) | equalish(B,E) # label(qg1_2) # label(negated_conjecture). [assumption].
% 0.43/1.00 15 group_element(e_1) # label(element_1) # label(axiom). [assumption].
% 0.43/1.00 16 group_element(e_2) # label(element_2) # label(axiom). [assumption].
% 0.43/1.00 17 group_element(e_3) # label(element_3) # label(axiom). [assumption].
% 0.43/1.00 28 product(A,A,A) # label(product_idempotence) # label(axiom). [assumption].
% 0.43/1.00 32 -group_element(A) | -group_element(B) | product(A,B,e_1) | product(A,B,e_2) | product(A,B,e_3) # label(product_total_function1) # label(axiom). [assumption].
% 0.43/1.00 39 -product(A,e_1,B) | -product(A,e_2,B). [resolve(9,c,2,a)].
% 0.43/1.00 40 -product(A,e_1,B) | -product(A,e_3,B). [resolve(9,c,3,a)].
% 0.43/1.00 42 -product(e_1,A,B) | -product(e_2,A,B). [resolve(10,c,2,a)].
% 0.43/1.00 43 -product(e_1,A,B) | -product(e_3,A,B). [resolve(10,c,3,a)].
% 0.43/1.00 67 -product(A,e_1,B) | -product(C,e_3,B) | -product(D,e_1,A) | -product(D,e_3,C). [resolve(14,e,3,a)].
% 0.43/1.00 94 -product(A,e_1,B) | -product(B,e_3,B) | -product(B,e_1,A). [factor(67,b,d)].
% 0.43/1.00 117 -group_element(A) | product(e_3,A,e_1) | product(e_3,A,e_2) | product(e_3,A,e_3). [resolve(32,a,17,a)].
% 0.43/1.00 118 -group_element(A) | product(e_2,A,e_1) | product(e_2,A,e_2) | product(e_2,A,e_3). [resolve(32,a,16,a)].
% 0.43/1.00 129 -product(e_2,e_1,e_2). [resolve(39,b,28,a)].
% 0.43/1.00 131 -product(e_3,e_1,e_3). [resolve(40,b,28,a)].
% 0.43/1.00 136 -product(e_2,e_1,e_1). [ur(42,a,28,a)].
% 0.43/1.00 138 -product(e_3,e_1,e_1). [ur(43,a,28,a)].
% 0.43/1.00 219 product(e_3,e_1,e_2). [resolve(117,a,15,a),unit_del(a,138),unit_del(c,131)].
% 0.43/1.00 229 -product(e_2,e_1,e_3). [resolve(219,a,94,c),unit_del(b,28)].
% 0.43/1.00 242 $F. [resolve(118,a,15,a),unit_del(a,136),unit_del(b,129),unit_del(c,229)].
% 0.43/1.00
% 0.43/1.00 % SZS output end Refutation
% 0.43/1.00 ============================== end of proof ==========================
% 0.43/1.00
% 0.43/1.00 ============================== STATISTICS ============================
% 0.43/1.00
% 0.43/1.00 Given=94. Generated=398. Kept=221. proofs=1.
% 0.43/1.00 Usable=88. Sos=102. Demods=0. Limbo=1, Disabled=92. Hints=0.
% 0.43/1.00 Megabytes=0.17.
% 0.43/1.00 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.43/1.00
% 0.43/1.00 ============================== end of statistics =====================
% 0.43/1.00
% 0.43/1.00 ============================== end of search =========================
% 0.43/1.00
% 0.43/1.00 THEOREM PROVED
% 0.43/1.00 % SZS status Unsatisfiable
% 0.43/1.00
% 0.43/1.00 Exiting with 1 proof.
% 0.43/1.00
% 0.43/1.00 Process 2034 exit (max_proofs) Mon Jun 13 16:42:56 2022
% 0.43/1.00 Prover9 interrupted
%------------------------------------------------------------------------------