TSTP Solution File: GRP123-7.003 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP123-7.003 : TPTP v8.1.0. Released v1.2.0.
% 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 11:17:17 EDT 2022
% Result : Unsatisfiable 0.73s 1.02s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP123-7.003 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 13:25:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/1.01 ============================== Prover9 ===============================
% 0.73/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.01 Process 19519 was started by sandbox on n026.cluster.edu,
% 0.73/1.01 Mon Jun 13 13:25:21 2022
% 0.73/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19352_n026.cluster.edu".
% 0.73/1.01 ============================== end of head ===========================
% 0.73/1.01
% 0.73/1.01 ============================== INPUT =================================
% 0.73/1.01
% 0.73/1.01 % Reading from file /tmp/Prover9_19352_n026.cluster.edu
% 0.73/1.01
% 0.73/1.01 set(prolog_style_variables).
% 0.73/1.01 set(auto2).
% 0.73/1.01 % set(auto2) -> set(auto).
% 0.73/1.01 % set(auto) -> set(auto_inference).
% 0.73/1.01 % set(auto) -> set(auto_setup).
% 0.73/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.01 % set(auto) -> set(auto_limits).
% 0.73/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.01 % set(auto) -> set(auto_denials).
% 0.73/1.01 % set(auto) -> set(auto_process).
% 0.73/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.01 % set(auto2) -> assign(stats, some).
% 0.73/1.01 % set(auto2) -> clear(echo_input).
% 0.73/1.01 % set(auto2) -> set(quiet).
% 0.73/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.01 % set(auto2) -> clear(print_given).
% 0.73/1.01 assign(lrs_ticks,-1).
% 0.73/1.01 assign(sos_limit,10000).
% 0.73/1.01 assign(order,kbo).
% 0.73/1.01 set(lex_order_vars).
% 0.73/1.01 clear(print_given).
% 0.73/1.01
% 0.73/1.01 % formulas(sos). % not echoed (26 formulas)
% 0.73/1.01
% 0.73/1.01 ============================== end of input ==========================
% 0.73/1.01
% 0.73/1.01 % From the command line: assign(max_seconds, 300).
% 0.73/1.01
% 0.73/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.01
% 0.73/1.01 % Formulas that are not ordinary clauses:
% 0.73/1.01
% 0.73/1.01 ============================== end of process non-clausal formulas ===
% 0.73/1.01
% 0.73/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.01
% 0.73/1.01 ============================== PREDICATE ELIMINATION =================
% 0.73/1.01 1 -product(A,e_1,B) | -next(A,C) | -greater(B,C) # label(no_redundancy) # label(axiom). [assumption].
% 0.73/1.01 2 next(e_1,e_2) # label(e_1_then_e_2) # label(axiom). [assumption].
% 0.73/1.01 3 next(e_2,e_3) # label(e_2_then_e_3) # label(axiom). [assumption].
% 0.73/1.01 Derived: -product(e_1,e_1,A) | -greater(A,e_2). [resolve(1,b,2,a)].
% 0.73/1.01 Derived: -product(e_2,e_1,A) | -greater(A,e_3). [resolve(1,b,3,a)].
% 0.73/1.01 4 -product(e_1,e_1,A) | -greater(A,e_2). [resolve(1,b,2,a)].
% 0.73/1.01 5 greater(e_2,e_1) # label(e_2_greater_e_1) # label(axiom). [assumption].
% 0.73/1.01 6 greater(e_3,e_1) # label(e_3_greater_e_1) # label(axiom). [assumption].
% 0.73/1.01 7 greater(e_3,e_2) # label(e_3_greater_e_2) # label(axiom). [assumption].
% 0.73/1.01 Derived: -product(e_1,e_1,e_3). [resolve(4,b,7,a)].
% 0.73/1.01 8 -product(e_2,e_1,A) | -greater(A,e_3). [resolve(1,b,3,a)].
% 0.73/1.01 9 -product1(A,B,C) | -product1(A,B,D) | equalish(C,D) # label(product1_total_function2) # label(axiom). [assumption].
% 0.73/1.01 10 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.73/1.01 11 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.73/1.01 12 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.73/1.01 13 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.73/1.01 14 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.73/1.01 15 -equalish(e_3,e_2) # label(e_3_is_not_e_2) # label(axiom). [assumption].
% 0.73/1.01 Derived: -product1(A,B,e_1) | -product1(A,B,e_2). [resolve(9,c,10,a)].
% 0.73/1.01 Derived: -product1(A,B,e_1) | -product1(A,B,e_3). [resolve(9,c,11,a)].
% 0.73/1.01 Derived: -product1(A,B,e_2) | -product1(A,B,e_3). [resolve(9,c,13,a)].
% 0.73/1.01 16 -product1(A,B,C) | -product1(A,D,C) | equalish(B,D) # label(product1_right_cancellation) # label(axiom). [assumption].
% 0.73/1.01 Derived: -product1(A,e_1,B) | -product1(A,e_2,B). [resolve(16,c,10,a)].
% 0.73/1.02 Derived: -product1(A,e_1,B) | -product1(A,e_3,B). [resolve(16,c,11,a)].
% 0.73/1.02 Derived: -product1(A,e_2,B) | -product1(A,e_3,B). [resolve(16,c,13,a)].
% 0.73/1.02 17 -product1(A,B,C) | -product1(D,B,C) | equalish(A,D) # label(product1_left_cancellation) # label(axiom). [assumption].
% 0.73/1.02 Derived: -product1(e_1,A,B) | -product1(e_2,A,B). [resolve(17,c,10,a)].
% 0.73/1.02 Derived: -product1(e_1,A,B) | -product1(e_3,A,B). [resolve(17,c,11,a)].
% 0.73/1.02 Derived: -product1(e_2,A,B) | -product1(e_3,A,B). [resolve(17,c,13,a)].
% 0.73/1.02 18 -product2(A,B,C) | -product2(A,B,D) | equalish(C,D) # label(product2_total_function2) # label(axiom). [assumption].
% 0.73/1.02 Derived: -product2(A,B,e_1) | -product2(A,B,e_2). [resolve(18,c,10,a)].
% 0.73/1.02 Derived: -product2(A,B,e_1) | -product2(A,B,e_3). [resolve(18,c,11,a)].
% 0.73/1.02 Derived: -product2(A,B,e_2) | -product2(A,B,e_3). [resolve(18,c,13,a)].
% 0.73/1.02 19 -product2(A,B,C) | -product2(A,D,C) | equalish(B,D) # label(product2_right_cancellation) # label(axiom). [assumption].
% 0.73/1.02 Derived: -product2(A,e_1,B) | -product2(A,e_2,B). [resolve(19,c,10,a)].
% 0.73/1.02 Derived: -product2(A,e_1,B) | -product2(A,e_3,B). [resolve(19,c,11,a)].
% 0.73/1.02 Derived: -product2(A,e_2,B) | -product2(A,e_3,B). [resolve(19,c,13,a)].
% 0.73/1.02 20 -product2(A,B,C) | -product2(D,B,C) | equalish(A,D) # label(product2_left_cancellation) # label(axiom). [assumption].
% 0.73/1.02 Derived: -product2(e_1,A,B) | -product2(e_2,A,B). [resolve(20,c,10,a)].
% 0.73/1.02 Derived: -product2(e_1,A,B) | -product2(e_3,A,B). [resolve(20,c,11,a)].
% 0.73/1.02 Derived: -product2(e_2,A,B) | -product2(e_3,A,B). [resolve(20,c,13,a)].
% 0.73/1.02
% 0.73/1.02 ============================== end predicate elimination =============
% 0.73/1.02
% 0.73/1.02 Auto_denials: (non-Horn, no changes).
% 0.73/1.02
% 0.73/1.02 Term ordering decisions:
% 0.73/1.02 Function symbol KB weights: e_1=1. e_2=1. e_3=1.
% 0.73/1.02
% 0.73/1.02 ============================== end of process initial clauses ========
% 0.73/1.02
% 0.73/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.02
% 0.73/1.02 ============================== end of clauses for search =============
% 0.73/1.02
% 0.73/1.02 ============================== SEARCH ================================
% 0.73/1.02
% 0.73/1.02 % Starting search at 0.01 seconds.
% 0.73/1.02
% 0.73/1.02 ============================== PROOF =================================
% 0.73/1.02 % SZS status Unsatisfiable
% 0.73/1.02 % SZS output start Refutation
% 0.73/1.02
% 0.73/1.02 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.73/1.02 % Length of proof is 28.
% 0.73/1.02 % Level of proof is 5.
% 0.73/1.02 % Maximum clause weight is 16.000.
% 0.73/1.02 % Given clauses 54.
% 0.73/1.02
% 0.73/1.02 10 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.73/1.02 13 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.73/1.02 16 -product1(A,B,C) | -product1(A,D,C) | equalish(B,D) # label(product1_right_cancellation) # label(axiom). [assumption].
% 0.73/1.02 17 -product1(A,B,C) | -product1(D,B,C) | equalish(A,D) # label(product1_left_cancellation) # label(axiom). [assumption].
% 0.73/1.02 18 -product2(A,B,C) | -product2(A,B,D) | equalish(C,D) # label(product2_total_function2) # label(axiom). [assumption].
% 0.73/1.02 21 group_element(e_1) # label(element_1) # label(axiom). [assumption].
% 0.73/1.02 22 group_element(e_2) # label(element_2) # label(axiom). [assumption].
% 0.73/1.02 23 group_element(e_3) # label(element_3) # label(axiom). [assumption].
% 0.73/1.02 24 product1(A,A,A) # label(product1_idempotence) # label(axiom). [assumption].
% 0.73/1.02 25 product2(A,A,A) # label(product2_idempotence) # label(axiom). [assumption].
% 0.73/1.02 26 -product1(A,B,C) | -product1(C,B,D) | product2(D,A,B) # label(qg1a) # label(negated_conjecture). [assumption].
% 0.73/1.02 27 -group_element(A) | -group_element(B) | product1(A,B,e_1) | product1(A,B,e_2) | product1(A,B,e_3) # label(product1_total_function1) # label(axiom). [assumption].
% 0.73/1.02 32 -product1(A,e_1,B) | -product1(A,e_2,B). [resolve(16,c,10,a)].
% 0.73/1.02 34 -product1(A,e_2,B) | -product1(A,e_3,B). [resolve(16,c,13,a)].
% 0.73/1.02 35 -product1(e_1,A,B) | -product1(e_2,A,B). [resolve(17,c,10,a)].
% 0.73/1.02 37 -product1(e_2,A,B) | -product1(e_3,A,B). [resolve(17,c,13,a)].
% 0.73/1.02 40 -product2(A,B,e_2) | -product2(A,B,e_3). [resolve(18,c,13,a)].
% 0.73/1.02 52 -group_element(A) | product1(e_3,A,e_1) | product1(e_3,A,e_2) | product1(e_3,A,e_3). [resolve(27,a,23,a)].
% 0.73/1.02 54 -group_element(A) | product1(e_1,A,e_1) | product1(e_1,A,e_2) | product1(e_1,A,e_3). [resolve(27,a,21,a)].
% 0.73/1.02 71 -product1(e_1,e_2,e_1). [ur(32,a,24,a)].
% 0.73/1.02 74 -product1(e_3,e_2,e_3). [resolve(34,b,24,a)].
% 0.73/1.02 76 -product1(e_1,e_2,e_2). [resolve(35,b,24,a)].
% 0.73/1.02 81 -product1(e_3,e_2,e_2). [ur(37,a,24,a)].
% 0.73/1.02 86 -product2(e_3,e_3,e_2). [resolve(40,b,25,a)].
% 0.73/1.02 100 product1(e_3,e_2,e_1). [resolve(52,a,22,a),unit_del(b,81),unit_del(c,74)].
% 0.73/1.02 103 -product1(e_1,e_2,A) | product2(A,e_3,e_2). [resolve(100,a,26,a)].
% 0.73/1.02 113 product1(e_1,e_2,e_3). [resolve(54,a,22,a),unit_del(a,71),unit_del(b,76)].
% 0.73/1.02 116 $F. [resolve(113,a,103,a),unit_del(a,86)].
% 0.73/1.02
% 0.73/1.02 % SZS output end Refutation
% 0.73/1.02 ============================== end of proof ==========================
% 0.73/1.02
% 0.73/1.02 ============================== STATISTICS ============================
% 0.73/1.02
% 0.73/1.02 Given=54. Generated=171. Kept=95. proofs=1.
% 0.73/1.02 Usable=54. Sos=41. Demods=0. Limbo=0, Disabled=47. Hints=0.
% 0.73/1.02 Megabytes=0.09.
% 0.73/1.02 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.73/1.02
% 0.73/1.02 ============================== end of statistics =====================
% 0.73/1.02
% 0.73/1.02 ============================== end of search =========================
% 0.73/1.02
% 0.73/1.02 THEOREM PROVED
% 0.73/1.02 % SZS status Unsatisfiable
% 0.73/1.02
% 0.73/1.02 Exiting with 1 proof.
% 0.73/1.02
% 0.73/1.02 Process 19519 exit (max_proofs) Mon Jun 13 13:25:21 2022
% 0.73/1.02 Prover9 interrupted
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