TSTP Solution File: GRP127-1.004 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP127-1.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 11:17:28 EDT 2022
% Result : Unsatisfiable 0.41s 0.98s
% Output : Refutation 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP127-1.004 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n018.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jun 13 04:56:27 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.41/0.97 ============================== Prover9 ===============================
% 0.41/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.97 Process 28605 was started by sandbox on n018.cluster.edu,
% 0.41/0.97 Mon Jun 13 04:56:27 2022
% 0.41/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28450_n018.cluster.edu".
% 0.41/0.97 ============================== end of head ===========================
% 0.41/0.97
% 0.41/0.97 ============================== INPUT =================================
% 0.41/0.97
% 0.41/0.97 % Reading from file /tmp/Prover9_28450_n018.cluster.edu
% 0.41/0.97
% 0.41/0.97 set(prolog_style_variables).
% 0.41/0.97 set(auto2).
% 0.41/0.97 % set(auto2) -> set(auto).
% 0.41/0.97 % set(auto) -> set(auto_inference).
% 0.41/0.97 % set(auto) -> set(auto_setup).
% 0.41/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.97 % set(auto) -> set(auto_limits).
% 0.41/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.97 % set(auto) -> set(auto_denials).
% 0.41/0.97 % set(auto) -> set(auto_process).
% 0.41/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.97 % set(auto2) -> assign(stats, some).
% 0.41/0.97 % set(auto2) -> clear(echo_input).
% 0.41/0.97 % set(auto2) -> set(quiet).
% 0.41/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.97 % set(auto2) -> clear(print_given).
% 0.41/0.97 assign(lrs_ticks,-1).
% 0.41/0.97 assign(sos_limit,10000).
% 0.41/0.97 assign(order,kbo).
% 0.41/0.97 set(lex_order_vars).
% 0.41/0.97 clear(print_given).
% 0.41/0.97
% 0.41/0.97 % formulas(sos). % not echoed (22 formulas)
% 0.41/0.97
% 0.41/0.97 ============================== end of input ==========================
% 0.41/0.97
% 0.41/0.97 % From the command line: assign(max_seconds, 300).
% 0.41/0.97
% 0.41/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.97
% 0.41/0.97 % Formulas that are not ordinary clauses:
% 0.41/0.97
% 0.41/0.97 ============================== end of process non-clausal formulas ===
% 0.41/0.97
% 0.41/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/0.97
% 0.41/0.97 ============================== PREDICATE ELIMINATION =================
% 0.41/0.97 1 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.41/0.97 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.41/0.97 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.41/0.97 4 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.41/0.97 5 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.41/0.97 6 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.41/0.97 7 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.41/0.97 8 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.41/0.97 9 -equalish(e_3,e_2) # label(e_3_is_not_e_2) # label(axiom). [assumption].
% 0.41/0.97 10 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.41/0.97 11 -equalish(e_4,e_1) # label(e_4_is_not_e_1) # label(axiom). [assumption].
% 0.41/0.97 12 -equalish(e_4,e_2) # label(e_4_is_not_e_2) # label(axiom). [assumption].
% 0.41/0.97 13 -equalish(e_4,e_3) # label(e_4_is_not_e_3) # label(axiom). [assumption].
% 0.41/0.97 Derived: -product(A,B,e_1) | -product(A,B,e_2). [resolve(1,c,2,a)].
% 0.41/0.97 Derived: -product(A,B,e_1) | -product(A,B,e_3). [resolve(1,c,3,a)].
% 0.41/0.97 Derived: -product(A,B,e_1) | -product(A,B,e_4). [resolve(1,c,4,a)].
% 0.41/0.97 Derived: -product(A,B,e_2) | -product(A,B,e_3). [resolve(1,c,6,a)].
% 0.41/0.97 Derived: -product(A,B,e_2) | -product(A,B,e_4). [resolve(1,c,7,a)].
% 0.41/0.97 Derived: -product(A,B,e_3) | -product(A,B,e_4). [resolve(1,c,10,a)].
% 0.41/0.97 14 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.41/0.97 Derived: -product(A,e_1,B) | -product(A,e_2,B). [resolve(14,c,2,a)].
% 0.41/0.97 Derived: -product(A,e_1,B) | -product(A,e_3,B). [resolve(14,c,3,a)].
% 0.41/0.97 Derived: -product(A,e_1,B) | -product(A,e_4,B). [resolve(14,c,4,a)].
% 0.41/0.98 Derived: -product(A,e_2,B) | -product(A,e_3,B). [resolve(14,c,6,a)].
% 0.41/0.98 Derived: -product(A,e_2,B) | -product(A,e_4,B). [resolve(14,c,7,a)].
% 0.41/0.98 Derived: -product(A,e_3,B) | -product(A,e_4,B). [resolve(14,c,10,a)].
% 0.41/0.98 15 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.41/0.98 Derived: -product(e_1,A,B) | -product(e_2,A,B). [resolve(15,c,2,a)].
% 0.41/0.98 Derived: -product(e_1,A,B) | -product(e_3,A,B). [resolve(15,c,3,a)].
% 0.41/0.98 Derived: -product(e_1,A,B) | -product(e_4,A,B). [resolve(15,c,4,a)].
% 0.41/0.98 Derived: -product(e_2,A,B) | -product(e_3,A,B). [resolve(15,c,6,a)].
% 0.41/0.98 Derived: -product(e_2,A,B) | -product(e_4,A,B). [resolve(15,c,7,a)].
% 0.41/0.98 Derived: -product(e_3,A,B) | -product(e_4,A,B). [resolve(15,c,10,a)].
% 0.41/0.98
% 0.41/0.98 ============================== end predicate elimination =============
% 0.41/0.98
% 0.41/0.98 Auto_denials: (non-Horn, no changes).
% 0.41/0.98
% 0.41/0.98 Term ordering decisions:
% 0.41/0.98 Function symbol KB weights: e_1=1. e_2=1. e_3=1. e_4=1.
% 0.41/0.98
% 0.41/0.98 ============================== end of process initial clauses ========
% 0.41/0.98
% 0.41/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.41/0.98
% 0.41/0.98 ============================== end of clauses for search =============
% 0.41/0.98
% 0.41/0.98 ============================== SEARCH ================================
% 0.41/0.98
% 0.41/0.98 % Starting search at 0.01 seconds.
% 0.41/0.98
% 0.41/0.98 ============================== PROOF =================================
% 0.41/0.98 % SZS status Unsatisfiable
% 0.41/0.98 % SZS output start Refutation
% 0.41/0.98
% 0.41/0.98 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.41/0.98 % Length of proof is 83.
% 0.41/0.98 % Level of proof is 11.
% 0.41/0.98 % Maximum clause weight is 20.000.
% 0.41/0.98 % Given clauses 146.
% 0.41/0.98
% 0.41/0.98 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.41/0.98 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.41/0.98 4 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.41/0.98 6 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.41/0.98 7 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.41/0.98 10 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.41/0.98 14 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.41/0.98 15 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.41/0.98 16 group_element(e_1) # label(element_1) # label(axiom). [assumption].
% 0.41/0.98 17 group_element(e_2) # label(element_2) # label(axiom). [assumption].
% 0.41/0.98 18 group_element(e_3) # label(element_3) # label(axiom). [assumption].
% 0.41/0.98 19 group_element(e_4) # label(element_4) # label(axiom). [assumption].
% 0.41/0.98 20 product(A,A,A) # label(product_idempotence) # label(axiom). [assumption].
% 0.41/0.98 21 -product(A,B,C) | -product(C,A,D) | product(D,A,B) # label(qg3) # label(negated_conjecture). [assumption].
% 0.41/0.98 22 -group_element(A) | -group_element(B) | product(A,B,e_1) | product(A,B,e_2) | product(A,B,e_3) | product(A,B,e_4) # label(product_total_function1) # label(axiom). [assumption].
% 0.41/0.98 29 -product(A,e_1,B) | -product(A,e_2,B). [resolve(14,c,2,a)].
% 0.41/0.98 30 -product(A,e_1,B) | -product(A,e_3,B). [resolve(14,c,3,a)].
% 0.41/0.98 31 -product(A,e_1,B) | -product(A,e_4,B). [resolve(14,c,4,a)].
% 0.41/0.98 32 -product(A,e_2,B) | -product(A,e_3,B). [resolve(14,c,6,a)].
% 0.41/0.98 33 -product(A,e_2,B) | -product(A,e_4,B). [resolve(14,c,7,a)].
% 0.41/0.98 34 -product(A,e_3,B) | -product(A,e_4,B). [resolve(14,c,10,a)].
% 0.41/0.98 35 -product(e_1,A,B) | -product(e_2,A,B). [resolve(15,c,2,a)].
% 0.41/0.98 36 -product(e_1,A,B) | -product(e_3,A,B). [resolve(15,c,3,a)].
% 0.41/0.98 37 -product(e_1,A,B) | -product(e_4,A,B). [resolve(15,c,4,a)].
% 0.41/0.98 38 -product(e_2,A,B) | -product(e_3,A,B). [resolve(15,c,6,a)].
% 0.41/0.98 39 -product(e_2,A,B) | -product(e_4,A,B). [resolve(15,c,7,a)].
% 0.41/0.98 40 -product(e_3,A,B) | -product(e_4,A,B). [resolve(15,c,10,a)].
% 0.41/0.98 44 -group_element(A) | product(e_4,A,e_1) | product(e_4,A,e_2) | product(e_4,A,e_3) | product(e_4,A,e_4). [resolve(22,a,19,a)].
% 0.41/0.98 45 -group_element(A) | product(e_3,A,e_1) | product(e_3,A,e_2) | product(e_3,A,e_3) | product(e_3,A,e_4). [resolve(22,a,18,a)].
% 0.41/0.98 46 -group_element(A) | product(e_2,A,e_1) | product(e_2,A,e_2) | product(e_2,A,e_3) | product(e_2,A,e_4). [resolve(22,a,17,a)].
% 0.41/0.98 47 -group_element(A) | product(e_1,A,e_1) | product(e_1,A,e_2) | product(e_1,A,e_3) | product(e_1,A,e_4). [resolve(22,a,16,a)].
% 0.41/0.98 64 -product(e_2,e_1,e_2). [resolve(29,b,20,a)].
% 0.41/0.98 66 -product(e_3,e_1,e_3). [resolve(30,b,20,a)].
% 0.41/0.98 67 -product(e_1,e_3,e_1). [ur(30,a,20,a)].
% 0.41/0.98 69 -product(e_1,e_4,e_1). [ur(31,a,20,a)].
% 0.41/0.98 70 -product(e_3,e_2,e_3). [resolve(32,b,20,a)].
% 0.41/0.98 71 -product(e_2,e_3,e_2). [ur(32,a,20,a)].
% 0.41/0.98 73 -product(e_2,e_4,e_2). [ur(33,a,20,a)].
% 0.41/0.98 74 -product(e_4,e_3,e_4). [resolve(34,b,20,a)].
% 0.41/0.98 75 -product(e_3,e_4,e_3). [ur(34,a,20,a)].
% 0.41/0.98 77 -product(e_2,e_1,e_1). [ur(35,a,20,a)].
% 0.41/0.98 78 -product(e_1,e_3,e_3). [resolve(36,b,20,a)].
% 0.41/0.98 79 -product(e_3,e_1,e_1). [ur(36,a,20,a)].
% 0.41/0.98 80 -product(e_1,e_4,e_4). [resolve(37,b,20,a)].
% 0.41/0.98 82 -product(e_2,e_3,e_3). [resolve(38,b,20,a)].
% 0.41/0.98 83 -product(e_3,e_2,e_2). [ur(38,a,20,a)].
% 0.41/0.98 84 -product(e_2,e_4,e_4). [resolve(39,b,20,a)].
% 0.41/0.98 86 -product(e_3,e_4,e_4). [resolve(40,b,20,a)].
% 0.41/0.98 87 -product(e_4,e_3,e_3). [ur(40,a,20,a)].
% 0.41/0.98 88 product(e_4,e_3,e_1) | product(e_4,e_3,e_2). [resolve(44,a,18,a),unit_del(c,87),unit_del(d,74)].
% 0.41/0.98 93 product(e_4,e_3,e_1) | -product(e_3,A,e_4) | product(e_2,e_3,A). [resolve(88,b,21,b)].
% 0.41/0.98 99 product(e_3,e_4,e_1) | product(e_3,e_4,e_2). [resolve(45,a,19,a),unit_del(c,75),unit_del(d,86)].
% 0.41/0.98 100 product(e_3,e_2,e_1) | product(e_3,e_2,e_4). [resolve(45,a,17,a),unit_del(b,83),unit_del(c,70)].
% 0.41/0.98 101 product(e_3,e_1,e_2) | product(e_3,e_1,e_4). [resolve(45,a,16,a),unit_del(a,79),unit_del(c,66)].
% 0.41/0.98 105 product(e_2,e_4,e_1) | product(e_2,e_4,e_3). [resolve(46,a,19,a),unit_del(b,73),unit_del(d,84)].
% 0.41/0.98 106 product(e_2,e_3,e_1) | product(e_2,e_3,e_4). [resolve(46,a,18,a),unit_del(b,71),unit_del(c,82)].
% 0.41/0.98 107 product(e_2,e_1,e_3) | product(e_2,e_1,e_4). [resolve(46,a,16,a),unit_del(a,77),unit_del(b,64)].
% 0.41/0.98 109 product(e_3,e_4,e_1) | -product(e_1,e_4,e_2). [resolve(99,b,36,b)].
% 0.41/0.98 110 product(e_3,e_4,e_1) | -product(e_3,e_1,e_2). [resolve(99,b,31,b)].
% 0.41/0.98 117 product(e_3,e_1,e_2) | -product(e_2,e_1,e_4). [resolve(101,b,38,b)].
% 0.41/0.98 120 product(e_1,e_4,e_2) | product(e_1,e_4,e_3). [resolve(47,a,19,a),unit_del(a,69),unit_del(d,80)].
% 0.41/0.98 121 product(e_1,e_3,e_2) | product(e_1,e_3,e_4). [resolve(47,a,18,a),unit_del(a,67),unit_del(c,78)].
% 0.41/0.98 123 product(e_2,e_4,e_1) | -product(e_1,e_4,e_3). [resolve(105,b,35,b)].
% 0.41/0.98 124 product(e_2,e_4,e_1) | -product(e_2,e_1,e_3). [resolve(105,b,31,b)].
% 0.41/0.98 127 product(e_2,e_3,e_1) | -product(e_1,e_3,e_4). [resolve(106,b,35,b)].
% 0.41/0.98 128 product(e_2,e_3,e_1) | -product(e_2,e_1,e_4). [resolve(106,b,30,b)].
% 0.41/0.98 137 product(e_3,e_1,e_2) | product(e_2,e_1,e_3). [resolve(117,b,107,b)].
% 0.41/0.98 147 product(e_2,e_4,e_1) | product(e_1,e_4,e_2). [resolve(123,b,120,b)].
% 0.41/0.98 148 product(e_2,e_3,e_1) | product(e_1,e_3,e_2). [resolve(127,b,121,b)].
% 0.41/0.98 149 product(e_2,e_3,e_1) | product(e_2,e_1,e_3). [resolve(128,b,107,b)].
% 0.41/0.98 153 product(e_2,e_1,e_3) | product(e_3,e_4,e_1). [resolve(137,a,110,b)].
% 0.41/0.98 160 product(e_1,e_4,e_2) | -product(e_2,e_3,e_1). [resolve(147,a,34,b)].
% 0.41/0.98 164 product(e_4,e_3,e_1) | product(e_3,e_2,e_1). [resolve(93,b,100,b),unit_del(b,71)].
% 0.41/0.98 173 product(e_2,e_1,e_3) | -product(e_3,e_2,e_1). [resolve(153,b,33,b)].
% 0.41/0.98 184 product(e_1,e_4,e_2) | product(e_1,e_3,e_2). [resolve(160,b,148,a)].
% 0.41/0.98 185 product(e_3,e_2,e_1) | -product(e_2,e_3,e_1). [resolve(164,a,39,b)].
% 0.41/0.98 208 product(e_1,e_3,e_2) | product(e_3,e_4,e_1). [resolve(184,a,109,b)].
% 0.41/0.98 212 product(e_3,e_2,e_1) | product(e_2,e_1,e_3). [resolve(185,b,149,a)].
% 0.41/0.98 243 product(e_1,e_3,e_2) | -product(e_2,e_4,e_1). [resolve(208,b,38,b)].
% 0.41/0.98 251 product(e_2,e_1,e_3). [resolve(212,a,173,b),merge(b)].
% 0.41/0.98 252 product(e_2,e_4,e_1). [back_unit_del(124),unit_del(b,251)].
% 0.41/0.98 254 product(e_1,e_3,e_2). [back_unit_del(243),unit_del(b,252)].
% 0.41/0.98 261 $F. [ur(21,b,251,a,c,66,a),unit_del(a,254)].
% 0.41/0.98
% 0.41/0.98 % SZS output end Refutation
% 0.41/0.98 ============================== end of proof ==========================
% 0.41/0.98
% 0.41/0.98 ============================== STATISTICS ============================
% 0.41/0.98
% 0.41/0.98 Given=146. Generated=499. Kept=245. proofs=1.
% 0.41/0.98 Usable=106. Sos=52. Demods=0. Limbo=5, Disabled=122. Hints=0.
% 0.41/0.98 Megabytes=0.16.
% 0.41/0.98 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.41/0.98
% 0.41/0.98 ============================== end of statistics =====================
% 0.41/0.98
% 0.41/0.98 ============================== end of search =========================
% 0.41/0.98
% 0.41/0.98 THEOREM PROVED
% 0.41/0.98 % SZS status Unsatisfiable
% 0.41/0.98
% 0.41/0.98 Exiting with 1 proof.
% 0.41/0.98
% 0.41/0.98 Process 28605 exit (max_proofs) Mon Jun 13 04:56:27 2022
% 0.41/0.98 Prover9 interrupted
%------------------------------------------------------------------------------