TSTP Solution File: GRP126-1.004 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP126-1.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 11:17:25 EDT 2022
% Result : Unsatisfiable 0.45s 0.99s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP126-1.004 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n028.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 07:46:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/0.98 ============================== Prover9 ===============================
% 0.45/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.45/0.98 Process 19841 was started by sandbox2 on n028.cluster.edu,
% 0.45/0.98 Mon Jun 13 07:46:08 2022
% 0.45/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19688_n028.cluster.edu".
% 0.45/0.98 ============================== end of head ===========================
% 0.45/0.98
% 0.45/0.98 ============================== INPUT =================================
% 0.45/0.98
% 0.45/0.98 % Reading from file /tmp/Prover9_19688_n028.cluster.edu
% 0.45/0.98
% 0.45/0.98 set(prolog_style_variables).
% 0.45/0.98 set(auto2).
% 0.45/0.98 % set(auto2) -> set(auto).
% 0.45/0.98 % set(auto) -> set(auto_inference).
% 0.45/0.98 % set(auto) -> set(auto_setup).
% 0.45/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.45/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/0.98 % set(auto) -> set(auto_limits).
% 0.45/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/0.98 % set(auto) -> set(auto_denials).
% 0.45/0.98 % set(auto) -> set(auto_process).
% 0.45/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.45/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.45/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.45/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.45/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.45/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.45/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.45/0.98 % set(auto2) -> assign(stats, some).
% 0.45/0.98 % set(auto2) -> clear(echo_input).
% 0.45/0.98 % set(auto2) -> set(quiet).
% 0.45/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.45/0.98 % set(auto2) -> clear(print_given).
% 0.45/0.98 assign(lrs_ticks,-1).
% 0.45/0.98 assign(sos_limit,10000).
% 0.45/0.98 assign(order,kbo).
% 0.45/0.98 set(lex_order_vars).
% 0.45/0.98 clear(print_given).
% 0.45/0.98
% 0.45/0.98 % formulas(sos). % not echoed (22 formulas)
% 0.45/0.98
% 0.45/0.98 ============================== end of input ==========================
% 0.45/0.98
% 0.45/0.98 % From the command line: assign(max_seconds, 300).
% 0.45/0.98
% 0.45/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/0.98
% 0.45/0.98 % Formulas that are not ordinary clauses:
% 0.45/0.98
% 0.45/0.98 ============================== end of process non-clausal formulas ===
% 0.45/0.98
% 0.45/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/0.98
% 0.45/0.98 ============================== PREDICATE ELIMINATION =================
% 0.45/0.98 1 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.45/0.98 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.45/0.98 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.45/0.98 4 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.45/0.98 5 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.45/0.98 6 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.45/0.98 7 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.45/0.98 8 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.45/0.98 9 -equalish(e_3,e_2) # label(e_3_is_not_e_2) # label(axiom). [assumption].
% 0.45/0.98 10 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.45/0.98 11 -equalish(e_4,e_1) # label(e_4_is_not_e_1) # label(axiom). [assumption].
% 0.45/0.98 12 -equalish(e_4,e_2) # label(e_4_is_not_e_2) # label(axiom). [assumption].
% 0.45/0.98 13 -equalish(e_4,e_3) # label(e_4_is_not_e_3) # label(axiom). [assumption].
% 0.45/0.98 Derived: -product(A,B,e_1) | -product(A,B,e_2). [resolve(1,c,2,a)].
% 0.45/0.98 Derived: -product(A,B,e_1) | -product(A,B,e_3). [resolve(1,c,3,a)].
% 0.45/0.98 Derived: -product(A,B,e_1) | -product(A,B,e_4). [resolve(1,c,4,a)].
% 0.45/0.98 Derived: -product(A,B,e_2) | -product(A,B,e_3). [resolve(1,c,6,a)].
% 0.45/0.98 Derived: -product(A,B,e_2) | -product(A,B,e_4). [resolve(1,c,7,a)].
% 0.45/0.98 Derived: -product(A,B,e_3) | -product(A,B,e_4). [resolve(1,c,10,a)].
% 0.45/0.98 14 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.45/0.98 Derived: -product(A,e_1,B) | -product(A,e_2,B). [resolve(14,c,2,a)].
% 0.45/0.98 Derived: -product(A,e_1,B) | -product(A,e_3,B). [resolve(14,c,3,a)].
% 0.45/0.98 Derived: -product(A,e_1,B) | -product(A,e_4,B). [resolve(14,c,4,a)].
% 0.45/0.99 Derived: -product(A,e_2,B) | -product(A,e_3,B). [resolve(14,c,6,a)].
% 0.45/0.99 Derived: -product(A,e_2,B) | -product(A,e_4,B). [resolve(14,c,7,a)].
% 0.45/0.99 Derived: -product(A,e_3,B) | -product(A,e_4,B). [resolve(14,c,10,a)].
% 0.45/0.99 15 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.45/0.99 Derived: -product(e_1,A,B) | -product(e_2,A,B). [resolve(15,c,2,a)].
% 0.45/0.99 Derived: -product(e_1,A,B) | -product(e_3,A,B). [resolve(15,c,3,a)].
% 0.45/0.99 Derived: -product(e_1,A,B) | -product(e_4,A,B). [resolve(15,c,4,a)].
% 0.45/0.99 Derived: -product(e_2,A,B) | -product(e_3,A,B). [resolve(15,c,6,a)].
% 0.45/0.99 Derived: -product(e_2,A,B) | -product(e_4,A,B). [resolve(15,c,7,a)].
% 0.45/0.99 Derived: -product(e_3,A,B) | -product(e_4,A,B). [resolve(15,c,10,a)].
% 0.45/0.99
% 0.45/0.99 ============================== end predicate elimination =============
% 0.45/0.99
% 0.45/0.99 Auto_denials: (non-Horn, no changes).
% 0.45/0.99
% 0.45/0.99 Term ordering decisions:
% 0.45/0.99 Function symbol KB weights: e_1=1. e_2=1. e_3=1. e_4=1.
% 0.45/0.99
% 0.45/0.99 ============================== end of process initial clauses ========
% 0.45/0.99
% 0.45/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.45/0.99
% 0.45/0.99 ============================== end of clauses for search =============
% 0.45/0.99
% 0.45/0.99 ============================== SEARCH ================================
% 0.45/0.99
% 0.45/0.99 % Starting search at 0.01 seconds.
% 0.45/0.99
% 0.45/0.99 ============================== PROOF =================================
% 0.45/0.99 % SZS status Unsatisfiable
% 0.45/0.99 % SZS output start Refutation
% 0.45/0.99
% 0.45/0.99 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.45/0.99 % Length of proof is 80.
% 0.45/0.99 % Level of proof is 13.
% 0.45/0.99 % Maximum clause weight is 20.000.
% 0.45/0.99 % Given clauses 140.
% 0.45/0.99
% 0.45/0.99 1 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.45/0.99 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.45/0.99 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.45/0.99 4 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.45/0.99 6 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.45/0.99 7 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.45/0.99 10 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.45/0.99 14 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.45/0.99 15 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.45/0.99 16 group_element(e_1) # label(element_1) # label(axiom). [assumption].
% 0.45/0.99 17 group_element(e_2) # label(element_2) # label(axiom). [assumption].
% 0.45/0.99 18 group_element(e_3) # label(element_3) # label(axiom). [assumption].
% 0.45/0.99 19 group_element(e_4) # label(element_4) # label(axiom). [assumption].
% 0.45/0.99 20 product(A,A,A) # label(product_idempotence) # label(axiom). [assumption].
% 0.45/0.99 21 -product(A,B,C) | -product(B,A,D) | product(C,D,B) # label(qg4) # label(negated_conjecture). [assumption].
% 0.45/0.99 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].
% 0.45/0.99 26 -product(A,B,e_2) | -product(A,B,e_3). [resolve(1,c,6,a)].
% 0.45/0.99 29 -product(A,e_1,B) | -product(A,e_2,B). [resolve(14,c,2,a)].
% 0.45/0.99 30 -product(A,e_1,B) | -product(A,e_3,B). [resolve(14,c,3,a)].
% 0.45/0.99 31 -product(A,e_1,B) | -product(A,e_4,B). [resolve(14,c,4,a)].
% 0.45/0.99 32 -product(A,e_2,B) | -product(A,e_3,B). [resolve(14,c,6,a)].
% 0.45/0.99 33 -product(A,e_2,B) | -product(A,e_4,B). [resolve(14,c,7,a)].
% 0.45/0.99 34 -product(A,e_3,B) | -product(A,e_4,B). [resolve(14,c,10,a)].
% 0.45/0.99 35 -product(e_1,A,B) | -product(e_2,A,B). [resolve(15,c,2,a)].
% 0.45/0.99 36 -product(e_1,A,B) | -product(e_3,A,B). [resolve(15,c,3,a)].
% 0.45/0.99 37 -product(e_1,A,B) | -product(e_4,A,B). [resolve(15,c,4,a)].
% 0.45/0.99 38 -product(e_2,A,B) | -product(e_3,A,B). [resolve(15,c,6,a)].
% 0.45/0.99 39 -product(e_2,A,B) | -product(e_4,A,B). [resolve(15,c,7,a)].
% 0.45/0.99 40 -product(e_3,A,B) | -product(e_4,A,B). [resolve(15,c,10,a)].
% 0.45/0.99 45 -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)].
% 0.45/0.99 46 -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)].
% 0.45/0.99 47 -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)].
% 0.45/0.99 48 -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)].
% 0.45/0.99 59 -product(e_3,e_3,e_2). [resolve(26,b,20,a)].
% 0.45/0.99 65 -product(e_2,e_1,e_2). [resolve(29,b,20,a)].
% 0.45/0.99 66 -product(e_1,e_2,e_1). [ur(29,a,20,a)].
% 0.45/0.99 67 -product(e_3,e_1,e_3). [resolve(30,b,20,a)].
% 0.45/0.99 68 -product(e_1,e_3,e_1). [ur(30,a,20,a)].
% 0.45/0.99 72 -product(e_2,e_3,e_2). [ur(32,a,20,a)].
% 0.45/0.99 74 -product(e_2,e_4,e_2). [ur(33,a,20,a)].
% 0.45/0.99 75 -product(e_4,e_3,e_4). [resolve(34,b,20,a)].
% 0.45/0.99 76 -product(e_3,e_4,e_3). [ur(34,a,20,a)].
% 0.45/0.99 77 -product(e_1,e_2,e_2). [resolve(35,b,20,a)].
% 0.45/0.99 78 -product(e_2,e_1,e_1). [ur(35,a,20,a)].
% 0.45/0.99 79 -product(e_1,e_3,e_3). [resolve(36,b,20,a)].
% 0.45/0.99 80 -product(e_3,e_1,e_1). [ur(36,a,20,a)].
% 0.45/0.99 83 -product(e_2,e_3,e_3). [resolve(38,b,20,a)].
% 0.45/0.99 85 -product(e_2,e_4,e_4). [resolve(39,b,20,a)].
% 0.45/0.99 87 -product(e_3,e_4,e_4). [resolve(40,b,20,a)].
% 0.45/0.99 88 -product(e_4,e_3,e_3). [ur(40,a,20,a)].
% 0.45/0.99 89 product(e_4,e_3,e_1) | product(e_4,e_3,e_2). [resolve(45,a,18,a),unit_del(c,88),unit_del(d,75)].
% 0.45/0.99 92 product(e_4,e_3,e_1) | -product(e_1,e_3,e_2). [resolve(89,b,37,b)].
% 0.45/0.99 95 product(e_4,e_3,e_1) | -product(e_3,e_4,A) | product(e_2,A,e_3). [resolve(89,b,21,a)].
% 0.45/0.99 100 product(e_3,e_4,e_1) | product(e_3,e_4,e_2). [resolve(46,a,19,a),unit_del(c,76),unit_del(d,87)].
% 0.45/0.99 102 product(e_3,e_1,e_2) | product(e_3,e_1,e_4). [resolve(46,a,16,a),unit_del(a,80),unit_del(c,67)].
% 0.45/0.99 106 product(e_2,e_4,e_1) | product(e_2,e_4,e_3). [resolve(47,a,19,a),unit_del(b,74),unit_del(d,85)].
% 0.45/0.99 107 product(e_2,e_3,e_1) | product(e_2,e_3,e_4). [resolve(47,a,18,a),unit_del(b,72),unit_del(c,83)].
% 0.45/0.99 108 product(e_2,e_1,e_3) | product(e_2,e_1,e_4). [resolve(47,a,16,a),unit_del(a,78),unit_del(b,65)].
% 0.45/0.99 111 product(e_3,e_4,e_1) | -product(e_3,e_1,e_2). [resolve(100,b,31,b)].
% 0.45/0.99 118 product(e_3,e_1,e_2) | -product(e_2,e_1,e_4). [resolve(102,b,38,b)].
% 0.45/0.99 122 product(e_1,e_3,e_2) | product(e_1,e_3,e_4). [resolve(48,a,18,a),unit_del(a,68),unit_del(c,79)].
% 0.45/0.99 123 product(e_1,e_2,e_3) | product(e_1,e_2,e_4). [resolve(48,a,17,a),unit_del(a,66),unit_del(b,77)].
% 0.45/0.99 125 product(e_2,e_4,e_1) | -product(e_2,e_1,e_3). [resolve(106,b,31,b)].
% 0.45/0.99 129 product(e_2,e_3,e_1) | -product(e_2,e_1,e_4). [resolve(107,b,30,b)].
% 0.45/0.99 138 product(e_3,e_1,e_2) | product(e_2,e_1,e_3). [resolve(118,b,108,b)].
% 0.45/0.99 142 product(e_1,e_3,e_2) | -product(e_1,e_2,e_4). [resolve(122,b,32,b)].
% 0.45/0.99 150 product(e_2,e_3,e_1) | product(e_2,e_1,e_3). [resolve(129,b,108,b)].
% 0.45/0.99 154 product(e_2,e_1,e_3) | product(e_3,e_4,e_1). [resolve(138,a,111,b)].
% 0.45/0.99 157 product(e_1,e_3,e_2) | product(e_1,e_2,e_3). [resolve(142,b,123,b)].
% 0.45/0.99 178 product(e_4,e_3,e_1) | product(e_2,e_1,e_3). [resolve(95,b,154,b),merge(c)].
% 0.45/0.99 179 product(e_1,e_2,e_3) | product(e_4,e_3,e_1). [resolve(157,a,92,b)].
% 0.45/0.99 199 product(e_2,e_1,e_3) | -product(e_2,e_3,e_1). [resolve(178,a,39,b)].
% 0.45/0.99 206 product(e_1,e_2,e_3) | -product(e_3,e_4,A) | product(e_1,A,e_3). [resolve(179,b,21,a)].
% 0.45/0.99 207 product(e_1,e_2,e_3) | -product(e_3,e_4,e_2). [factor(206,a,c)].
% 0.45/0.99 226 product(e_2,e_1,e_3). [resolve(199,b,150,a),merge(b)].
% 0.45/0.99 227 product(e_2,e_4,e_1). [back_unit_del(125),unit_del(b,226)].
% 0.45/0.99 235 -product(e_1,e_2,e_3). [ur(21,b,226,a,c,59,a)].
% 0.45/0.99 236 -product(e_3,e_4,e_2). [back_unit_del(207),unit_del(a,235)].
% 0.45/0.99 253 product(e_3,e_4,e_1). [back_unit_del(100),unit_del(b,236)].
% 0.45/0.99 267 $F. [ur(38,a,227,a),unit_del(a,253)].
% 0.45/0.99
% 0.45/0.99 % SZS output end Refutation
% 0.45/0.99 ============================== end of proof ==========================
% 0.45/0.99
% 0.45/0.99 ============================== STATISTICS ============================
% 0.45/0.99
% 0.45/0.99 Given=140. Generated=503. Kept=251. proofs=1.
% 0.45/0.99 Usable=75. Sos=37. Demods=0. Limbo=2, Disabled=177. Hints=0.
% 0.45/0.99 Megabytes=0.15.
% 0.45/0.99 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.45/0.99
% 0.45/0.99 ============================== end of statistics =====================
% 0.45/0.99
% 0.45/0.99 ============================== end of search =========================
% 0.45/0.99
% 0.45/0.99 THEOREM PROVED
% 0.45/0.99 % SZS status Unsatisfiable
% 0.45/0.99
% 0.45/0.99 Exiting with 1 proof.
% 0.45/0.99
% 0.45/0.99 Process 19841 exit (max_proofs) Mon Jun 13 07:46:08 2022
% 0.45/0.99 Prover9 interrupted
%------------------------------------------------------------------------------