TSTP Solution File: GRP133-1.003 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP133-1.003 : 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 11:17:38 EDT 2022
% Result : Unsatisfiable 0.84s 1.12s
% Output : Refutation 0.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP133-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.13 % 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 : Tue Jun 14 12:25:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.04 ============================== Prover9 ===============================
% 0.43/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.04 Process 25894 was started by sandbox2 on n026.cluster.edu,
% 0.43/1.04 Tue Jun 14 12:25:37 2022
% 0.43/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25579_n026.cluster.edu".
% 0.43/1.04 ============================== end of head ===========================
% 0.43/1.04
% 0.43/1.04 ============================== INPUT =================================
% 0.43/1.04
% 0.43/1.04 % Reading from file /tmp/Prover9_25579_n026.cluster.edu
% 0.43/1.04
% 0.43/1.04 set(prolog_style_variables).
% 0.43/1.04 set(auto2).
% 0.43/1.04 % set(auto2) -> set(auto).
% 0.43/1.04 % set(auto) -> set(auto_inference).
% 0.43/1.04 % set(auto) -> set(auto_setup).
% 0.43/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.04 % set(auto) -> set(auto_limits).
% 0.43/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.04 % set(auto) -> set(auto_denials).
% 0.43/1.04 % set(auto) -> set(auto_process).
% 0.43/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.04 % set(auto2) -> assign(stats, some).
% 0.43/1.04 % set(auto2) -> clear(echo_input).
% 0.43/1.04 % set(auto2) -> set(quiet).
% 0.43/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.04 % set(auto2) -> clear(print_given).
% 0.43/1.04 assign(lrs_ticks,-1).
% 0.43/1.04 assign(sos_limit,10000).
% 0.43/1.04 assign(order,kbo).
% 0.43/1.04 set(lex_order_vars).
% 0.43/1.04 clear(print_given).
% 0.43/1.04
% 0.43/1.04 % formulas(sos). % not echoed (14 formulas)
% 0.43/1.04
% 0.43/1.04 ============================== end of input ==========================
% 0.43/1.04
% 0.43/1.04 % From the command line: assign(max_seconds, 300).
% 0.43/1.04
% 0.43/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.04
% 0.43/1.04 % Formulas that are not ordinary clauses:
% 0.43/1.04
% 0.43/1.04 ============================== end of process non-clausal formulas ===
% 0.43/1.04
% 0.43/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.04
% 0.43/1.04 ============================== PREDICATE ELIMINATION =================
% 0.43/1.04 1 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.43/1.04 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.43/1.04 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.43/1.04 4 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.43/1.04 5 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.43/1.04 6 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.43/1.04 7 -equalish(e_3,e_2) # label(e_3_is_not_e_2) # label(axiom). [assumption].
% 0.43/1.04 Derived: -product(A,B,e_1) | -product(A,B,e_2). [resolve(1,c,2,a)].
% 0.43/1.04 Derived: -product(A,B,e_1) | -product(A,B,e_3). [resolve(1,c,3,a)].
% 0.43/1.04 Derived: -product(A,B,e_2) | -product(A,B,e_3). [resolve(1,c,5,a)].
% 0.43/1.04 8 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.43/1.04 Derived: -product(A,e_1,B) | -product(A,e_2,B). [resolve(8,c,2,a)].
% 0.43/1.04 Derived: -product(A,e_1,B) | -product(A,e_3,B). [resolve(8,c,3,a)].
% 0.43/1.04 Derived: -product(A,e_2,B) | -product(A,e_3,B). [resolve(8,c,5,a)].
% 0.43/1.04 9 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.43/1.04 Derived: -product(e_1,A,B) | -product(e_2,A,B). [resolve(9,c,2,a)].
% 0.43/1.04 Derived: -product(e_1,A,B) | -product(e_3,A,B). [resolve(9,c,3,a)].
% 0.43/1.04 Derived: -product(e_2,A,B) | -product(e_3,A,B). [resolve(9,c,5,a)].
% 0.43/1.04
% 0.43/1.04 ============================== end predicate elimination =============
% 0.43/1.04
% 0.43/1.04 Auto_denials: (non-Horn, no changes).
% 0.43/1.04
% 0.43/1.04 Term ordering decisions:
% 0.43/1.04 Function symbol KB weights: e_1=1. e_2=1. e_3=1.
% 0.43/1.04
% 0.43/1.04 ============================== end of process initial clauses ========
% 0.43/1.04
% 0.43/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.84/1.12
% 0.84/1.12 ============================== end of clauses for search =============
% 0.84/1.12
% 0.84/1.12 ============================== SEARCH ================================
% 0.84/1.12
% 0.84/1.12 % Starting search at 0.01 seconds.
% 0.84/1.12
% 0.84/1.12 ============================== PROOF =================================
% 0.84/1.12 % SZS status Unsatisfiable
% 0.84/1.12 % SZS output start Refutation
% 0.84/1.12
% 0.84/1.12 % Proof 1 at 0.09 (+ 0.01) seconds.
% 0.84/1.12 % Length of proof is 98.
% 0.84/1.12 % Level of proof is 29.
% 0.84/1.12 % Maximum clause weight is 20.000.
% 0.84/1.12 % Given clauses 288.
% 0.84/1.12
% 0.84/1.12 1 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.84/1.12 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.84/1.12 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.84/1.12 5 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.84/1.12 8 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.84/1.12 9 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.84/1.12 10 group_element(e_1) # label(element_1) # label(axiom). [assumption].
% 0.84/1.12 11 group_element(e_2) # label(element_2) # label(axiom). [assumption].
% 0.84/1.12 12 group_element(e_3) # label(element_3) # label(axiom). [assumption].
% 0.84/1.12 13 -product(A,B,C) | -product(B,A,D) | product(C,D,A) # label(qg3) # label(negated_conjecture). [assumption].
% 0.84/1.12 14 -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].
% 0.84/1.12 15 -product(A,B,e_1) | -product(A,B,e_2). [resolve(1,c,2,a)].
% 0.84/1.12 16 -product(A,B,e_1) | -product(A,B,e_3). [resolve(1,c,3,a)].
% 0.84/1.12 17 -product(A,B,e_2) | -product(A,B,e_3). [resolve(1,c,5,a)].
% 0.84/1.12 18 -product(A,e_1,B) | -product(A,e_2,B). [resolve(8,c,2,a)].
% 0.84/1.12 19 -product(A,e_1,B) | -product(A,e_3,B). [resolve(8,c,3,a)].
% 0.84/1.12 20 -product(A,e_2,B) | -product(A,e_3,B). [resolve(8,c,5,a)].
% 0.84/1.12 21 -product(e_1,A,B) | -product(e_2,A,B). [resolve(9,c,2,a)].
% 0.84/1.12 22 -product(e_1,A,B) | -product(e_3,A,B). [resolve(9,c,3,a)].
% 0.84/1.12 23 -product(e_2,A,B) | -product(e_3,A,B). [resolve(9,c,5,a)].
% 0.84/1.12 24 -product(A,A,B) | product(B,B,A). [factor(13,a,b)].
% 0.84/1.12 25 -group_element(A) | product(A,A,e_1) | product(A,A,e_2) | product(A,A,e_3). [factor(14,a,b)].
% 0.84/1.12 26 -group_element(A) | product(e_3,A,e_1) | product(e_3,A,e_2) | product(e_3,A,e_3). [resolve(14,a,12,a)].
% 0.84/1.12 27 -group_element(A) | product(e_2,A,e_1) | product(e_2,A,e_2) | product(e_2,A,e_3). [resolve(14,a,11,a)].
% 0.84/1.12 28 -group_element(A) | product(e_1,A,e_1) | product(e_1,A,e_2) | product(e_1,A,e_3). [resolve(14,a,10,a)].
% 0.84/1.12 32 product(e_3,e_3,e_1) | product(e_3,e_3,e_2) | product(e_3,e_3,e_3). [resolve(25,a,12,a)].
% 0.84/1.12 33 product(e_2,e_2,e_1) | product(e_2,e_2,e_2) | product(e_2,e_2,e_3). [resolve(25,a,11,a)].
% 0.84/1.12 34 product(e_1,e_1,e_1) | product(e_1,e_1,e_2) | product(e_1,e_1,e_3). [resolve(25,a,10,a)].
% 0.84/1.12 35 product(e_3,e_2,e_1) | product(e_3,e_2,e_2) | product(e_3,e_2,e_3). [resolve(26,a,11,a)].
% 0.84/1.12 36 product(e_3,e_1,e_1) | product(e_3,e_1,e_2) | product(e_3,e_1,e_3). [resolve(26,a,10,a)].
% 0.84/1.12 38 product(e_3,e_3,e_1) | product(e_3,e_3,e_2) | -product(e_1,e_3,e_3). [resolve(32,c,22,b)].
% 0.84/1.12 40 product(e_3,e_3,e_1) | product(e_3,e_3,e_2) | -product(e_3,e_1,e_3). [resolve(32,c,19,b)].
% 0.84/1.12 43 product(e_2,e_2,e_1) | product(e_2,e_2,e_2) | product(e_3,e_3,e_2). [resolve(33,c,24,a)].
% 0.84/1.12 51 product(e_3,e_2,e_1) | product(e_3,e_2,e_2) | -product(e_2,e_2,e_3). [resolve(35,c,23,b)].
% 0.84/1.12 56 product(e_2,e_3,e_1) | product(e_2,e_3,e_2) | product(e_2,e_3,e_3). [resolve(27,a,12,a)].
% 0.84/1.12 57 product(e_2,e_1,e_1) | product(e_2,e_1,e_2) | product(e_2,e_1,e_3). [resolve(27,a,10,a)].
% 0.84/1.12 63 product(e_1,e_3,e_1) | product(e_1,e_3,e_2) | product(e_1,e_3,e_3). [resolve(28,a,12,a)].
% 0.84/1.12 64 product(e_1,e_2,e_1) | product(e_1,e_2,e_2) | product(e_1,e_2,e_3). [resolve(28,a,11,a)].
% 0.84/1.12 65 product(e_3,e_3,e_1) | product(e_3,e_3,e_2) | product(e_3,e_1,e_1) | product(e_3,e_1,e_2). [resolve(40,c,36,c)].
% 0.84/1.12 66 product(e_2,e_2,e_1) | product(e_2,e_2,e_2) | -product(e_2,e_3,e_2). [resolve(43,c,23,b)].
% 0.84/1.12 68 product(e_2,e_2,e_1) | product(e_2,e_2,e_2) | -product(e_3,e_2,e_2). [resolve(43,c,20,b)].
% 0.84/1.12 79 product(e_3,e_2,e_1) | product(e_3,e_2,e_2) | product(e_2,e_2,e_1) | product(e_2,e_2,e_2). [resolve(51,c,33,c)].
% 0.84/1.12 83 product(e_2,e_3,e_1) | product(e_2,e_3,e_2) | -product(e_2,e_2,e_3). [resolve(56,c,20,b)].
% 0.84/1.12 88 product(e_2,e_1,e_1) | product(e_2,e_1,e_2) | -product(e_1,e_1,e_3). [resolve(57,c,21,b)].
% 0.84/1.12 89 product(e_2,e_1,e_1) | product(e_2,e_1,e_2) | -product(e_1,e_2,A) | product(A,e_3,e_1). [resolve(57,c,13,b)].
% 0.84/1.12 93 product(e_1,e_3,e_1) | product(e_1,e_3,e_2) | product(e_3,e_3,e_1) | product(e_3,e_3,e_2). [resolve(63,c,38,c)].
% 0.84/1.12 100 product(e_1,e_2,e_1) | product(e_1,e_2,e_2) | -product(e_1,e_1,e_3). [resolve(64,c,18,b)].
% 0.84/1.12 105 product(e_2,e_3,e_1) | product(e_2,e_3,e_2) | product(e_2,e_2,e_1) | product(e_2,e_2,e_2). [resolve(83,c,33,c)].
% 0.84/1.12 107 product(e_2,e_1,e_1) | product(e_2,e_1,e_2) | product(e_1,e_1,e_1) | product(e_1,e_1,e_2). [resolve(88,c,34,c)].
% 0.84/1.12 110 product(e_1,e_2,e_1) | product(e_1,e_2,e_2) | product(e_1,e_1,e_1) | product(e_1,e_1,e_2). [resolve(100,c,34,c)].
% 0.84/1.12 121 product(e_3,e_3,e_1) | product(e_3,e_1,e_1) | product(e_3,e_1,e_2) | product(e_2,e_2,e_3). [resolve(65,b,24,a)].
% 0.84/1.12 127 product(e_3,e_2,e_1) | product(e_2,e_2,e_1) | product(e_2,e_2,e_2). [resolve(79,b,68,c),merge(d),merge(e)].
% 0.84/1.12 130 product(e_2,e_2,e_1) | product(e_2,e_2,e_2) | -product(e_2,e_3,A) | product(A,e_1,e_2). [resolve(127,a,13,b)].
% 0.84/1.12 131 product(e_2,e_2,e_1) | product(e_2,e_2,e_2) | -product(e_2,e_3,A) | product(e_1,A,e_3). [resolve(127,a,13,a)].
% 0.84/1.12 145 product(e_2,e_1,e_1) | product(e_2,e_1,e_2) | product(e_3,e_3,e_1) | product(e_1,e_2,e_1) | product(e_1,e_2,e_2). [resolve(89,c,64,c)].
% 0.84/1.12 153 product(e_1,e_3,e_1) | product(e_1,e_3,e_2) | product(e_3,e_3,e_1) | product(e_2,e_2,e_3). [resolve(93,d,24,a)].
% 0.84/1.12 178 product(e_2,e_3,e_1) | product(e_2,e_2,e_1) | product(e_2,e_2,e_2). [resolve(105,b,66,c),merge(d),merge(e)].
% 0.84/1.12 217 product(e_3,e_1,e_1) | product(e_3,e_1,e_2) | product(e_2,e_2,e_3) | product(e_1,e_1,e_3). [resolve(121,a,24,a)].
% 0.84/1.12 233 product(e_2,e_2,e_1) | product(e_2,e_2,e_2) | product(e_1,e_1,e_2). [resolve(130,c,178,a),merge(d),merge(e)].
% 0.84/1.12 234 product(e_2,e_2,e_1) | product(e_1,e_1,e_2) | -product(e_1,e_2,e_2). [resolve(233,b,21,b)].
% 0.84/1.12 235 product(e_2,e_2,e_1) | product(e_1,e_1,e_2) | -product(e_2,e_1,e_2). [resolve(233,b,18,b)].
% 0.84/1.12 238 product(e_2,e_2,e_1) | product(e_1,e_1,e_2) | product(e_1,e_2,e_1) | product(e_1,e_1,e_1). [resolve(234,c,110,b),merge(e)].
% 0.84/1.12 239 product(e_2,e_2,e_1) | product(e_1,e_1,e_2) | product(e_2,e_1,e_1) | product(e_1,e_1,e_1). [resolve(235,c,107,b),merge(e)].
% 0.84/1.12 248 product(e_2,e_2,e_1) | product(e_2,e_2,e_2) | product(e_1,e_1,e_3). [resolve(131,c,178,a),merge(d),merge(e)].
% 0.84/1.12 249 product(e_2,e_2,e_1) | product(e_1,e_1,e_3) | -product(e_1,e_2,e_2). [resolve(248,b,21,b)].
% 0.84/1.12 250 product(e_2,e_2,e_1) | product(e_1,e_1,e_3) | -product(e_2,e_1,e_2). [resolve(248,b,18,b)].
% 0.84/1.12 273 product(e_1,e_3,e_1) | product(e_1,e_3,e_2) | product(e_2,e_2,e_3) | product(e_1,e_1,e_3). [resolve(153,c,24,a)].
% 0.84/1.12 305 product(e_3,e_1,e_1) | product(e_2,e_2,e_3) | product(e_1,e_1,e_3) | -product(e_1,e_1,e_2). [resolve(217,b,22,b)].
% 0.84/1.12 314 product(e_1,e_1,e_2) | product(e_1,e_2,e_1) | product(e_1,e_1,e_1). [resolve(238,a,24,a),merge(d)].
% 0.84/1.12 315 product(e_1,e_1,e_2) | product(e_1,e_1,e_1) | -product(e_2,e_1,A) | product(A,e_1,e_2). [resolve(314,b,13,b)].
% 0.84/1.12 317 product(e_1,e_1,e_2) | product(e_1,e_1,e_1) | -product(e_2,e_1,e_1). [factor(315,a,d)].
% 0.84/1.12 318 product(e_1,e_1,e_2) | product(e_2,e_1,e_1) | product(e_1,e_1,e_1). [resolve(239,a,24,a),merge(d)].
% 0.84/1.12 319 product(e_1,e_1,e_2) | product(e_1,e_1,e_1). [resolve(318,b,317,c),merge(c),merge(d)].
% 0.84/1.12 322 product(e_1,e_1,e_1) | product(e_2,e_2,e_1). [resolve(319,a,24,a)].
% 0.84/1.12 328 product(e_1,e_1,e_1) | -product(e_2,e_2,A) | product(e_1,A,e_2). [resolve(322,b,13,a)].
% 0.84/1.12 329 product(e_2,e_1,e_1) | product(e_2,e_1,e_2) | product(e_1,e_2,e_1) | product(e_1,e_2,e_2) | product(e_1,e_1,e_3). [resolve(145,c,24,a)].
% 0.84/1.12 351 product(e_1,e_3,e_1) | product(e_1,e_3,e_2) | product(e_1,e_1,e_3) | product(e_1,e_1,e_1). [resolve(273,c,328,b),merge(e)].
% 0.84/1.12 387 product(e_3,e_1,e_1) | product(e_2,e_2,e_3) | product(e_1,e_1,e_3) | product(e_1,e_1,e_1). [resolve(305,d,319,a)].
% 0.84/1.12 426 product(e_1,e_3,e_1) | product(e_1,e_1,e_3) | product(e_1,e_1,e_1) | -product(e_1,e_1,e_2). [resolve(351,b,19,b)].
% 0.84/1.12 472 product(e_1,e_3,e_1) | product(e_1,e_1,e_3) | product(e_1,e_1,e_1). [resolve(426,d,319,a),merge(d)].
% 0.84/1.12 474 product(e_1,e_1,e_3) | product(e_1,e_1,e_1) | -product(e_3,e_1,A) | product(A,e_1,e_3). [resolve(472,a,13,b)].
% 0.84/1.12 476 product(e_1,e_1,e_3) | product(e_1,e_1,e_1) | -product(e_3,e_1,e_1). [factor(474,a,d)].
% 0.84/1.12 477 product(e_1,e_1,e_3) | product(e_1,e_1,e_1) | product(e_2,e_2,e_3). [resolve(476,c,387,a),merge(d),merge(e)].
% 0.84/1.12 486 product(e_1,e_1,e_3) | product(e_1,e_1,e_1) | -product(e_2,e_2,e_1). [resolve(477,c,16,b)].
% 0.84/1.12 515 product(e_1,e_1,e_3) | product(e_1,e_1,e_1). [resolve(486,c,322,b),merge(c)].
% 0.84/1.12 523 product(e_1,e_1,e_1) | -product(e_1,e_1,e_2). [resolve(515,a,17,b)].
% 0.84/1.12 538 product(e_1,e_1,e_1). [resolve(523,b,319,a),merge(b)].
% 0.84/1.12 543 -product(e_2,e_1,e_1). [ur(21,a,538,a)].
% 0.84/1.12 545 -product(e_1,e_2,e_1). [ur(18,a,538,a)].
% 0.84/1.12 546 -product(e_1,e_1,e_3). [ur(16,a,538,a)].
% 0.84/1.12 547 -product(e_1,e_1,e_2). [ur(15,a,538,a)].
% 0.84/1.12 638 product(e_2,e_1,e_2) | product(e_1,e_2,e_2). [back_unit_del(329),unit_del(a,543),unit_del(c,545),unit_del(e,546)].
% 0.84/1.12 712 product(e_2,e_2,e_1) | -product(e_2,e_1,e_2). [back_unit_del(250),unit_del(b,546)].
% 0.84/1.12 713 product(e_2,e_2,e_1) | -product(e_1,e_2,e_2). [back_unit_del(249),unit_del(b,546)].
% 0.84/1.12 744 -product(e_2,e_2,e_1). [ur(24,b,547,a)].
% 0.84/1.12 746 -product(e_1,e_2,e_2). [back_unit_del(713),unit_del(a,744)].
% 0.84/1.12 747 -product(e_2,e_1,e_2). [back_unit_del(712),unit_del(a,744)].
% 0.84/1.12 767 $F. [back_unit_del(638),unit_del(a,747),unit_del(b,746)].
% 0.84/1.12
% 0.84/1.12 % SZS output end Refutation
% 0.84/1.12 ============================== end of proof ==========================
% 0.84/1.12
% 0.84/1.12 ============================== STATISTICS ============================
% 0.84/1.12
% 0.84/1.12 Given=288. Generated=1842. Kept=757. proofs=1.
% 0.84/1.12 Usable=45. Sos=95. Demods=0. Limbo=21, Disabled=619. Hints=0.
% 0.84/1.12 Megabytes=0.51.
% 0.84/1.12 User_CPU=0.09, System_CPU=0.01, Wall_clock=0.
% 0.84/1.12
% 0.84/1.12 ============================== end of statistics =====================
% 0.84/1.12
% 0.84/1.12 ============================== end of search =========================
% 0.84/1.12
% 0.84/1.12 THEOREM PROVED
% 0.84/1.12 % SZS status Unsatisfiable
% 0.84/1.12
% 0.84/1.12 Exiting with 1 proof.
% 0.84/1.12
% 0.84/1.12 Process 25894 exit (max_proofs) Tue Jun 14 12:25:37 2022
% 0.84/1.12 Prover9 interrupted
%------------------------------------------------------------------------------