TSTP Solution File: GRP125-2.005 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP125-2.005 : 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 11:17:24 EDT 2022
% Result : Unsatisfiable 0.71s 1.03s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP125-2.005 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.12 % 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 13:17:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.97 ============================== Prover9 ===============================
% 0.42/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.97 Process 2428 was started by sandbox on n012.cluster.edu,
% 0.42/0.97 Mon Jun 13 13:17:41 2022
% 0.42/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2274_n012.cluster.edu".
% 0.42/0.97 ============================== end of head ===========================
% 0.42/0.97
% 0.42/0.97 ============================== INPUT =================================
% 0.42/0.97
% 0.42/0.97 % Reading from file /tmp/Prover9_2274_n012.cluster.edu
% 0.42/0.97
% 0.42/0.97 set(prolog_style_variables).
% 0.42/0.97 set(auto2).
% 0.42/0.97 % set(auto2) -> set(auto).
% 0.42/0.97 % set(auto) -> set(auto_inference).
% 0.42/0.97 % set(auto) -> set(auto_setup).
% 0.42/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.97 % set(auto) -> set(auto_limits).
% 0.42/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.97 % set(auto) -> set(auto_denials).
% 0.42/0.97 % set(auto) -> set(auto_process).
% 0.42/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.97 % set(auto2) -> assign(stats, some).
% 0.42/0.97 % set(auto2) -> clear(echo_input).
% 0.42/0.97 % set(auto2) -> set(quiet).
% 0.42/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.97 % set(auto2) -> clear(print_given).
% 0.42/0.97 assign(lrs_ticks,-1).
% 0.42/0.97 assign(sos_limit,10000).
% 0.42/0.97 assign(order,kbo).
% 0.42/0.97 set(lex_order_vars).
% 0.42/0.97 clear(print_given).
% 0.42/0.97
% 0.42/0.97 % formulas(sos). % not echoed (46 formulas)
% 0.42/0.97
% 0.42/0.97 ============================== end of input ==========================
% 0.42/0.97
% 0.42/0.97 % From the command line: assign(max_seconds, 300).
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.97
% 0.42/0.97 % Formulas that are not ordinary clauses:
% 0.42/0.97
% 0.42/0.97 ============================== end of process non-clausal formulas ===
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.97
% 0.42/0.97 ============================== PREDICATE ELIMINATION =================
% 0.42/0.97 1 -product(A,e_1,B) | -next(A,C) | -greater(B,C) # label(no_redundancy) # label(axiom). [assumption].
% 0.42/0.97 2 next(e_1,e_2) # label(e_1_then_e_2) # label(axiom). [assumption].
% 0.42/0.97 3 next(e_2,e_3) # label(e_2_then_e_3) # label(axiom). [assumption].
% 0.42/0.97 4 next(e_3,e_4) # label(e_3_then_e_4) # label(axiom). [assumption].
% 0.42/0.97 5 next(e_4,e_5) # label(e_4_then_e_5) # label(axiom). [assumption].
% 0.42/0.97 Derived: -product(e_1,e_1,A) | -greater(A,e_2). [resolve(1,b,2,a)].
% 0.42/0.97 Derived: -product(e_2,e_1,A) | -greater(A,e_3). [resolve(1,b,3,a)].
% 0.42/0.97 Derived: -product(e_3,e_1,A) | -greater(A,e_4). [resolve(1,b,4,a)].
% 0.42/0.97 Derived: -product(e_4,e_1,A) | -greater(A,e_5). [resolve(1,b,5,a)].
% 0.42/0.97 6 -product(e_1,e_1,A) | -greater(A,e_2). [resolve(1,b,2,a)].
% 0.42/0.97 7 greater(e_2,e_1) # label(e_2_greater_e_1) # label(axiom). [assumption].
% 0.42/0.97 8 greater(e_3,e_1) # label(e_3_greater_e_1) # label(axiom). [assumption].
% 0.42/0.97 9 greater(e_4,e_1) # label(e_4_greater_e_1) # label(axiom). [assumption].
% 0.42/0.97 10 greater(e_5,e_1) # label(e_5_greater_e_1) # label(axiom). [assumption].
% 0.42/0.97 11 greater(e_3,e_2) # label(e_3_greater_e_2) # label(axiom). [assumption].
% 0.42/0.97 12 greater(e_4,e_2) # label(e_4_greater_e_2) # label(axiom). [assumption].
% 0.42/0.97 13 greater(e_5,e_2) # label(e_5_greater_e_2) # label(axiom). [assumption].
% 0.42/0.97 14 greater(e_4,e_3) # label(e_4_greater_e_3) # label(axiom). [assumption].
% 0.42/0.97 15 greater(e_5,e_3) # label(e_5_greater_e_3) # label(axiom). [assumption].
% 0.42/0.97 16 greater(e_5,e_4) # label(e_5_greater_e_4) # label(axiom). [assumption].
% 0.42/0.97 Derived: -product(e_1,e_1,e_3). [resolve(6,b,11,a)].
% 0.42/0.97 Derived: -product(e_1,e_1,e_4). [resolve(6,b,12,a)].
% 0.42/0.97 Derived: -product(e_1,e_1,e_5). [resolve(6,b,13,a)].
% 0.42/0.97 17 -product(e_2,e_1,A) | -greater(A,e_3). [resolve(1,b,3,a)].
% 0.42/0.97 Derived: -product(e_2,e_1,e_4). [resolve(17,b,14,a)].
% 0.42/0.97 Derived: -product(e_2,e_1,e_5). [resolve(17,b,15,a)].
% 0.42/0.97 18 -product(e_3,e_1,A) | -greater(A,e_4). [resolve(1,b,4,a)].
% 0.42/0.97 Derived: -product(e_3,e_1,e_5). [resolve(18,b,16,a)].
% 0.42/0.97 19 -product(e_4,e_1,A) | -greater(A,e_5). [resolve(1,b,5,a)].
% 0.42/0.97 20 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.42/0.97 21 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.42/0.97 22 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.42/0.97 23 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.42/0.97 24 -equalish(e_1,e_5) # label(e_1_is_not_e_5) # label(axiom). [assumption].
% 0.42/0.97 25 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.42/0.97 26 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.42/0.97 27 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.42/0.97 28 -equalish(e_2,e_5) # label(e_2_is_not_e_5) # label(axiom). [assumption].
% 0.42/0.97 29 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.42/0.97 30 -equalish(e_3,e_2) # label(e_3_is_not_e_2) # label(axiom). [assumption].
% 0.42/0.97 31 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.42/0.97 32 -equalish(e_3,e_5) # label(e_3_is_not_e_5) # label(axiom). [assumption].
% 0.42/0.97 33 -equalish(e_4,e_1) # label(e_4_is_not_e_1) # label(axiom). [assumption].
% 0.42/0.97 34 -equalish(e_4,e_2) # label(e_4_is_not_e_2) # label(axiom). [assumption].
% 0.42/0.97 35 -equalish(e_4,e_3) # label(e_4_is_not_e_3) # label(axiom). [assumption].
% 0.42/0.97 36 -equalish(e_4,e_5) # label(e_4_is_not_e_5) # label(axiom). [assumption].
% 0.42/0.97 37 -equalish(e_5,e_1) # label(e_5_is_not_e_1) # label(axiom). [assumption].
% 0.42/0.97 38 -equalish(e_5,e_2) # label(e_5_is_not_e_2) # label(axiom). [assumption].
% 0.42/0.97 39 -equalish(e_5,e_3) # label(e_5_is_not_e_3) # label(axiom). [assumption].
% 0.42/0.97 40 -equalish(e_5,e_4) # label(e_5_is_not_e_4) # label(axiom). [assumption].
% 0.42/0.97 Derived: -product(A,B,e_1) | -product(A,B,e_2). [resolve(20,c,21,a)].
% 0.42/0.97 Derived: -product(A,B,e_1) | -product(A,B,e_3). [resolve(20,c,22,a)].
% 0.42/0.97 Derived: -product(A,B,e_1) | -product(A,B,e_4). [resolve(20,c,23,a)].
% 0.42/0.97 Derived: -product(A,B,e_1) | -product(A,B,e_5). [resolve(20,c,24,a)].
% 0.42/0.97 Derived: -product(A,B,e_2) | -product(A,B,e_3). [resolve(20,c,26,a)].
% 0.42/0.97 Derived: -product(A,B,e_2) | -product(A,B,e_4). [resolve(20,c,27,a)].
% 0.42/0.97 Derived: -product(A,B,e_2) | -product(A,B,e_5). [resolve(20,c,28,a)].
% 0.42/0.97 Derived: -product(A,B,e_3) | -product(A,B,e_4). [resolve(20,c,31,a)].
% 0.42/0.97 Derived: -product(A,B,e_3) | -product(A,B,e_5). [resolve(20,c,32,a)].
% 0.42/0.97 Derived: -product(A,B,e_4) | -product(A,B,e_5). [resolve(20,c,36,a)].
% 0.42/0.97 41 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.42/0.97 Derived: -product(A,e_1,B) | -product(A,e_2,B). [resolve(41,c,21,a)].
% 0.42/0.97 Derived: -product(A,e_1,B) | -product(A,e_3,B). [resolve(41,c,22,a)].
% 0.42/0.97 Derived: -product(A,e_1,B) | -product(A,e_4,B). [resolve(41,c,23,a)].
% 0.42/0.97 Derived: -product(A,e_1,B) | -product(A,e_5,B). [resolve(41,c,24,a)].
% 0.42/0.97 Derived: -product(A,e_2,B) | -product(A,e_3,B). [resolve(41,c,26,a)].
% 0.42/0.97 Derived: -product(A,e_2,B) | -product(A,e_4,B). [resolve(41,c,27,a)].
% 0.42/0.97 Derived: -product(A,e_2,B) | -product(A,e_5,B). [resolve(41,c,28,a)].
% 0.42/0.97 Derived: -product(A,e_3,B) | -product(A,e_4,B). [resolve(41,c,31,a)].
% 0.42/0.97 Derived: -product(A,e_3,B) | -product(A,e_5,B). [resolve(41,c,32,a)].
% 0.42/0.97 Derived: -product(A,e_4,B) | -product(A,e_5,B). [resolve(41,c,36,a)].
% 0.42/0.97 42 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.42/0.97 Derived: -product(e_1,A,B) | -product(e_2,A,B). [resolve(42,c,21,a)].
% 0.42/0.97 Derived: -product(e_1,A,B) | -product(e_3,A,B). [resolve(42,c,22,a)].
% 0.42/0.97 Derived: -product(e_1,A,B) | -product(e_4,A,B). [resolve(42,c,23,a)].
% 0.42/0.97 Derived: -product(e_1,A,B) | -product(e_5,A,B). [resolve(42,c,24,a)].
% 0.42/0.97 Derived: -product(e_2,A,B) | -product(e_3,A,B). [resolve(42,c,26,a)].
% 0.42/0.97 Derived: -product(e_2,A,B) | -product(e_4,A,B). [resolve(42,c,27,a)].
% 0.42/0.97 Derived: -product(e_2,A,B) | -product(e_5,A,B). [resolve(42,c,28,a)].
% 0.42/0.97 Derived: -product(e_3,A,B) | -product(e_4,A,B). [resolve(42,c,31,a)].
% 0.71/1.03 Derived: -product(e_3,A,B) | -product(e_5,A,B). [resolve(42,c,32,a)].
% 0.71/1.03 Derived: -product(e_4,A,B) | -product(e_5,A,B). [resolve(42,c,36,a)].
% 0.71/1.03
% 0.71/1.03 ============================== end predicate elimination =============
% 0.71/1.03
% 0.71/1.03 Auto_denials: (non-Horn, no changes).
% 0.71/1.03
% 0.71/1.03 Term ordering decisions:
% 0.71/1.03 Function symbol KB weights: e_1=1. e_2=1. e_3=1. e_4=1. e_5=1.
% 0.71/1.03
% 0.71/1.03 ============================== end of process initial clauses ========
% 0.71/1.03
% 0.71/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.03
% 0.71/1.03 ============================== end of clauses for search =============
% 0.71/1.03
% 0.71/1.03 ============================== SEARCH ================================
% 0.71/1.03
% 0.71/1.03 % Starting search at 0.02 seconds.
% 0.71/1.03
% 0.71/1.03 ============================== PROOF =================================
% 0.71/1.03 % SZS status Unsatisfiable
% 0.71/1.03 % SZS output start Refutation
% 0.71/1.03
% 0.71/1.03 % Proof 1 at 0.07 (+ 0.00) seconds.
% 0.71/1.03 % Length of proof is 156.
% 0.71/1.03 % Level of proof is 17.
% 0.71/1.03 % Maximum clause weight is 24.000.
% 0.71/1.03 % Given clauses 322.
% 0.71/1.03
% 0.71/1.03 1 -product(A,e_1,B) | -next(A,C) | -greater(B,C) # label(no_redundancy) # label(axiom). [assumption].
% 0.71/1.03 3 next(e_2,e_3) # label(e_2_then_e_3) # label(axiom). [assumption].
% 0.71/1.03 4 next(e_3,e_4) # label(e_3_then_e_4) # label(axiom). [assumption].
% 0.71/1.03 14 greater(e_4,e_3) # label(e_4_greater_e_3) # label(axiom). [assumption].
% 0.71/1.03 15 greater(e_5,e_3) # label(e_5_greater_e_3) # label(axiom). [assumption].
% 0.71/1.03 16 greater(e_5,e_4) # label(e_5_greater_e_4) # label(axiom). [assumption].
% 0.71/1.03 17 -product(e_2,e_1,A) | -greater(A,e_3). [resolve(1,b,3,a)].
% 0.71/1.03 18 -product(e_3,e_1,A) | -greater(A,e_4). [resolve(1,b,4,a)].
% 0.71/1.03 20 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.71/1.03 21 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.71/1.03 22 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.71/1.03 23 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.71/1.03 24 -equalish(e_1,e_5) # label(e_1_is_not_e_5) # label(axiom). [assumption].
% 0.71/1.03 26 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.71/1.03 27 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.71/1.03 28 -equalish(e_2,e_5) # label(e_2_is_not_e_5) # label(axiom). [assumption].
% 0.71/1.03 31 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.71/1.03 32 -equalish(e_3,e_5) # label(e_3_is_not_e_5) # label(axiom). [assumption].
% 0.71/1.03 36 -equalish(e_4,e_5) # label(e_4_is_not_e_5) # label(axiom). [assumption].
% 0.71/1.03 41 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.71/1.03 42 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.71/1.03 43 group_element(e_1) # label(element_1) # label(axiom). [assumption].
% 0.71/1.03 44 group_element(e_2) # label(element_2) # label(axiom). [assumption].
% 0.71/1.03 45 group_element(e_3) # label(element_3) # label(axiom). [assumption].
% 0.71/1.03 46 group_element(e_4) # label(element_4) # label(axiom). [assumption].
% 0.71/1.03 47 group_element(e_5) # label(element_5) # label(axiom). [assumption].
% 0.71/1.03 48 product(A,A,A) # label(product_idempotence) # label(axiom). [assumption].
% 0.71/1.03 49 -product(A,B,C) | -product(B,A,D) | product(C,D,A) # label(qg3) # label(negated_conjecture). [assumption].
% 0.71/1.03 50 -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) | product(A,B,e_5) # label(product_total_function1) # label(axiom). [assumption].
% 0.71/1.03 54 -product(e_2,e_1,e_4). [resolve(17,b,14,a)].
% 0.71/1.03 55 -product(e_2,e_1,e_5). [resolve(17,b,15,a)].
% 0.71/1.03 56 -product(e_3,e_1,e_5). [resolve(18,b,16,a)].
% 0.71/1.03 58 -product(A,B,e_1) | -product(A,B,e_3). [resolve(20,c,22,a)].
% 0.71/1.03 59 -product(A,B,e_1) | -product(A,B,e_4). [resolve(20,c,23,a)].
% 0.71/1.03 60 -product(A,B,e_1) | -product(A,B,e_5). [resolve(20,c,24,a)].
% 0.71/1.03 64 -product(A,B,e_3) | -product(A,B,e_4). [resolve(20,c,31,a)].
% 0.71/1.03 66 -product(A,B,e_4) | -product(A,B,e_5). [resolve(20,c,36,a)].
% 0.71/1.03 67 -product(A,e_1,B) | -product(A,e_2,B). [resolve(41,c,21,a)].
% 0.71/1.03 68 -product(A,e_1,B) | -product(A,e_3,B). [resolve(41,c,22,a)].
% 0.71/1.03 69 -product(A,e_1,B) | -product(A,e_4,B). [resolve(41,c,23,a)].
% 0.71/1.03 70 -product(A,e_1,B) | -product(A,e_5,B). [resolve(41,c,24,a)].
% 0.71/1.03 71 -product(A,e_2,B) | -product(A,e_3,B). [resolve(41,c,26,a)].
% 0.71/1.03 72 -product(A,e_2,B) | -product(A,e_4,B). [resolve(41,c,27,a)].
% 0.71/1.03 73 -product(A,e_2,B) | -product(A,e_5,B). [resolve(41,c,28,a)].
% 0.71/1.03 74 -product(A,e_3,B) | -product(A,e_4,B). [resolve(41,c,31,a)].
% 0.71/1.03 75 -product(A,e_3,B) | -product(A,e_5,B). [resolve(41,c,32,a)].
% 0.71/1.03 76 -product(A,e_4,B) | -product(A,e_5,B). [resolve(41,c,36,a)].
% 0.71/1.03 77 -product(e_1,A,B) | -product(e_2,A,B). [resolve(42,c,21,a)].
% 0.71/1.03 78 -product(e_1,A,B) | -product(e_3,A,B). [resolve(42,c,22,a)].
% 0.71/1.03 79 -product(e_1,A,B) | -product(e_4,A,B). [resolve(42,c,23,a)].
% 0.71/1.03 80 -product(e_1,A,B) | -product(e_5,A,B). [resolve(42,c,24,a)].
% 0.71/1.03 82 -product(e_2,A,B) | -product(e_4,A,B). [resolve(42,c,27,a)].
% 0.71/1.03 83 -product(e_2,A,B) | -product(e_5,A,B). [resolve(42,c,28,a)].
% 0.71/1.03 84 -product(e_3,A,B) | -product(e_4,A,B). [resolve(42,c,31,a)].
% 0.71/1.03 85 -product(e_3,A,B) | -product(e_5,A,B). [resolve(42,c,32,a)].
% 0.71/1.03 86 -product(e_4,A,B) | -product(e_5,A,B). [resolve(42,c,36,a)].
% 0.71/1.03 91 -group_element(A) | product(e_5,A,e_1) | product(e_5,A,e_2) | product(e_5,A,e_3) | product(e_5,A,e_4) | product(e_5,A,e_5). [resolve(50,a,47,a)].
% 0.71/1.03 92 -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) | product(e_4,A,e_5). [resolve(50,a,46,a)].
% 0.71/1.03 93 -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) | product(e_3,A,e_5). [resolve(50,a,45,a)].
% 0.71/1.03 94 -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) | product(e_2,A,e_5). [resolve(50,a,44,a)].
% 0.71/1.03 95 -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) | product(e_1,A,e_5). [resolve(50,a,43,a)].
% 0.71/1.03 103 -product(e_3,e_3,e_1). [resolve(58,b,48,a)].
% 0.71/1.03 105 -product(e_5,e_5,e_1). [resolve(60,b,48,a)].
% 0.71/1.03 112 -product(e_4,e_4,e_3). [resolve(64,b,48,a)].
% 0.71/1.03 116 -product(e_5,e_5,e_4). [resolve(66,b,48,a)].
% 0.71/1.03 118 -product(e_2,e_1,e_2). [resolve(67,b,48,a)].
% 0.71/1.03 119 -product(e_1,e_2,e_1). [ur(67,a,48,a)].
% 0.71/1.03 120 -product(e_3,e_1,e_3). [resolve(68,b,48,a)].
% 0.71/1.03 121 -product(e_1,e_3,e_1). [ur(68,a,48,a)].
% 0.71/1.03 122 -product(e_4,e_1,e_4). [resolve(69,b,48,a)].
% 0.71/1.03 123 -product(e_1,e_4,e_1). [ur(69,a,48,a)].
% 0.71/1.03 124 -product(e_5,e_1,e_5). [resolve(70,b,48,a)].
% 0.71/1.03 128 -product(e_4,e_2,e_4). [resolve(72,b,48,a)].
% 0.71/1.03 129 -product(e_2,e_4,e_2). [ur(72,a,48,a)].
% 0.71/1.03 132 -product(e_4,e_3,e_4). [resolve(74,b,48,a)].
% 0.71/1.03 135 -product(e_3,e_5,e_3). [ur(75,a,48,a)].
% 0.71/1.03 136 -product(e_5,e_4,e_5). [resolve(76,b,48,a)].
% 0.71/1.03 138 -product(e_1,e_2,e_2). [resolve(77,b,48,a)].
% 0.71/1.03 139 -product(e_2,e_1,e_1). [ur(77,a,48,a)].
% 0.71/1.03 140 -product(e_1,e_3,e_3). [resolve(78,b,48,a)].
% 0.71/1.03 141 -product(e_3,e_1,e_1). [ur(78,a,48,a)].
% 0.71/1.03 142 -product(e_1,e_4,e_4). [resolve(79,b,48,a)].
% 0.71/1.03 143 -product(e_4,e_1,e_1). [ur(79,a,48,a)].
% 0.71/1.03 145 -product(e_5,e_1,e_1). [ur(80,a,48,a)].
% 0.71/1.03 148 -product(e_2,e_4,e_4). [resolve(82,b,48,a)].
% 0.71/1.03 149 -product(e_4,e_2,e_2). [ur(82,a,48,a)].
% 0.71/1.03 153 -product(e_4,e_3,e_3). [ur(84,a,48,a)].
% 0.71/1.03 154 -product(e_3,e_5,e_5). [resolve(85,b,48,a)].
% 0.71/1.03 157 -product(e_5,e_4,e_4). [ur(86,a,48,a)].
% 0.71/1.03 158 product(e_5,e_4,e_1) | product(e_5,e_4,e_2) | product(e_5,e_4,e_3). [resolve(91,a,46,a),unit_del(d,157),unit_del(e,136)].
% 0.71/1.03 161 product(e_5,e_1,e_2) | product(e_5,e_1,e_3) | product(e_5,e_1,e_4). [resolve(91,a,43,a),unit_del(a,145),unit_del(e,124)].
% 0.71/1.03 163 product(e_5,e_4,e_1) | product(e_5,e_4,e_2) | -product(e_1,e_4,e_3). [resolve(158,c,80,b)].
% 0.71/1.03 175 product(e_4,e_3,e_1) | product(e_4,e_3,e_2) | product(e_4,e_3,e_5). [resolve(92,a,45,a),unit_del(c,153),unit_del(d,132)].
% 0.71/1.03 176 product(e_4,e_2,e_1) | product(e_4,e_2,e_3) | product(e_4,e_2,e_5). [resolve(92,a,44,a),unit_del(b,149),unit_del(d,128)].
% 0.71/1.03 177 product(e_4,e_1,e_2) | product(e_4,e_1,e_3) | product(e_4,e_1,e_5). [resolve(92,a,43,a),unit_del(a,143),unit_del(d,122)].
% 0.71/1.03 183 product(e_5,e_1,e_2) | product(e_5,e_1,e_3) | -product(e_3,e_1,e_4). [resolve(161,c,85,b)].
% 0.71/1.03 186 product(e_3,e_5,e_1) | product(e_3,e_5,e_2) | product(e_3,e_5,e_4). [resolve(93,a,47,a),unit_del(c,135),unit_del(e,154)].
% 0.71/1.03 189 product(e_3,e_1,e_2) | product(e_3,e_1,e_4). [resolve(93,a,43,a),unit_del(a,141),unit_del(c,120),unit_del(e,56)].
% 0.71/1.03 191 product(e_3,e_1,e_2) | -product(e_1,e_3,A) | product(e_4,A,e_3). [resolve(189,b,49,a)].
% 0.71/1.03 193 product(e_2,e_4,e_1) | product(e_2,e_4,e_3) | product(e_2,e_4,e_5). [resolve(94,a,46,a),unit_del(b,129),unit_del(d,148)].
% 0.71/1.03 195 product(e_2,e_1,e_3). [resolve(94,a,43,a),unit_del(a,139),unit_del(b,118),unit_del(d,54),unit_del(e,55)].
% 0.71/1.03 196 -product(e_1,e_2,A) | product(A,e_3,e_1). [resolve(195,a,49,b)].
% 0.71/1.03 197 -product(e_1,e_2,A) | product(e_3,A,e_2). [resolve(195,a,49,a)].
% 0.71/1.03 198 -product(e_5,e_1,e_3). [ur(83,a,195,a)].
% 0.71/1.03 199 -product(e_4,e_1,e_3). [ur(82,a,195,a)].
% 0.71/1.03 201 -product(e_2,e_4,e_3). [ur(69,a,195,a)].
% 0.71/1.03 202 -product(e_1,e_2,e_3). [ur(49,b,195,a,c,103,a)].
% 0.71/1.03 205 product(e_5,e_1,e_2) | -product(e_3,e_1,e_4). [back_unit_del(183),unit_del(b,198)].
% 0.71/1.03 207 product(e_4,e_1,e_2) | product(e_4,e_1,e_5). [back_unit_del(177),unit_del(b,199)].
% 0.71/1.03 209 product(e_2,e_4,e_1) | product(e_2,e_4,e_5). [back_unit_del(193),unit_del(b,201)].
% 0.71/1.03 210 product(e_5,e_1,e_2) | product(e_3,e_1,e_2). [resolve(205,b,189,b)].
% 0.71/1.03 212 product(e_1,e_4,e_2) | product(e_1,e_4,e_3) | product(e_1,e_4,e_5). [resolve(95,a,46,a),unit_del(a,123),unit_del(d,142)].
% 0.71/1.03 213 product(e_1,e_3,e_2) | product(e_1,e_3,e_4) | product(e_1,e_3,e_5). [resolve(95,a,45,a),unit_del(a,121),unit_del(c,140)].
% 0.71/1.03 214 product(e_1,e_2,e_4) | product(e_1,e_2,e_5). [resolve(95,a,44,a),unit_del(a,119),unit_del(b,138),unit_del(c,202)].
% 0.71/1.03 215 product(e_4,e_1,e_2) | -product(e_1,e_4,A) | product(A,e_5,e_1). [resolve(207,b,49,b)].
% 0.71/1.03 223 product(e_2,e_4,e_1) | -product(e_4,e_2,A) | product(A,e_5,e_4). [resolve(209,b,49,b)].
% 0.71/1.03 225 product(e_3,e_1,e_2) | -product(e_4,e_1,e_2). [resolve(210,a,86,b)].
% 0.71/1.03 228 product(e_1,e_2,e_4) | product(e_3,e_5,e_2). [resolve(214,b,197,a)].
% 0.71/1.03 229 product(e_1,e_2,e_4) | product(e_5,e_3,e_1). [resolve(214,b,196,a)].
% 0.71/1.03 234 product(e_1,e_2,e_4) | -product(e_3,e_1,e_2). [resolve(228,b,70,b)].
% 0.71/1.03 238 product(e_1,e_2,e_4) | -product(e_4,e_3,e_1). [resolve(229,b,86,b)].
% 0.71/1.03 252 product(e_4,e_3,e_1) | product(e_4,e_3,e_2) | -product(e_4,e_1,e_5). [resolve(175,c,68,b)].
% 0.71/1.03 264 product(e_3,e_5,e_1) | product(e_3,e_5,e_2) | -product(e_3,e_1,e_4). [resolve(186,c,70,b)].
% 0.71/1.03 292 product(e_1,e_3,e_2) | product(e_1,e_3,e_4) | -product(e_1,e_2,e_5). [resolve(213,c,71,b)].
% 0.71/1.03 296 product(e_4,e_1,e_2) | product(e_1,e_4,e_2) | product(e_1,e_4,e_3). [resolve(215,b,212,c),unit_del(b,105)].
% 0.71/1.03 298 product(e_2,e_4,e_1) | product(e_4,e_2,e_1) | product(e_4,e_2,e_3). [resolve(223,b,176,c),unit_del(b,116)].
% 0.71/1.03 309 product(e_4,e_3,e_1) | product(e_4,e_3,e_2) | product(e_4,e_1,e_2). [resolve(252,c,207,b)].
% 0.71/1.03 326 product(e_3,e_5,e_1) | product(e_3,e_5,e_2) | product(e_3,e_1,e_2). [resolve(264,c,189,b)].
% 0.71/1.03 350 product(e_1,e_3,e_2) | product(e_1,e_3,e_4) | product(e_1,e_2,e_4). [resolve(292,c,214,b)].
% 0.71/1.03 351 product(e_1,e_4,e_2) | product(e_1,e_4,e_3) | product(e_3,e_1,e_2). [resolve(296,a,225,b)].
% 0.71/1.03 352 product(e_1,e_4,e_2) | product(e_1,e_4,e_3) | -product(e_3,e_1,e_2). [resolve(296,a,84,b)].
% 0.71/1.03 365 product(e_2,e_4,e_1) | product(e_4,e_2,e_1) | product(e_3,e_5,e_4). [resolve(298,c,223,b),merge(c)].
% 0.71/1.03 371 product(e_4,e_3,e_1) | product(e_4,e_1,e_2) | -product(e_1,e_3,e_2). [resolve(309,b,79,b)].
% 0.71/1.03 395 product(e_3,e_5,e_1) | product(e_3,e_1,e_2) | -product(e_3,e_4,e_2). [resolve(326,b,76,b)].
% 0.71/1.03 420 product(e_1,e_3,e_2) | product(e_1,e_2,e_4) | product(e_3,e_1,e_2). [resolve(350,b,191,b),unit_del(d,112)].
% 0.71/1.03 426 product(e_1,e_4,e_2) | product(e_1,e_4,e_3). [resolve(352,c,351,c),merge(c),merge(d)].
% 0.71/1.03 429 product(e_1,e_4,e_2) | product(e_5,e_4,e_1) | product(e_5,e_4,e_2). [resolve(426,b,163,c)].
% 0.71/1.03 458 product(e_2,e_4,e_1) | product(e_3,e_5,e_4) | product(e_1,e_5,e_4). [resolve(365,b,223,b),merge(c)].
% 0.71/1.03 473 product(e_1,e_3,e_2) | product(e_1,e_2,e_4). [resolve(420,c,234,b),merge(c)].
% 0.71/1.03 474 product(e_1,e_2,e_4) | product(e_4,e_3,e_1) | product(e_4,e_1,e_2). [resolve(473,a,371,c)].
% 0.71/1.03 496 product(e_1,e_4,e_2) | product(e_5,e_4,e_1) | -product(e_3,e_4,e_2). [resolve(429,c,85,b)].
% 0.71/1.03 571 product(e_2,e_4,e_1) | product(e_1,e_5,e_4) | -product(e_3,e_5,e_1). [resolve(458,b,59,b)].
% 0.71/1.03 586 product(e_1,e_2,e_4) | product(e_4,e_1,e_2). [resolve(474,b,238,b),merge(c)].
% 0.71/1.03 590 product(e_1,e_2,e_4) | product(e_3,e_1,e_2). [resolve(586,b,225,b)].
% 0.71/1.03 594 product(e_1,e_2,e_4). [resolve(590,b,234,b),merge(b)].
% 0.71/1.03 597 product(e_3,e_4,e_2). [resolve(594,a,197,a)].
% 0.71/1.03 603 -product(e_1,e_5,e_4). [ur(73,a,594,a)].
% 0.71/1.03 608 product(e_1,e_4,e_2) | product(e_5,e_4,e_1). [back_unit_del(496),unit_del(c,597)].
% 0.71/1.03 609 product(e_3,e_5,e_1) | product(e_3,e_1,e_2). [back_unit_del(395),unit_del(c,597)].
% 0.71/1.03 619 product(e_2,e_4,e_1) | -product(e_3,e_5,e_1). [back_unit_del(571),unit_del(b,603)].
% 0.71/1.03 650 -product(e_1,e_4,e_2). [resolve(597,a,78,b)].
% 0.71/1.03 651 -product(e_3,e_1,e_2). [resolve(597,a,69,b)].
% 0.71/1.03 660 product(e_5,e_4,e_1). [back_unit_del(608),unit_del(a,650)].
% 0.71/1.03 690 product(e_3,e_5,e_1). [back_unit_del(609),unit_del(b,651)].
% 0.71/1.03 700 product(e_2,e_4,e_1). [back_unit_del(619),unit_del(b,690)].
% 0.71/1.03 739 $F. [resolve(660,a,83,b),unit_del(a,700)].
% 0.71/1.03
% 0.71/1.03 % SZS output end Refutation
% 0.71/1.03 ============================== end of proof ==========================
% 0.71/1.03
% 0.71/1.03 ============================== STATISTICS ============================
% 0.71/1.03
% 0.71/1.03 Given=322. Generated=1430. Kept=696. proofs=1.
% 0.71/1.03 Usable=131. Sos=55. Demods=0. Limbo=0, Disabled=596. Hints=0.
% 0.71/1.03 Megabytes=0.45.
% 0.71/1.03 User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.71/1.03
% 0.71/1.03 ============================== end of statistics =====================
% 0.71/1.03
% 0.71/1.03 ============================== end of search =========================
% 0.71/1.03
% 0.71/1.03 THEOREM PROVED
% 0.71/1.03 % SZS status Unsatisfiable
% 0.71/1.03
% 0.71/1.03 Exiting with 1 proof.
% 0.71/1.03
% 0.71/1.03 Process 2428 exit (max_proofs) Mon Jun 13 13:17:41 2022
% 0.71/1.03 Prover9 interrupted
%------------------------------------------------------------------------------