TSTP Solution File: GRP124-3.004 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP124-3.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 11:17:20 EDT 2022
% Result : Unsatisfiable 0.74s 1.05s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP124-3.004 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 09:40:43 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 16785 was started by sandbox on n013.cluster.edu,
% 0.43/1.00 Mon Jun 13 09:40:44 2022
% 0.43/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16632_n013.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_16632_n013.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (44 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00
% 0.43/1.00 ============================== end of process non-clausal formulas ===
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.00
% 0.43/1.00 ============================== PREDICATE ELIMINATION =================
% 0.43/1.00 1 -cycle(A,B) | -cycle(A,C) | equalish(B,C) # label(cycle1) # label(axiom). [assumption].
% 0.43/1.00 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.43/1.00 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.43/1.00 4 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.43/1.00 5 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.43/1.00 6 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.43/1.00 7 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.43/1.00 8 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.43/1.00 9 -equalish(e_3,e_2) # label(e_3_is_not_e_2) # label(axiom). [assumption].
% 0.43/1.00 10 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.43/1.00 11 -equalish(e_4,e_1) # label(e_4_is_not_e_1) # label(axiom). [assumption].
% 0.43/1.00 12 -equalish(e_4,e_2) # label(e_4_is_not_e_2) # label(axiom). [assumption].
% 0.43/1.00 13 -equalish(e_4,e_3) # label(e_4_is_not_e_3) # label(axiom). [assumption].
% 0.43/1.00 Derived: -cycle(A,e_1) | -cycle(A,e_2). [resolve(1,c,2,a)].
% 0.43/1.00 Derived: -cycle(A,e_1) | -cycle(A,e_3). [resolve(1,c,3,a)].
% 0.43/1.00 Derived: -cycle(A,e_1) | -cycle(A,e_4). [resolve(1,c,4,a)].
% 0.43/1.00 Derived: -cycle(A,e_2) | -cycle(A,e_3). [resolve(1,c,6,a)].
% 0.43/1.00 Derived: -cycle(A,e_2) | -cycle(A,e_4). [resolve(1,c,7,a)].
% 0.43/1.00 Derived: -cycle(A,e_3) | -cycle(A,e_4). [resolve(1,c,10,a)].
% 0.43/1.00 14 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.43/1.00 Derived: -product(A,B,e_1) | -product(A,B,e_2). [resolve(14,c,2,a)].
% 0.43/1.00 Derived: -product(A,B,e_1) | -product(A,B,e_3). [resolve(14,c,3,a)].
% 0.43/1.00 Derived: -product(A,B,e_1) | -product(A,B,e_4). [resolve(14,c,4,a)].
% 0.43/1.00 Derived: -product(A,B,e_2) | -product(A,B,e_3). [resolve(14,c,6,a)].
% 0.43/1.00 Derived: -product(A,B,e_2) | -product(A,B,e_4). [resolve(14,c,7,a)].
% 0.43/1.00 Derived: -product(A,B,e_3) | -product(A,B,e_4). [resolve(14,c,10,a)].
% 0.43/1.00 15 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.43/1.00 Derived: -product(A,e_1,B) | -product(A,e_2,B). [resolve(15,c,2,a)].
% 0.43/1.00 Derived: -product(A,e_1,B) | -product(A,e_3,B). [resolve(15,c,3,a)].
% 0.43/1.00 Derived: -product(A,e_1,B) | -product(A,e_4,B). [resolve(15,c,4,a)].
% 0.43/1.00 Derived: -product(A,e_2,B) | -product(A,e_3,B). [resolve(15,c,6,a)].
% 0.43/1.00 Derived: -product(A,e_2,B) | -product(A,e_4,B). [resolve(15,c,7,a)].
% 0.43/1.00 Derived: -product(A,e_3,B) | -product(A,e_4,B). [resolve(15,c,10,a)].
% 0.43/1.00 16 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.43/1.00 Derived: -product(e_1,A,B) | -product(e_2,A,B). [resolve(16,c,2,a)].
% 0.43/1.00 Derived: -product(e_1,A,B) | -product(e_3,A,B). [resolve(16,c,3,a)].
% 0.43/1.00 Derived: -product(e_1,A,B) | -product(e_4,A,B). [resolve(16,c,4,a)].
% 0.43/1.00 Derived: -product(e_2,A,B) | -product(e_3,A,B). [resolve(16,c,6,a)].
% 0.43/1.00 Derived: -product(e_2,A,B) | -product(e_4,A,B). [resolve(16,c,7,a)].
% 0.43/1.00 Derived: -product(e_3,A,B) | -product(e_4,A,B). [resolve(16,c,10,a)].
% 0.43/1.00 17 -cycle(A,B) | -product(A,e_1,C) | -greater(B,e_0) | -next(A,D) | equalish(C,D) # label(cycle7) # label(axiom). [assumption].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_1) | -greater(B,e_0) | -next(A,e_2). [resolve(17,e,2,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_1) | -greater(B,e_0) | -next(A,e_3). [resolve(17,e,3,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_1) | -greater(B,e_0) | -next(A,e_4). [resolve(17,e,4,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_2) | -greater(B,e_0) | -next(A,e_1). [resolve(17,e,5,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_2) | -greater(B,e_0) | -next(A,e_3). [resolve(17,e,6,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_2) | -greater(B,e_0) | -next(A,e_4). [resolve(17,e,7,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_3) | -greater(B,e_0) | -next(A,e_1). [resolve(17,e,8,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_3) | -greater(B,e_0) | -next(A,e_2). [resolve(17,e,9,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_3) | -greater(B,e_0) | -next(A,e_4). [resolve(17,e,10,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_4) | -greater(B,e_0) | -next(A,e_1). [resolve(17,e,11,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_4) | -greater(B,e_0) | -next(A,e_2). [resolve(17,e,12,a)].
% 0.43/1.00 Derived: -cycle(A,B) | -product(A,e_1,e_4) | -greater(B,e_0) | -next(A,e_3). [resolve(17,e,13,a)].
% 0.43/1.00 18 -cycle(A,B) | -cycle(C,D) | -next(A,C) | -greater(B,e_0) | -next(D,E) | equalish(B,E) # label(cycle4) # label(axiom). [assumption].
% 0.43/1.00 Derived: -cycle(A,e_1) | -cycle(B,C) | -next(A,B) | -greater(e_1,e_0) | -next(C,e_2). [resolve(18,f,2,a)].
% 0.43/1.00 Derived: -cycle(A,e_1) | -cycle(B,C) | -next(A,B) | -greater(e_1,e_0) | -next(C,e_3). [resolve(18,f,3,a)].
% 0.43/1.00 Derived: -cycle(A,e_1) | -cycle(B,C) | -next(A,B) | -greater(e_1,e_0) | -next(C,e_4). [resolve(18,f,4,a)].
% 0.43/1.00 Derived: -cycle(A,e_2) | -cycle(B,C) | -next(A,B) | -greater(e_2,e_0) | -next(C,e_1). [resolve(18,f,5,a)].
% 0.43/1.00 Derived: -cycle(A,e_2) | -cycle(B,C) | -next(A,B) | -greater(e_2,e_0) | -next(C,e_3). [resolve(18,f,6,a)].
% 0.43/1.00 Derived: -cycle(A,e_2) | -cycle(B,C) | -next(A,B) | -greater(e_2,e_0) | -next(C,e_4). [resolve(18,f,7,a)].
% 0.43/1.00 Derived: -cycle(A,e_3) | -cycle(B,C) | -next(A,B) | -greater(e_3,e_0) | -next(C,e_1). [resolve(18,f,8,a)].
% 0.43/1.00 Derived: -cycle(A,e_3) | -cycle(B,C) | -next(A,B) | -greater(e_3,e_0) | -next(C,e_2). [resolve(18,f,9,a)].
% 0.43/1.00 Derived: -cycle(A,e_3) | -cycle(B,C) | -next(A,B) | -greater(e_3,e_0) | -next(C,e_4). [resolve(18,f,10,a)].
% 0.43/1.00 Derived: -cycle(A,e_4) | -cycle(B,C) | -next(A,B) | -greater(e_4,e_0) | -next(C,e_1). [resolve(18,f,11,a)].
% 0.43/1.00 Derived: -cycle(A,e_4) | -cycle(B,C) | -next(A,B) | -greater(e_4,e_0) | -next(C,e_2). [resolve(18,f,12,a)].
% 0.43/1.00 Derived: -cycle(A,e_4) | -cycle(B,C) | -next(A,B) | -greater(e_4,e_0) | -next(C,e_3). [resolve(18,f,13,a)].
% 0.43/1.00 19 -product(A,B,C) | -product(D,E,C) | -product(F,A,B) | -product(F,D,E) | equalish(A,D) # label(qg2_1) # label(negated_conjecture). [assumption].
% 0.74/1.05 Derived: -product(e_1,A,B) | -product(e_2,C,B) | -product(D,e_1,A) | -product(D,e_2,C). [resolve(19,e,2,a)].
% 0.74/1.05 Derived: -product(e_1,A,B) | -product(e_3,C,B) | -product(D,e_1,A) | -product(D,e_3,C). [resolve(19,e,3,a)].
% 0.74/1.05 Derived: -product(e_1,A,B) | -product(e_4,C,B) | -product(D,e_1,A) | -product(D,e_4,C). [resolve(19,e,4,a)].
% 0.74/1.05 Derived: -product(e_2,A,B) | -product(e_3,C,B) | -product(D,e_2,A) | -product(D,e_3,C). [resolve(19,e,6,a)].
% 0.74/1.05 Derived: -product(e_2,A,B) | -product(e_4,C,B) | -product(D,e_2,A) | -product(D,e_4,C). [resolve(19,e,7,a)].
% 0.74/1.05 Derived: -product(e_3,A,B) | -product(e_4,C,B) | -product(D,e_3,A) | -product(D,e_4,C). [resolve(19,e,10,a)].
% 0.74/1.05 20 -product(A,B,C) | -product(D,E,C) | -product(F,A,B) | -product(F,D,E) | equalish(B,E) # label(qg2_2) # label(negated_conjecture). [assumption].
% 0.74/1.05 Derived: -product(A,e_1,B) | -product(C,e_2,B) | -product(D,A,e_1) | -product(D,C,e_2). [resolve(20,e,2,a)].
% 0.74/1.05 Derived: -product(A,e_1,B) | -product(C,e_3,B) | -product(D,A,e_1) | -product(D,C,e_3). [resolve(20,e,3,a)].
% 0.74/1.05 Derived: -product(A,e_1,B) | -product(C,e_4,B) | -product(D,A,e_1) | -product(D,C,e_4). [resolve(20,e,4,a)].
% 0.74/1.05 Derived: -product(A,e_2,B) | -product(C,e_3,B) | -product(D,A,e_2) | -product(D,C,e_3). [resolve(20,e,6,a)].
% 0.74/1.05 Derived: -product(A,e_2,B) | -product(C,e_4,B) | -product(D,A,e_2) | -product(D,C,e_4). [resolve(20,e,7,a)].
% 0.74/1.05 Derived: -product(A,e_3,B) | -product(C,e_4,B) | -product(D,A,e_3) | -product(D,C,e_4). [resolve(20,e,10,a)].
% 0.74/1.05
% 0.74/1.05 ============================== end predicate elimination =============
% 0.74/1.05
% 0.74/1.05 Auto_denials: (non-Horn, no changes).
% 0.74/1.05
% 0.74/1.05 Term ordering decisions:
% 0.74/1.05 Function symbol KB weights: e_1=1. e_2=1. e_3=1. e_4=1. e_0=1.
% 0.74/1.05
% 0.74/1.05 ============================== end of process initial clauses ========
% 0.74/1.05
% 0.74/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.05
% 0.74/1.05 ============================== end of clauses for search =============
% 0.74/1.05
% 0.74/1.05 ============================== SEARCH ================================
% 0.74/1.05
% 0.74/1.05 % Starting search at 0.02 seconds.
% 0.74/1.05
% 0.74/1.05 ============================== PROOF =================================
% 0.74/1.05 % SZS status Unsatisfiable
% 0.74/1.05 % SZS output start Refutation
% 0.74/1.05
% 0.74/1.05 % Proof 1 at 0.06 (+ 0.00) seconds.
% 0.74/1.05 % Length of proof is 88.
% 0.74/1.05 % Level of proof is 14.
% 0.74/1.05 % Maximum clause weight is 20.000.
% 0.74/1.05 % Given clauses 269.
% 0.74/1.05
% 0.74/1.05 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.74/1.05 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.74/1.05 4 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.74/1.05 5 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.74/1.05 6 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.74/1.05 7 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.74/1.05 8 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.74/1.05 10 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.74/1.05 15 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.74/1.05 16 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.74/1.05 17 -cycle(A,B) | -product(A,e_1,C) | -greater(B,e_0) | -next(A,D) | equalish(C,D) # label(cycle7) # label(axiom). [assumption].
% 0.74/1.05 18 -cycle(A,B) | -cycle(C,D) | -next(A,C) | -greater(B,e_0) | -next(D,E) | equalish(B,E) # label(cycle4) # label(axiom). [assumption].
% 0.74/1.05 20 -product(A,B,C) | -product(D,E,C) | -product(F,A,B) | -product(F,D,E) | equalish(B,E) # label(qg2_2) # label(negated_conjecture). [assumption].
% 0.74/1.05 21 group_element(e_1) # label(element_1) # label(axiom). [assumption].
% 0.74/1.05 22 group_element(e_2) # label(element_2) # label(axiom). [assumption].
% 0.74/1.05 23 group_element(e_3) # label(element_3) # label(axiom). [assumption].
% 0.74/1.05 24 group_element(e_4) # label(element_4) # label(axiom). [assumption].
% 0.74/1.05 25 next(e_0,e_1) # label(e_0_then_e_1) # label(axiom). [assumption].
% 0.74/1.05 28 next(e_3,e_4) # label(e_3_then_e_4) # label(axiom). [assumption].
% 0.74/1.05 29 greater(e_1,e_0) # label(e_1_greater_e_0) # label(axiom). [assumption].
% 0.74/1.05 30 greater(e_2,e_0) # label(e_2_greater_e_0) # label(axiom). [assumption].
% 0.74/1.05 31 greater(e_3,e_0) # label(e_3_greater_e_0) # label(axiom). [assumption].
% 0.74/1.05 38 greater(e_4,e_3) # label(e_4_greater_e_3) # label(axiom). [assumption].
% 0.74/1.05 39 cycle(e_4,e_0) # label(cycle3) # label(axiom). [assumption].
% 0.74/1.05 40 product(A,A,A) # label(product_idempotence) # label(axiom). [assumption].
% 0.74/1.05 41 -cycle(A,e_0) | -product(A,e_1,B) | -greater(B,A) # label(cycle6) # label(axiom). [assumption].
% 0.74/1.05 43 -group_element(A) | cycle(A,e_0) | cycle(A,e_1) | cycle(A,e_2) | cycle(A,e_3) # label(cycle2) # label(axiom). [assumption].
% 0.74/1.05 44 -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].
% 0.74/1.05 57 -product(A,e_1,B) | -product(A,e_2,B). [resolve(15,c,2,a)].
% 0.74/1.05 58 -product(A,e_1,B) | -product(A,e_3,B). [resolve(15,c,3,a)].
% 0.74/1.05 59 -product(A,e_1,B) | -product(A,e_4,B). [resolve(15,c,4,a)].
% 0.74/1.05 62 -product(A,e_3,B) | -product(A,e_4,B). [resolve(15,c,10,a)].
% 0.74/1.05 63 -product(e_1,A,B) | -product(e_2,A,B). [resolve(16,c,2,a)].
% 0.74/1.05 64 -product(e_1,A,B) | -product(e_3,A,B). [resolve(16,c,3,a)].
% 0.74/1.05 65 -product(e_1,A,B) | -product(e_4,A,B). [resolve(16,c,4,a)].
% 0.74/1.05 66 -product(e_2,A,B) | -product(e_3,A,B). [resolve(16,c,6,a)].
% 0.74/1.05 67 -product(e_2,A,B) | -product(e_4,A,B). [resolve(16,c,7,a)].
% 0.74/1.05 68 -product(e_3,A,B) | -product(e_4,A,B). [resolve(16,c,10,a)].
% 0.74/1.05 74 -cycle(A,B) | -product(A,e_1,e_2) | -greater(B,e_0) | -next(A,e_4). [resolve(17,e,7,a)].
% 0.74/1.05 87 -cycle(A,e_2) | -cycle(B,C) | -next(A,B) | -greater(e_2,e_0) | -next(C,e_1). [resolve(18,f,5,a)].
% 0.74/1.05 88 -cycle(A,e_2) | -cycle(B,C) | -next(A,B) | -next(C,e_1). [copy(87),unit_del(d,30)].
% 0.74/1.05 93 -cycle(A,e_3) | -cycle(B,C) | -next(A,B) | -greater(e_3,e_0) | -next(C,e_1). [resolve(18,f,8,a)].
% 0.74/1.05 94 -cycle(A,e_3) | -cycle(B,C) | -next(A,B) | -next(C,e_1). [copy(93),unit_del(d,31)].
% 0.74/1.05 112 -product(A,e_1,B) | -product(C,e_3,B) | -product(D,A,e_1) | -product(D,C,e_3). [resolve(20,e,3,a)].
% 0.74/1.05 113 -product(A,e_1,B) | -product(C,e_4,B) | -product(D,A,e_1) | -product(D,C,e_4). [resolve(20,e,4,a)].
% 0.74/1.05 174 -product(A,e_1,e_3) | -product(e_3,A,e_1). [factor(112,b,d),unit_del(b,40)].
% 0.74/1.05 178 -product(A,e_1,e_4) | -product(e_4,A,e_1). [factor(113,b,d),unit_del(b,40)].
% 0.74/1.05 213 cycle(e_3,e_0) | cycle(e_3,e_1) | cycle(e_3,e_2) | cycle(e_3,e_3). [resolve(43,a,23,a)].
% 0.74/1.05 216 -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(44,a,24,a)].
% 0.74/1.05 217 -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(44,a,23,a)].
% 0.74/1.05 218 -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(44,a,22,a)].
% 0.74/1.05 236 -product(e_2,e_1,e_2). [resolve(57,b,40,a)].
% 0.74/1.05 238 -product(e_3,e_1,e_3). [resolve(58,b,40,a)].
% 0.74/1.05 240 -product(e_4,e_1,e_4). [resolve(59,b,40,a)].
% 0.74/1.05 246 -product(e_4,e_3,e_4). [resolve(62,b,40,a)].
% 0.74/1.05 247 -product(e_3,e_4,e_3). [ur(62,a,40,a)].
% 0.74/1.05 249 -product(e_2,e_1,e_1). [ur(63,a,40,a)].
% 0.74/1.05 251 -product(e_3,e_1,e_1). [ur(64,a,40,a)].
% 0.74/1.05 253 -product(e_4,e_1,e_1). [ur(65,a,40,a)].
% 0.74/1.05 258 -product(e_3,e_4,e_4). [resolve(68,b,40,a)].
% 0.74/1.05 259 -product(e_4,e_3,e_3). [ur(68,a,40,a)].
% 0.74/1.05 286 -cycle(e_3,e_2). [ur(88,b,39,a,c,28,a,d,25,a)].
% 0.74/1.05 287 cycle(e_3,e_0) | cycle(e_3,e_1) | cycle(e_3,e_3). [back_unit_del(213),unit_del(c,286)].
% 0.74/1.05 298 -cycle(e_3,e_3). [ur(94,b,39,a,c,28,a,d,25,a)].
% 0.74/1.05 299 cycle(e_3,e_0) | cycle(e_3,e_1). [back_unit_del(287),unit_del(c,298)].
% 0.74/1.05 393 product(e_4,e_3,e_1) | product(e_4,e_3,e_2). [resolve(216,a,23,a),unit_del(c,259),unit_del(d,246)].
% 0.74/1.05 395 product(e_4,e_1,e_2) | product(e_4,e_1,e_3). [resolve(216,a,21,a),unit_del(a,253),unit_del(d,240)].
% 0.74/1.05 411 product(e_4,e_3,e_1) | -product(e_4,e_1,e_2). [resolve(393,b,58,b)].
% 0.74/1.05 429 product(e_4,e_1,e_2) | -product(e_3,e_4,e_1). [resolve(395,b,174,a)].
% 0.74/1.05 445 product(e_4,e_1,e_2) | -product(e_2,e_1,e_3). [resolve(395,b,67,b)].
% 0.74/1.05 464 product(e_3,e_4,e_1) | product(e_3,e_4,e_2). [resolve(217,a,24,a),unit_del(c,247),unit_del(d,258)].
% 0.74/1.05 466 product(e_3,e_1,e_2) | product(e_3,e_1,e_4). [resolve(217,a,21,a),unit_del(a,251),unit_del(c,238)].
% 0.74/1.05 484 product(e_3,e_4,e_1) | -product(e_3,e_1,e_2). [resolve(464,b,59,b)].
% 0.74/1.05 504 product(e_3,e_1,e_2) | -product(e_4,e_3,e_1). [resolve(466,b,178,a)].
% 0.74/1.05 520 product(e_3,e_1,e_2) | -product(e_2,e_1,e_4). [resolve(466,b,66,b)].
% 0.74/1.05 521 product(e_3,e_1,e_2) | -cycle(e_3,e_0). [resolve(466,b,41,b),unit_del(c,38)].
% 0.74/1.05 522 product(e_3,e_1,e_2) | cycle(e_3,e_1). [resolve(521,b,299,a)].
% 0.74/1.05 525 product(e_2,e_1,e_3) | product(e_2,e_1,e_4). [resolve(218,a,21,a),unit_del(a,249),unit_del(b,236)].
% 0.74/1.05 559 product(e_3,e_4,e_1) | cycle(e_3,e_1). [resolve(484,b,522,a)].
% 0.74/1.05 561 cycle(e_3,e_1) | product(e_4,e_1,e_2). [resolve(559,a,429,b)].
% 0.74/1.05 595 cycle(e_3,e_1) | -product(e_3,e_1,e_2). [resolve(561,b,68,b)].
% 0.74/1.05 615 cycle(e_3,e_1). [resolve(595,b,522,a),merge(b)].
% 0.74/1.05 641 -product(e_3,e_1,e_2). [ur(74,a,615,a,c,29,a,d,28,a)].
% 0.74/1.05 651 -product(e_2,e_1,e_4). [back_unit_del(520),unit_del(a,641)].
% 0.74/1.05 666 -product(e_4,e_3,e_1). [back_unit_del(504),unit_del(a,641)].
% 0.74/1.05 669 product(e_2,e_1,e_3). [back_unit_del(525),unit_del(b,651)].
% 0.74/1.05 673 -product(e_4,e_1,e_2). [back_unit_del(411),unit_del(a,666)].
% 0.74/1.05 691 $F. [back_unit_del(445),unit_del(a,673),unit_del(b,669)].
% 0.74/1.05
% 0.74/1.05 % SZS output end Refutation
% 0.74/1.05 ============================== end of proof ==========================
% 0.74/1.05
% 0.74/1.05 ============================== STATISTICS ============================
% 0.74/1.05
% 0.74/1.05 Given=269. Generated=1000. Kept=658. proofs=1.
% 0.74/1.05 Usable=216. Sos=195. Demods=0. Limbo=22, Disabled=329. Hints=0.
% 0.74/1.05 Megabytes=0.41.
% 0.74/1.05 User_CPU=0.06, System_CPU=0.00, Wall_clock=0.
% 0.74/1.05
% 0.74/1.05 ============================== end of statistics =====================
% 0.74/1.05
% 0.74/1.05 ============================== end of search =========================
% 0.74/1.05
% 0.74/1.05 THEOREM PROVED
% 0.74/1.05 % SZS status Unsatisfiable
% 0.74/1.05
% 0.74/1.05 Exiting with 1 proof.
% 0.74/1.05
% 0.74/1.05 Process 16785 exit (max_proofs) Mon Jun 13 09:40:44 2022
% 0.74/1.05 Prover9 interrupted
%------------------------------------------------------------------------------