TSTP Solution File: GRP126-3.004 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP126-3.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 11:17:26 EDT 2022
% Result : Unsatisfiable 0.75s 1.05s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP126-3.004 : TPTP v8.1.0. Released v1.2.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 13:25:24 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.73/1.01 ============================== Prover9 ===============================
% 0.73/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.01 Process 24076 was started by sandbox2 on n019.cluster.edu,
% 0.73/1.01 Mon Jun 13 13:25:25 2022
% 0.73/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23923_n019.cluster.edu".
% 0.73/1.01 ============================== end of head ===========================
% 0.73/1.01
% 0.73/1.01 ============================== INPUT =================================
% 0.73/1.01
% 0.73/1.01 % Reading from file /tmp/Prover9_23923_n019.cluster.edu
% 0.73/1.01
% 0.73/1.01 set(prolog_style_variables).
% 0.73/1.01 set(auto2).
% 0.73/1.01 % set(auto2) -> set(auto).
% 0.73/1.01 % set(auto) -> set(auto_inference).
% 0.73/1.01 % set(auto) -> set(auto_setup).
% 0.73/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.01 % set(auto) -> set(auto_limits).
% 0.73/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.01 % set(auto) -> set(auto_denials).
% 0.73/1.01 % set(auto) -> set(auto_process).
% 0.73/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.01 % set(auto2) -> assign(stats, some).
% 0.73/1.01 % set(auto2) -> clear(echo_input).
% 0.73/1.01 % set(auto2) -> set(quiet).
% 0.73/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.01 % set(auto2) -> clear(print_given).
% 0.73/1.01 assign(lrs_ticks,-1).
% 0.73/1.01 assign(sos_limit,10000).
% 0.73/1.01 assign(order,kbo).
% 0.73/1.01 set(lex_order_vars).
% 0.73/1.01 clear(print_given).
% 0.73/1.01
% 0.73/1.01 % formulas(sos). % not echoed (43 formulas)
% 0.73/1.01
% 0.73/1.01 ============================== end of input ==========================
% 0.73/1.01
% 0.73/1.01 % From the command line: assign(max_seconds, 300).
% 0.73/1.01
% 0.73/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.01
% 0.73/1.01 % Formulas that are not ordinary clauses:
% 0.73/1.01
% 0.73/1.01 ============================== end of process non-clausal formulas ===
% 0.73/1.01
% 0.73/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.01
% 0.73/1.01 ============================== PREDICATE ELIMINATION =================
% 0.73/1.01 1 -cycle(A,B) | -cycle(A,C) | equalish(B,C) # label(cycle1) # label(axiom). [assumption].
% 0.73/1.01 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.73/1.01 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.73/1.01 4 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.73/1.01 5 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.73/1.01 6 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.73/1.01 7 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.73/1.01 8 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.73/1.01 9 -equalish(e_3,e_2) # label(e_3_is_not_e_2) # label(axiom). [assumption].
% 0.73/1.01 10 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.73/1.01 11 -equalish(e_4,e_1) # label(e_4_is_not_e_1) # label(axiom). [assumption].
% 0.73/1.01 12 -equalish(e_4,e_2) # label(e_4_is_not_e_2) # label(axiom). [assumption].
% 0.73/1.01 13 -equalish(e_4,e_3) # label(e_4_is_not_e_3) # label(axiom). [assumption].
% 0.73/1.01 Derived: -cycle(A,e_1) | -cycle(A,e_2). [resolve(1,c,2,a)].
% 0.73/1.01 Derived: -cycle(A,e_1) | -cycle(A,e_3). [resolve(1,c,3,a)].
% 0.73/1.01 Derived: -cycle(A,e_1) | -cycle(A,e_4). [resolve(1,c,4,a)].
% 0.73/1.01 Derived: -cycle(A,e_2) | -cycle(A,e_3). [resolve(1,c,6,a)].
% 0.73/1.01 Derived: -cycle(A,e_2) | -cycle(A,e_4). [resolve(1,c,7,a)].
% 0.73/1.01 Derived: -cycle(A,e_3) | -cycle(A,e_4). [resolve(1,c,10,a)].
% 0.73/1.01 14 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.73/1.01 Derived: -product(A,B,e_1) | -product(A,B,e_2). [resolve(14,c,2,a)].
% 0.73/1.01 Derived: -product(A,B,e_1) | -product(A,B,e_3). [resolve(14,c,3,a)].
% 0.73/1.01 Derived: -product(A,B,e_1) | -product(A,B,e_4). [resolve(14,c,4,a)].
% 0.73/1.01 Derived: -product(A,B,e_2) | -product(A,B,e_3). [resolve(14,c,6,a)].
% 0.73/1.02 Derived: -product(A,B,e_2) | -product(A,B,e_4). [resolve(14,c,7,a)].
% 0.73/1.02 Derived: -product(A,B,e_3) | -product(A,B,e_4). [resolve(14,c,10,a)].
% 0.73/1.02 15 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.73/1.02 Derived: -product(A,e_1,B) | -product(A,e_2,B). [resolve(15,c,2,a)].
% 0.73/1.02 Derived: -product(A,e_1,B) | -product(A,e_3,B). [resolve(15,c,3,a)].
% 0.73/1.02 Derived: -product(A,e_1,B) | -product(A,e_4,B). [resolve(15,c,4,a)].
% 0.73/1.02 Derived: -product(A,e_2,B) | -product(A,e_3,B). [resolve(15,c,6,a)].
% 0.73/1.02 Derived: -product(A,e_2,B) | -product(A,e_4,B). [resolve(15,c,7,a)].
% 0.73/1.02 Derived: -product(A,e_3,B) | -product(A,e_4,B). [resolve(15,c,10,a)].
% 0.73/1.02 16 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.73/1.02 Derived: -product(e_1,A,B) | -product(e_2,A,B). [resolve(16,c,2,a)].
% 0.73/1.02 Derived: -product(e_1,A,B) | -product(e_3,A,B). [resolve(16,c,3,a)].
% 0.73/1.02 Derived: -product(e_1,A,B) | -product(e_4,A,B). [resolve(16,c,4,a)].
% 0.73/1.02 Derived: -product(e_2,A,B) | -product(e_3,A,B). [resolve(16,c,6,a)].
% 0.73/1.02 Derived: -product(e_2,A,B) | -product(e_4,A,B). [resolve(16,c,7,a)].
% 0.73/1.02 Derived: -product(e_3,A,B) | -product(e_4,A,B). [resolve(16,c,10,a)].
% 0.73/1.02 17 -cycle(A,B) | -product(A,e_1,C) | -greater(B,e_0) | -next(A,D) | equalish(C,D) # label(cycle7) # label(axiom). [assumption].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_1) | -greater(B,e_0) | -next(A,e_2). [resolve(17,e,2,a)].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_1) | -greater(B,e_0) | -next(A,e_3). [resolve(17,e,3,a)].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_1) | -greater(B,e_0) | -next(A,e_4). [resolve(17,e,4,a)].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_2) | -greater(B,e_0) | -next(A,e_1). [resolve(17,e,5,a)].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_2) | -greater(B,e_0) | -next(A,e_3). [resolve(17,e,6,a)].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_2) | -greater(B,e_0) | -next(A,e_4). [resolve(17,e,7,a)].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_3) | -greater(B,e_0) | -next(A,e_1). [resolve(17,e,8,a)].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_3) | -greater(B,e_0) | -next(A,e_2). [resolve(17,e,9,a)].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_3) | -greater(B,e_0) | -next(A,e_4). [resolve(17,e,10,a)].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_4) | -greater(B,e_0) | -next(A,e_1). [resolve(17,e,11,a)].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_4) | -greater(B,e_0) | -next(A,e_2). [resolve(17,e,12,a)].
% 0.73/1.02 Derived: -cycle(A,B) | -product(A,e_1,e_4) | -greater(B,e_0) | -next(A,e_3). [resolve(17,e,13,a)].
% 0.73/1.02 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].
% 0.73/1.02 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)].
% 0.73/1.02 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)].
% 0.73/1.02 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)].
% 0.73/1.02 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)].
% 0.73/1.02 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)].
% 0.73/1.02 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)].
% 0.73/1.02 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)].
% 0.73/1.02 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)].
% 0.73/1.02 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)].
% 0.73/1.02 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)].
% 0.73/1.02 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)].
% 0.73/1.02 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)].
% 0.73/1.02
% 0.73/1.02 ============================== end predicate elimination =============
% 0.73/1.02
% 0.73/1.02 Auto_denials: (non-Horn, no changes).
% 0.75/1.05
% 0.75/1.05 Term ordering decisions:
% 0.75/1.05 Function symbol KB weights: e_1=1. e_2=1. e_3=1. e_4=1. e_0=1.
% 0.75/1.05
% 0.75/1.05 ============================== end of process initial clauses ========
% 0.75/1.05
% 0.75/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.05
% 0.75/1.05 ============================== end of clauses for search =============
% 0.75/1.05
% 0.75/1.05 ============================== SEARCH ================================
% 0.75/1.05
% 0.75/1.05 % Starting search at 0.02 seconds.
% 0.75/1.05
% 0.75/1.05 ============================== PROOF =================================
% 0.75/1.05 % SZS status Unsatisfiable
% 0.75/1.05 % SZS output start Refutation
% 0.75/1.05
% 0.75/1.05 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.75/1.05 % Length of proof is 125.
% 0.75/1.05 % Level of proof is 15.
% 0.75/1.05 % Maximum clause weight is 20.000.
% 0.75/1.05 % Given clauses 337.
% 0.75/1.05
% 0.75/1.05 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.75/1.05 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.75/1.05 4 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.75/1.05 5 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.75/1.05 6 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.75/1.05 7 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.75/1.05 8 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.75/1.05 10 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.75/1.05 14 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.75/1.05 15 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.75/1.05 16 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.75/1.05 17 -cycle(A,B) | -product(A,e_1,C) | -greater(B,e_0) | -next(A,D) | equalish(C,D) # label(cycle7) # label(axiom). [assumption].
% 0.75/1.05 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].
% 0.75/1.05 19 group_element(e_1) # label(element_1) # label(axiom). [assumption].
% 0.75/1.05 20 group_element(e_2) # label(element_2) # label(axiom). [assumption].
% 0.75/1.05 21 group_element(e_3) # label(element_3) # label(axiom). [assumption].
% 0.75/1.05 22 group_element(e_4) # label(element_4) # label(axiom). [assumption].
% 0.75/1.05 23 next(e_0,e_1) # label(e_0_then_e_1) # label(axiom). [assumption].
% 0.75/1.05 26 next(e_3,e_4) # label(e_3_then_e_4) # label(axiom). [assumption].
% 0.75/1.05 27 greater(e_1,e_0) # label(e_1_greater_e_0) # label(axiom). [assumption].
% 0.75/1.05 28 greater(e_2,e_0) # label(e_2_greater_e_0) # label(axiom). [assumption].
% 0.75/1.05 29 greater(e_3,e_0) # label(e_3_greater_e_0) # label(axiom). [assumption].
% 0.75/1.05 36 greater(e_4,e_3) # label(e_4_greater_e_3) # label(axiom). [assumption].
% 0.75/1.05 37 cycle(e_4,e_0) # label(cycle3) # label(axiom). [assumption].
% 0.75/1.05 38 product(A,A,A) # label(product_idempotence) # label(axiom). [assumption].
% 0.75/1.05 39 -cycle(A,e_0) | -product(A,e_1,B) | -greater(B,A) # label(cycle6) # label(axiom). [assumption].
% 0.75/1.05 41 -product(A,B,C) | -product(B,A,D) | product(C,D,B) # label(qg4) # label(negated_conjecture). [assumption].
% 0.75/1.05 42 -group_element(A) | cycle(A,e_0) | cycle(A,e_1) | cycle(A,e_2) | cycle(A,e_3) # label(cycle2) # label(axiom). [assumption].
% 0.75/1.05 43 -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].
% 0.75/1.05 53 -product(A,B,e_2) | -product(A,B,e_3). [resolve(14,c,6,a)].
% 0.75/1.05 56 -product(A,e_1,B) | -product(A,e_2,B). [resolve(15,c,2,a)].
% 0.75/1.05 57 -product(A,e_1,B) | -product(A,e_3,B). [resolve(15,c,3,a)].
% 0.75/1.05 58 -product(A,e_1,B) | -product(A,e_4,B). [resolve(15,c,4,a)].
% 0.75/1.05 59 -product(A,e_2,B) | -product(A,e_3,B). [resolve(15,c,6,a)].
% 0.75/1.05 60 -product(A,e_2,B) | -product(A,e_4,B). [resolve(15,c,7,a)].
% 0.75/1.05 61 -product(A,e_3,B) | -product(A,e_4,B). [resolve(15,c,10,a)].
% 0.75/1.05 62 -product(e_1,A,B) | -product(e_2,A,B). [resolve(16,c,2,a)].
% 0.75/1.05 63 -product(e_1,A,B) | -product(e_3,A,B). [resolve(16,c,3,a)].
% 0.75/1.05 64 -product(e_1,A,B) | -product(e_4,A,B). [resolve(16,c,4,a)].
% 0.75/1.05 65 -product(e_2,A,B) | -product(e_3,A,B). [resolve(16,c,6,a)].
% 0.75/1.05 66 -product(e_2,A,B) | -product(e_4,A,B). [resolve(16,c,7,a)].
% 0.75/1.05 67 -product(e_3,A,B) | -product(e_4,A,B). [resolve(16,c,10,a)].
% 0.75/1.05 73 -cycle(A,B) | -product(A,e_1,e_2) | -greater(B,e_0) | -next(A,e_4). [resolve(17,e,7,a)].
% 0.75/1.05 86 -cycle(A,e_2) | -cycle(B,C) | -next(A,B) | -greater(e_2,e_0) | -next(C,e_1). [resolve(18,f,5,a)].
% 0.75/1.05 87 -cycle(A,e_2) | -cycle(B,C) | -next(A,B) | -next(C,e_1). [copy(86),unit_del(d,28)].
% 0.75/1.05 92 -cycle(A,e_3) | -cycle(B,C) | -next(A,B) | -greater(e_3,e_0) | -next(C,e_1). [resolve(18,f,8,a)].
% 0.75/1.05 93 -cycle(A,e_3) | -cycle(B,C) | -next(A,B) | -next(C,e_1). [copy(92),unit_del(d,29)].
% 0.75/1.05 155 cycle(e_3,e_0) | cycle(e_3,e_1) | cycle(e_3,e_2) | cycle(e_3,e_3). [resolve(42,a,21,a)].
% 0.75/1.05 158 -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(43,a,22,a)].
% 0.75/1.05 159 -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(43,a,21,a)].
% 0.75/1.05 160 -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(43,a,20,a)].
% 0.75/1.05 161 -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(43,a,19,a)].
% 0.75/1.05 172 -product(e_3,e_3,e_2). [resolve(53,b,38,a)].
% 0.75/1.05 178 -product(e_2,e_1,e_2). [resolve(56,b,38,a)].
% 0.75/1.05 179 -product(e_1,e_2,e_1). [ur(56,a,38,a)].
% 0.75/1.05 180 -product(e_3,e_1,e_3). [resolve(57,b,38,a)].
% 0.75/1.05 182 -product(e_4,e_1,e_4). [resolve(58,b,38,a)].
% 0.75/1.05 184 -product(e_3,e_2,e_3). [resolve(59,b,38,a)].
% 0.75/1.05 185 -product(e_2,e_3,e_2). [ur(59,a,38,a)].
% 0.75/1.05 186 -product(e_4,e_2,e_4). [resolve(60,b,38,a)].
% 0.75/1.05 187 -product(e_2,e_4,e_2). [ur(60,a,38,a)].
% 0.75/1.05 188 -product(e_4,e_3,e_4). [resolve(61,b,38,a)].
% 0.75/1.05 189 -product(e_3,e_4,e_3). [ur(61,a,38,a)].
% 0.75/1.05 190 -product(e_1,e_2,e_2). [resolve(62,b,38,a)].
% 0.75/1.05 191 -product(e_2,e_1,e_1). [ur(62,a,38,a)].
% 0.75/1.05 193 -product(e_3,e_1,e_1). [ur(63,a,38,a)].
% 0.75/1.05 195 -product(e_4,e_1,e_1). [ur(64,a,38,a)].
% 0.75/1.05 196 -product(e_2,e_3,e_3). [resolve(65,b,38,a)].
% 0.75/1.05 197 -product(e_3,e_2,e_2). [ur(65,a,38,a)].
% 0.75/1.05 198 -product(e_2,e_4,e_4). [resolve(66,b,38,a)].
% 0.75/1.05 199 -product(e_4,e_2,e_2). [ur(66,a,38,a)].
% 0.75/1.05 200 -product(e_3,e_4,e_4). [resolve(67,b,38,a)].
% 0.75/1.05 201 -product(e_4,e_3,e_3). [ur(67,a,38,a)].
% 0.75/1.05 228 -cycle(e_3,e_2). [ur(87,b,37,a,c,26,a,d,23,a)].
% 0.75/1.05 229 cycle(e_3,e_0) | cycle(e_3,e_1) | cycle(e_3,e_3). [back_unit_del(155),unit_del(c,228)].
% 0.75/1.05 240 -cycle(e_3,e_3). [ur(93,b,37,a,c,26,a,d,23,a)].
% 0.75/1.05 241 cycle(e_3,e_0) | cycle(e_3,e_1). [back_unit_del(229),unit_del(c,240)].
% 0.75/1.05 287 product(e_4,e_3,e_1) | product(e_4,e_3,e_2). [resolve(158,a,21,a),unit_del(c,201),unit_del(d,188)].
% 0.75/1.05 288 product(e_4,e_2,e_1) | product(e_4,e_2,e_3). [resolve(158,a,20,a),unit_del(b,199),unit_del(d,186)].
% 0.75/1.05 289 product(e_4,e_1,e_2) | product(e_4,e_1,e_3). [resolve(158,a,19,a),unit_del(a,195),unit_del(d,182)].
% 0.75/1.05 291 product(e_4,e_3,e_1) | -product(e_4,e_1,e_2). [resolve(287,b,57,b)].
% 0.75/1.05 293 product(e_4,e_3,e_1) | -product(e_3,e_4,A) | product(e_2,A,e_3). [resolve(287,b,41,a)].
% 0.75/1.05 294 product(e_4,e_2,e_1) | -product(e_1,e_2,e_3). [resolve(288,b,64,b)].
% 0.75/1.05 295 product(e_4,e_2,e_1) | -product(e_4,e_1,e_3). [resolve(288,b,56,b)].
% 0.75/1.05 297 product(e_4,e_2,e_1) | -product(e_2,e_4,A) | product(e_3,A,e_2). [resolve(288,b,41,a)].
% 0.75/1.05 305 product(e_4,e_2,e_1) | product(e_4,e_1,e_2). [resolve(295,b,289,b)].
% 0.75/1.05 306 product(e_4,e_1,e_2) | -product(e_3,e_2,e_1). [resolve(305,a,67,b)].
% 0.75/1.05 309 product(e_3,e_4,e_1) | product(e_3,e_4,e_2). [resolve(159,a,22,a),unit_del(c,189),unit_del(d,200)].
% 0.75/1.05 310 product(e_3,e_2,e_1) | product(e_3,e_2,e_4). [resolve(159,a,20,a),unit_del(b,197),unit_del(c,184)].
% 0.75/1.05 311 product(e_3,e_1,e_2) | product(e_3,e_1,e_4). [resolve(159,a,19,a),unit_del(a,193),unit_del(c,180)].
% 0.75/1.05 312 product(e_2,e_4,e_1) | product(e_2,e_4,e_3). [resolve(160,a,22,a),unit_del(b,187),unit_del(d,198)].
% 0.75/1.05 313 product(e_2,e_3,e_1) | product(e_2,e_3,e_4). [resolve(160,a,21,a),unit_del(b,185),unit_del(c,196)].
% 0.75/1.05 314 product(e_2,e_1,e_3) | product(e_2,e_1,e_4). [resolve(160,a,19,a),unit_del(a,191),unit_del(b,178)].
% 0.75/1.05 317 product(e_3,e_4,e_1) | -product(e_3,e_1,e_2). [resolve(309,b,58,b)].
% 0.75/1.05 320 product(e_3,e_2,e_1) | -product(e_1,e_2,e_4). [resolve(310,b,63,b)].
% 0.75/1.05 321 product(e_3,e_2,e_1) | -product(e_3,e_1,e_4). [resolve(310,b,56,b)].
% 0.75/1.05 327 product(e_3,e_1,e_2) | -product(e_2,e_1,e_4). [resolve(311,b,65,b)].
% 0.75/1.05 330 product(e_3,e_1,e_2) | -cycle(e_3,e_0). [resolve(311,b,39,b),unit_del(c,36)].
% 0.75/1.05 331 product(e_3,e_1,e_2) | cycle(e_3,e_1). [resolve(330,b,241,a)].
% 0.75/1.05 334 product(e_1,e_2,e_3) | product(e_1,e_2,e_4). [resolve(161,a,20,a),unit_del(a,179),unit_del(b,190)].
% 0.75/1.05 341 product(e_2,e_4,e_1) | product(e_4,e_2,e_1). [resolve(312,b,297,b),unit_del(c,172)].
% 0.75/1.05 343 product(e_2,e_4,e_1) | -product(e_2,e_1,e_3). [resolve(312,b,58,b)].
% 0.75/1.05 347 product(e_2,e_3,e_1) | -product(e_2,e_1,e_4). [resolve(313,b,57,b)].
% 0.75/1.05 359 product(e_3,e_4,e_1) | cycle(e_3,e_1). [resolve(317,b,331,a)].
% 0.75/1.05 363 cycle(e_3,e_1) | -product(e_2,e_4,e_1). [resolve(359,a,65,b)].
% 0.75/1.05 369 product(e_3,e_2,e_1) | product(e_3,e_1,e_2). [resolve(321,b,311,b)].
% 0.75/1.05 370 product(e_3,e_1,e_2) | product(e_2,e_1,e_3). [resolve(327,b,314,b)].
% 0.75/1.05 379 product(e_1,e_2,e_3) | product(e_3,e_2,e_1). [resolve(334,b,320,b)].
% 0.75/1.05 382 product(e_2,e_4,e_1) | -product(e_3,e_2,e_1). [resolve(341,b,67,b)].
% 0.75/1.05 391 product(e_2,e_3,e_1) | product(e_2,e_1,e_3). [resolve(347,b,314,b)].
% 0.75/1.05 396 product(e_3,e_1,e_2) | product(e_4,e_1,e_2). [resolve(369,a,306,b)].
% 0.75/1.05 399 product(e_2,e_1,e_3) | product(e_3,e_4,e_1). [resolve(370,a,317,b)].
% 0.75/1.05 433 product(e_2,e_4,e_1) | product(e_1,e_2,e_3). [resolve(382,b,379,b)].
% 0.75/1.05 457 product(e_3,e_1,e_2) | product(e_4,e_3,e_1). [resolve(396,b,291,b)].
% 0.75/1.05 464 product(e_2,e_1,e_3) | product(e_4,e_3,e_1). [resolve(399,b,293,b),merge(c)].
% 0.75/1.05 484 product(e_1,e_2,e_3) | product(e_4,e_2,e_1) | product(e_3,e_1,e_2). [resolve(433,a,297,b)].
% 0.75/1.05 501 product(e_3,e_1,e_2) | -product(e_4,e_2,e_1). [resolve(457,b,59,b)].
% 0.75/1.05 504 product(e_2,e_1,e_3) | -product(e_2,e_3,e_1). [resolve(464,b,66,b)].
% 0.75/1.05 530 product(e_2,e_1,e_3). [resolve(504,b,391,a),merge(b)].
% 0.75/1.05 531 product(e_2,e_4,e_1). [back_unit_del(343),unit_del(b,530)].
% 0.75/1.05 534 cycle(e_3,e_1). [back_unit_del(363),unit_del(b,531)].
% 0.75/1.05 566 -product(e_3,e_1,e_2). [ur(73,a,534,a,c,27,a,d,26,a)].
% 0.75/1.05 570 -product(e_4,e_2,e_1). [back_unit_del(501),unit_del(a,566)].
% 0.75/1.05 572 product(e_1,e_2,e_3). [back_unit_del(484),unit_del(b,570),unit_del(c,566)].
% 0.75/1.05 591 $F. [back_unit_del(294),unit_del(a,570),unit_del(b,572)].
% 0.75/1.05
% 0.75/1.05 % SZS output end Refutation
% 0.75/1.05 ============================== end of proof ==========================
% 0.75/1.05
% 0.75/1.05 ============================== STATISTICS ============================
% 0.75/1.05
% 0.75/1.05 Given=337. Generated=1125. Kept=560. proofs=1.
% 0.75/1.05 Usable=216. Sos=71. Demods=0. Limbo=21, Disabled=343. Hints=0.
% 0.75/1.05 Megabytes=0.35.
% 0.75/1.05 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.75/1.05
% 0.75/1.05 ============================== end of statistics =====================
% 0.75/1.05
% 0.75/1.05 ============================== end of search =========================
% 0.75/1.05
% 0.75/1.05 THEOREM PROVED
% 0.75/1.05 % SZS status Unsatisfiable
% 0.75/1.05
% 0.75/1.05 Exiting with 1 proof.
% 0.75/1.05
% 0.75/1.05 Process 24076 exit (max_proofs) Mon Jun 13 13:25:25 2022
% 0.75/1.05 Prover9 interrupted
%------------------------------------------------------------------------------