TSTP Solution File: GRP128-4.003 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP128-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 11:17:31 EDT 2022
% Result : Unsatisfiable 0.73s 1.00s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP128-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 12:32:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/0.99 ============================== Prover9 ===============================
% 0.44/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.44/0.99 Process 12381 was started by sandbox on n010.cluster.edu,
% 0.44/0.99 Tue Jun 14 12:32:55 2022
% 0.44/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12228_n010.cluster.edu".
% 0.44/0.99 ============================== end of head ===========================
% 0.44/0.99
% 0.44/0.99 ============================== INPUT =================================
% 0.44/0.99
% 0.44/0.99 % Reading from file /tmp/Prover9_12228_n010.cluster.edu
% 0.44/0.99
% 0.44/0.99 set(prolog_style_variables).
% 0.44/0.99 set(auto2).
% 0.44/0.99 % set(auto2) -> set(auto).
% 0.44/0.99 % set(auto) -> set(auto_inference).
% 0.44/0.99 % set(auto) -> set(auto_setup).
% 0.44/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.44/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/0.99 % set(auto) -> set(auto_limits).
% 0.44/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/0.99 % set(auto) -> set(auto_denials).
% 0.44/0.99 % set(auto) -> set(auto_process).
% 0.44/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.44/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.44/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.44/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.44/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.44/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.44/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.44/0.99 % set(auto2) -> assign(stats, some).
% 0.44/0.99 % set(auto2) -> clear(echo_input).
% 0.44/0.99 % set(auto2) -> set(quiet).
% 0.44/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.44/0.99 % set(auto2) -> clear(print_given).
% 0.44/0.99 assign(lrs_ticks,-1).
% 0.44/0.99 assign(sos_limit,10000).
% 0.44/0.99 assign(order,kbo).
% 0.44/0.99 set(lex_order_vars).
% 0.44/0.99 clear(print_given).
% 0.44/0.99
% 0.44/0.99 % formulas(sos). % not echoed (18 formulas)
% 0.44/0.99
% 0.44/0.99 ============================== end of input ==========================
% 0.44/0.99
% 0.44/0.99 % From the command line: assign(max_seconds, 300).
% 0.44/0.99
% 0.44/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/0.99
% 0.44/0.99 % Formulas that are not ordinary clauses:
% 0.44/0.99
% 0.44/0.99 ============================== end of process non-clausal formulas ===
% 0.44/0.99
% 0.44/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/0.99
% 0.44/0.99 ============================== PREDICATE ELIMINATION =================
% 0.44/0.99 1 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.44/0.99 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.44/0.99 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.44/0.99 4 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.44/0.99 5 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.44/0.99 6 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.44/0.99 7 -equalish(e_3,e_2) # label(e_3_is_not_e_2) # label(axiom). [assumption].
% 0.44/0.99 Derived: -product(A,B,e_1) | -product(A,B,e_2). [resolve(1,c,2,a)].
% 0.44/0.99 Derived: -product(A,B,e_1) | -product(A,B,e_3). [resolve(1,c,3,a)].
% 0.44/0.99 Derived: -product(A,B,e_2) | -product(A,B,e_3). [resolve(1,c,5,a)].
% 0.44/0.99 8 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.44/0.99 Derived: -product(A,e_1,B) | -product(A,e_2,B). [resolve(8,c,2,a)].
% 0.44/0.99 Derived: -product(A,e_1,B) | -product(A,e_3,B). [resolve(8,c,3,a)].
% 0.44/0.99 Derived: -product(A,e_2,B) | -product(A,e_3,B). [resolve(8,c,5,a)].
% 0.44/0.99 9 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.44/0.99 Derived: -product(e_1,A,B) | -product(e_2,A,B). [resolve(9,c,2,a)].
% 0.44/0.99 Derived: -product(e_1,A,B) | -product(e_3,A,B). [resolve(9,c,3,a)].
% 0.44/0.99 Derived: -product(e_2,A,B) | -product(e_3,A,B). [resolve(9,c,5,a)].
% 0.44/0.99
% 0.44/0.99 ============================== end predicate elimination =============
% 0.44/0.99
% 0.44/0.99 Auto_denials: (non-Horn, no changes).
% 0.44/0.99
% 0.44/0.99 Term ordering decisions:
% 0.44/0.99 Function symbol KB weights: e_1=1. e_2=1. e_3=1.
% 0.44/0.99
% 0.44/0.99 ============================== end of process initial clauses ========
% 0.44/0.99
% 0.44/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.00
% 0.73/1.00 ============================== end of clauses for search =============
% 0.73/1.00
% 0.73/1.00 ============================== SEARCH ================================
% 0.73/1.00
% 0.73/1.00 % Starting search at 0.01 seconds.
% 0.73/1.00
% 0.73/1.00 ============================== PROOF =================================
% 0.73/1.00 % SZS status Unsatisfiable
% 0.73/1.00 % SZS output start Refutation
% 0.73/1.00
% 0.73/1.00 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.73/1.00 % Length of proof is 46.
% 0.73/1.00 % Level of proof is 12.
% 0.73/1.00 % Maximum clause weight is 16.000.
% 0.73/1.00 % Given clauses 63.
% 0.73/1.00
% 0.73/1.00 1 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.73/1.00 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.73/1.00 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.73/1.00 5 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.73/1.00 8 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.73/1.00 9 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.73/1.00 10 group_element(e_1) # label(element_1) # label(axiom). [assumption].
% 0.73/1.00 11 group_element(e_2) # label(element_2) # label(axiom). [assumption].
% 0.73/1.00 12 group_element(e_3) # label(element_3) # label(axiom). [assumption].
% 0.73/1.00 13 product(A,B,C) | -product(A,C,D) | -product(C,B,D) # label(qg3_1) # label(negated_conjecture). [assumption].
% 0.73/1.00 14 product(A,B,C) | -product(D,A,C) | -product(D,B,A) # label(qg3_2) # label(negated_conjecture). [assumption].
% 0.73/1.00 15 -product(A,B,C) | -product(C,B,D) | product(A,C,D) # label(qg3) # label(negated_conjecture). [assumption].
% 0.73/1.00 16 -group_element(A) | -group_element(B) | product(e_1,A,B) | product(e_2,A,B) | product(e_3,A,B) # label(row_surjectivity) # label(axiom). [assumption].
% 0.73/1.00 19 -product(A,B,e_1) | -product(A,B,e_2). [resolve(1,c,2,a)].
% 0.73/1.00 20 -product(A,B,e_1) | -product(A,B,e_3). [resolve(1,c,3,a)].
% 0.73/1.00 21 -product(A,B,e_2) | -product(A,B,e_3). [resolve(1,c,5,a)].
% 0.73/1.00 22 -product(A,e_1,B) | -product(A,e_2,B). [resolve(8,c,2,a)].
% 0.73/1.00 23 -product(A,e_1,B) | -product(A,e_3,B). [resolve(8,c,3,a)].
% 0.73/1.00 26 -product(e_1,A,B) | -product(e_3,A,B). [resolve(9,c,3,a)].
% 0.73/1.00 28 product(A,A,A) | -product(A,A,B). [factor(13,b,c)].
% 0.73/1.00 29 product(A,A,A) | -product(B,A,A). [factor(14,b,c)].
% 0.73/1.00 30 -product(A,B,A) | product(A,A,A). [factor(15,a,b)].
% 0.73/1.00 31 -group_element(A) | product(e_1,A,A) | product(e_2,A,A) | product(e_3,A,A). [factor(16,a,b)].
% 0.73/1.00 34 -group_element(A) | product(e_1,e_3,A) | product(e_2,e_3,A) | product(e_3,e_3,A). [resolve(16,a,12,a)].
% 0.73/1.00 36 -group_element(A) | product(e_1,e_1,A) | product(e_2,e_1,A) | product(e_3,e_1,A). [resolve(16,a,10,a)].
% 0.73/1.00 54 product(e_1,e_1,e_1) | product(e_2,e_1,e_1) | product(e_3,e_1,e_1). [resolve(31,a,10,a)].
% 0.73/1.00 61 product(e_1,e_3,e_2) | product(e_2,e_3,e_2) | product(e_3,e_3,e_2). [resolve(34,a,11,a)].
% 0.73/1.00 62 product(e_1,e_3,e_1) | product(e_2,e_3,e_1) | product(e_3,e_3,e_1). [resolve(34,a,10,a)].
% 0.73/1.00 72 product(e_1,e_1,e_1) | product(e_2,e_1,e_1). [resolve(54,c,29,b),merge(c)].
% 0.73/1.00 73 product(e_1,e_1,e_1). [resolve(72,b,29,b),merge(b)].
% 0.73/1.00 74 -product(e_3,e_1,e_1). [ur(26,a,73,a)].
% 0.73/1.00 76 -product(e_1,e_3,e_1). [ur(23,a,73,a)].
% 0.73/1.00 77 -product(e_1,e_2,e_1). [ur(22,a,73,a)].
% 0.73/1.00 78 -product(e_1,e_1,e_3). [ur(20,a,73,a)].
% 0.73/1.00 80 product(e_2,e_3,e_1) | product(e_3,e_3,e_1). [back_unit_del(62),unit_del(a,76)].
% 0.73/1.00 82 product(e_2,e_1,e_3) | product(e_3,e_1,e_3). [resolve(36,a,12,a),unit_del(a,78)].
% 0.73/1.00 84 product(e_2,e_3,e_1) | product(e_3,e_3,e_3). [resolve(80,b,28,b)].
% 0.73/1.00 100 product(e_2,e_1,e_3) | product(e_3,e_3,e_3). [resolve(82,b,30,a)].
% 0.73/1.00 120 product(e_2,e_3,e_1) | -product(e_3,e_3,e_1). [resolve(84,b,20,b)].
% 0.73/1.00 125 product(e_2,e_1,e_3) | -product(e_3,e_3,e_2). [resolve(100,b,21,b)].
% 0.73/1.00 131 product(e_2,e_3,e_1). [resolve(120,b,80,b),merge(b)].
% 0.73/1.00 141 -product(e_2,e_3,e_2). [ur(19,a,131,a)].
% 0.73/1.00 142 -product(e_1,e_3,e_2). [ur(15,b,131,a,c,77,a)].
% 0.73/1.00 143 -product(e_2,e_1,e_3). [ur(14,a,74,a,b,131,a)].
% 0.73/1.00 158 product(e_3,e_3,e_2). [back_unit_del(61),unit_del(a,142),unit_del(b,141)].
% 0.73/1.00 161 $F. [back_unit_del(125),unit_del(a,143),unit_del(b,158)].
% 0.73/1.00
% 0.73/1.00 % SZS output end Refutation
% 0.73/1.00 ============================== end of proof ==========================
% 0.73/1.00
% 0.73/1.00 ============================== STATISTICS ============================
% 0.73/1.00
% 0.73/1.00 Given=63. Generated=272. Kept=151. proofs=1.
% 0.73/1.00 Usable=46. Sos=39. Demods=0. Limbo=18, Disabled=75. Hints=0.
% 0.73/1.00 Megabytes=0.11.
% 0.73/1.00 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.73/1.00
% 0.73/1.00 ============================== end of statistics =====================
% 0.73/1.00
% 0.73/1.00 ============================== end of search =========================
% 0.73/1.00
% 0.73/1.00 THEOREM PROVED
% 0.73/1.00 % SZS status Unsatisfiable
% 0.73/1.00
% 0.73/1.00 Exiting with 1 proof.
% 0.73/1.00
% 0.73/1.00 Process 12381 exit (max_proofs) Tue Jun 14 12:32:55 2022
% 0.73/1.00 Prover9 interrupted
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