TSTP Solution File: GRP123-4.003 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP123-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 11:17:16 EDT 2022
% Result : Unsatisfiable 0.67s 0.99s
% Output : Refutation 0.67s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP123-4.003 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 13 18:40:25 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.67/0.98 ============================== Prover9 ===============================
% 0.67/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.98 Process 19974 was started by sandbox2 on n019.cluster.edu,
% 0.67/0.98 Mon Jun 13 18:40:25 2022
% 0.67/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19813_n019.cluster.edu".
% 0.67/0.98 ============================== end of head ===========================
% 0.67/0.98
% 0.67/0.98 ============================== INPUT =================================
% 0.67/0.98
% 0.67/0.98 % Reading from file /tmp/Prover9_19813_n019.cluster.edu
% 0.67/0.98
% 0.67/0.98 set(prolog_style_variables).
% 0.67/0.98 set(auto2).
% 0.67/0.98 % set(auto2) -> set(auto).
% 0.67/0.98 % set(auto) -> set(auto_inference).
% 0.67/0.98 % set(auto) -> set(auto_setup).
% 0.67/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.98 % set(auto) -> set(auto_limits).
% 0.67/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.98 % set(auto) -> set(auto_denials).
% 0.67/0.98 % set(auto) -> set(auto_process).
% 0.67/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.98 % set(auto2) -> assign(stats, some).
% 0.67/0.98 % set(auto2) -> clear(echo_input).
% 0.67/0.98 % set(auto2) -> set(quiet).
% 0.67/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.98 % set(auto2) -> clear(print_given).
% 0.67/0.98 assign(lrs_ticks,-1).
% 0.67/0.98 assign(sos_limit,10000).
% 0.67/0.98 assign(order,kbo).
% 0.67/0.98 set(lex_order_vars).
% 0.67/0.98 clear(print_given).
% 0.67/0.98
% 0.67/0.98 % formulas(sos). % not echoed (18 formulas)
% 0.67/0.98
% 0.67/0.98 ============================== end of input ==========================
% 0.67/0.98
% 0.67/0.98 % From the command line: assign(max_seconds, 300).
% 0.67/0.98
% 0.67/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.98
% 0.67/0.98 % Formulas that are not ordinary clauses:
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% 0.67/0.98 ============================== end of process non-clausal formulas ===
% 0.67/0.98
% 0.67/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.67/0.98
% 0.67/0.98 ============================== PREDICATE ELIMINATION =================
% 0.67/0.98 1 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.67/0.98 2 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.67/0.98 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.67/0.98 4 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.67/0.98 5 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.67/0.98 6 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.67/0.98 7 -equalish(e_3,e_2) # label(e_3_is_not_e_2) # label(axiom). [assumption].
% 0.67/0.98 Derived: -product(A,B,e_1) | -product(A,B,e_2). [resolve(1,c,2,a)].
% 0.67/0.98 Derived: -product(A,B,e_1) | -product(A,B,e_3). [resolve(1,c,3,a)].
% 0.67/0.98 Derived: -product(A,B,e_2) | -product(A,B,e_3). [resolve(1,c,5,a)].
% 0.67/0.98 8 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.67/0.98 Derived: -product(A,e_1,B) | -product(A,e_2,B). [resolve(8,c,2,a)].
% 0.67/0.98 Derived: -product(A,e_1,B) | -product(A,e_3,B). [resolve(8,c,3,a)].
% 0.67/0.98 Derived: -product(A,e_2,B) | -product(A,e_3,B). [resolve(8,c,5,a)].
% 0.67/0.98 9 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.67/0.98 Derived: -product(e_1,A,B) | -product(e_2,A,B). [resolve(9,c,2,a)].
% 0.67/0.98 Derived: -product(e_1,A,B) | -product(e_3,A,B). [resolve(9,c,3,a)].
% 0.67/0.98 Derived: -product(e_2,A,B) | -product(e_3,A,B). [resolve(9,c,5,a)].
% 0.67/0.98 10 -product(A,B,C) | -product(D,E,C) | -product(F,B,A) | -product(F,E,D) | equalish(A,D) # label(qg1_1) # label(negated_conjecture). [assumption].
% 0.67/0.98 Derived: -product(e_1,A,B) | -product(e_2,C,B) | -product(D,A,e_1) | -product(D,C,e_2). [resolve(10,e,2,a)].
% 0.67/0.98 Derived: -product(e_1,A,B) | -product(e_3,C,B) | -product(D,A,e_1) | -product(D,C,e_3). [resolve(10,e,3,a)].
% 0.67/0.99 Derived: -product(e_2,A,B) | -product(e_3,C,B) | -product(D,A,e_2) | -product(D,C,e_3). [resolve(10,e,5,a)].
% 0.67/0.99 11 -product(A,B,C) | -product(D,E,C) | -product(F,B,A) | -product(F,E,D) | equalish(B,E) # label(qg1_2) # label(negated_conjecture). [assumption].
% 0.67/0.99 Derived: -product(A,e_1,B) | -product(C,e_2,B) | -product(D,e_1,A) | -product(D,e_2,C). [resolve(11,e,2,a)].
% 0.67/0.99 Derived: -product(A,e_1,B) | -product(C,e_3,B) | -product(D,e_1,A) | -product(D,e_3,C). [resolve(11,e,3,a)].
% 0.67/0.99 Derived: -product(A,e_2,B) | -product(C,e_3,B) | -product(D,e_2,A) | -product(D,e_3,C). [resolve(11,e,5,a)].
% 0.67/0.99
% 0.67/0.99 ============================== end predicate elimination =============
% 0.67/0.99
% 0.67/0.99 Auto_denials: (non-Horn, no changes).
% 0.67/0.99
% 0.67/0.99 Term ordering decisions:
% 0.67/0.99 Function symbol KB weights: e_1=1. e_2=1. e_3=1.
% 0.67/0.99
% 0.67/0.99 ============================== end of process initial clauses ========
% 0.67/0.99
% 0.67/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.67/0.99
% 0.67/0.99 ============================== end of clauses for search =============
% 0.67/0.99
% 0.67/0.99 ============================== SEARCH ================================
% 0.67/0.99
% 0.67/0.99 % Starting search at 0.01 seconds.
% 0.67/0.99
% 0.67/0.99 ============================== PROOF =================================
% 0.67/0.99 % SZS status Unsatisfiable
% 0.67/0.99 % SZS output start Refutation
% 0.67/0.99
% 0.67/0.99 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.67/0.99 % Length of proof is 24.
% 0.67/0.99 % Level of proof is 4.
% 0.67/0.99 % Maximum clause weight is 16.000.
% 0.67/0.99 % Given clauses 40.
% 0.67/0.99
% 0.67/0.99 1 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.67/0.99 3 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.67/0.99 5 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.67/0.99 8 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.67/0.99 11 -product(A,B,C) | -product(D,E,C) | -product(F,B,A) | -product(F,E,D) | equalish(B,E) # label(qg1_2) # label(negated_conjecture). [assumption].
% 0.67/0.99 12 group_element(e_1) # label(element_1) # label(axiom). [assumption].
% 0.67/0.99 13 group_element(e_2) # label(element_2) # label(axiom). [assumption].
% 0.67/0.99 14 group_element(e_3) # label(element_3) # label(axiom). [assumption].
% 0.67/0.99 15 product(A,A,A) # label(product_idempotence) # label(axiom). [assumption].
% 0.67/0.99 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].
% 0.67/0.99 20 -product(A,B,e_1) | -product(A,B,e_3). [resolve(1,c,3,a)].
% 0.67/0.99 21 -product(A,B,e_2) | -product(A,B,e_3). [resolve(1,c,5,a)].
% 0.67/0.99 23 -product(A,e_1,B) | -product(A,e_3,B). [resolve(8,c,3,a)].
% 0.67/0.99 24 -product(A,e_2,B) | -product(A,e_3,B). [resolve(8,c,5,a)].
% 0.67/0.99 33 -product(A,e_2,B) | -product(C,e_3,B) | -product(D,e_2,A) | -product(D,e_3,C). [resolve(11,e,5,a)].
% 0.67/0.99 47 -product(A,e_2,A) | -product(B,e_3,A) | -product(A,e_3,B). [factor(33,a,c)].
% 0.67/0.99 49 -group_element(A) | product(e_1,e_3,A) | product(e_2,e_3,A) | product(e_3,e_3,A). [resolve(16,a,14,a)].
% 0.67/0.99 69 -product(e_3,e_3,e_1). [resolve(20,b,15,a)].
% 0.67/0.99 71 -product(e_3,e_3,e_2). [resolve(21,b,15,a)].
% 0.67/0.99 76 -product(e_1,e_3,e_1). [ur(23,a,15,a)].
% 0.67/0.99 78 -product(e_2,e_3,e_2). [ur(24,a,15,a)].
% 0.67/0.99 118 product(e_1,e_3,e_2). [resolve(49,a,13,a),unit_del(b,78),unit_del(c,71)].
% 0.67/0.99 119 product(e_2,e_3,e_1). [resolve(49,a,12,a),unit_del(a,76),unit_del(c,69)].
% 0.67/0.99 120 $F. [resolve(118,a,47,b),unit_del(a,15),unit_del(b,119)].
% 0.67/0.99
% 0.67/0.99 % SZS output end Refutation
% 0.67/0.99 ============================== end of proof ==========================
% 0.67/0.99
% 0.67/0.99 ============================== STATISTICS ============================
% 0.67/0.99
% 0.67/0.99 Given=40. Generated=189. Kept=108. proofs=1.
% 0.67/0.99 Usable=37. Sos=65. Demods=0. Limbo=0, Disabled=39. Hints=0.
% 0.67/0.99 Megabytes=0.09.
% 0.67/0.99 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.67/0.99
% 0.67/0.99 ============================== end of statistics =====================
% 0.67/0.99
% 0.67/0.99 ============================== end of search =========================
% 0.67/0.99
% 0.67/0.99 THEOREM PROVED
% 0.67/0.99 % SZS status Unsatisfiable
% 0.67/0.99
% 0.67/0.99 Exiting with 1 proof.
% 0.67/0.99
% 0.67/0.99 Process 19974 exit (max_proofs) Mon Jun 13 18:40:25 2022
% 0.67/0.99 Prover9 interrupted
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