TSTP Solution File: GRP126-2.004 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP126-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 0.40s 0.97s
% Output : Refutation 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP126-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n007.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 23:05:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.40/0.96 ============================== Prover9 ===============================
% 0.40/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.40/0.96 Process 15808 was started by sandbox2 on n007.cluster.edu,
% 0.40/0.96 Mon Jun 13 23:05:55 2022
% 0.40/0.96 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_15655_n007.cluster.edu".
% 0.40/0.96 ============================== end of head ===========================
% 0.40/0.96
% 0.40/0.96 ============================== INPUT =================================
% 0.40/0.96
% 0.40/0.96 % Reading from file /tmp/Prover9_15655_n007.cluster.edu
% 0.40/0.96
% 0.40/0.96 set(prolog_style_variables).
% 0.40/0.96 set(auto2).
% 0.40/0.96 % set(auto2) -> set(auto).
% 0.40/0.96 % set(auto) -> set(auto_inference).
% 0.40/0.96 % set(auto) -> set(auto_setup).
% 0.40/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.40/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.40/0.96 % set(auto) -> set(auto_limits).
% 0.40/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.40/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.40/0.96 % set(auto) -> set(auto_denials).
% 0.40/0.96 % set(auto) -> set(auto_process).
% 0.40/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.40/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.40/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.40/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.40/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.40/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.40/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.40/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.40/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.40/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.40/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.40/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.40/0.96 % set(auto2) -> assign(stats, some).
% 0.40/0.96 % set(auto2) -> clear(echo_input).
% 0.40/0.96 % set(auto2) -> set(quiet).
% 0.40/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.40/0.96 % set(auto2) -> clear(print_given).
% 0.40/0.96 assign(lrs_ticks,-1).
% 0.40/0.96 assign(sos_limit,10000).
% 0.40/0.96 assign(order,kbo).
% 0.40/0.96 set(lex_order_vars).
% 0.40/0.96 clear(print_given).
% 0.40/0.96
% 0.40/0.96 % formulas(sos). % not echoed (32 formulas)
% 0.40/0.96
% 0.40/0.96 ============================== end of input ==========================
% 0.40/0.96
% 0.40/0.96 % From the command line: assign(max_seconds, 300).
% 0.40/0.96
% 0.40/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.40/0.96
% 0.40/0.96 % Formulas that are not ordinary clauses:
% 0.40/0.96
% 0.40/0.96 ============================== end of process non-clausal formulas ===
% 0.40/0.96
% 0.40/0.96 ============================== PROCESS INITIAL CLAUSES ===============
% 0.40/0.96
% 0.40/0.96 ============================== PREDICATE ELIMINATION =================
% 0.40/0.96 1 -product(A,e_1,B) | -next(A,C) | -greater(B,C) # label(no_redundancy) # label(axiom). [assumption].
% 0.40/0.96 2 next(e_1,e_2) # label(e_1_then_e_2) # label(axiom). [assumption].
% 0.40/0.96 3 next(e_2,e_3) # label(e_2_then_e_3) # label(axiom). [assumption].
% 0.40/0.96 4 next(e_3,e_4) # label(e_3_then_e_4) # label(axiom). [assumption].
% 0.40/0.96 Derived: -product(e_1,e_1,A) | -greater(A,e_2). [resolve(1,b,2,a)].
% 0.40/0.96 Derived: -product(e_2,e_1,A) | -greater(A,e_3). [resolve(1,b,3,a)].
% 0.40/0.96 Derived: -product(e_3,e_1,A) | -greater(A,e_4). [resolve(1,b,4,a)].
% 0.40/0.96 5 -product(e_1,e_1,A) | -greater(A,e_2). [resolve(1,b,2,a)].
% 0.40/0.96 6 greater(e_2,e_1) # label(e_2_greater_e_1) # label(axiom). [assumption].
% 0.40/0.96 7 greater(e_3,e_1) # label(e_3_greater_e_1) # label(axiom). [assumption].
% 0.40/0.96 8 greater(e_4,e_1) # label(e_4_greater_e_1) # label(axiom). [assumption].
% 0.40/0.96 9 greater(e_3,e_2) # label(e_3_greater_e_2) # label(axiom). [assumption].
% 0.40/0.96 10 greater(e_4,e_2) # label(e_4_greater_e_2) # label(axiom). [assumption].
% 0.40/0.96 11 greater(e_4,e_3) # label(e_4_greater_e_3) # label(axiom). [assumption].
% 0.40/0.96 Derived: -product(e_1,e_1,e_3). [resolve(5,b,9,a)].
% 0.40/0.96 Derived: -product(e_1,e_1,e_4). [resolve(5,b,10,a)].
% 0.40/0.96 12 -product(e_2,e_1,A) | -greater(A,e_3). [resolve(1,b,3,a)].
% 0.40/0.96 Derived: -product(e_2,e_1,e_4). [resolve(12,b,11,a)].
% 0.40/0.96 13 -product(e_3,e_1,A) | -greater(A,e_4). [resolve(1,b,4,a)].
% 0.40/0.96 14 -product(A,B,C) | -product(A,B,D) | equalish(C,D) # label(product_total_function2) # label(axiom). [assumption].
% 0.40/0.96 15 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.40/0.96 16 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.40/0.96 17 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.40/0.96 18 -equalish(e_2,e_1) # label(e_2_is_not_e_1) # label(axiom). [assumption].
% 0.40/0.97 19 -equalish(e_2,e_3) # label(e_2_is_not_e_3) # label(axiom). [assumption].
% 0.40/0.97 20 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.40/0.97 21 -equalish(e_3,e_1) # label(e_3_is_not_e_1) # label(axiom). [assumption].
% 0.40/0.97 22 -equalish(e_3,e_2) # label(e_3_is_not_e_2) # label(axiom). [assumption].
% 0.40/0.97 23 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.40/0.97 24 -equalish(e_4,e_1) # label(e_4_is_not_e_1) # label(axiom). [assumption].
% 0.40/0.97 25 -equalish(e_4,e_2) # label(e_4_is_not_e_2) # label(axiom). [assumption].
% 0.40/0.97 26 -equalish(e_4,e_3) # label(e_4_is_not_e_3) # label(axiom). [assumption].
% 0.40/0.97 Derived: -product(A,B,e_1) | -product(A,B,e_2). [resolve(14,c,15,a)].
% 0.40/0.97 Derived: -product(A,B,e_1) | -product(A,B,e_3). [resolve(14,c,16,a)].
% 0.40/0.97 Derived: -product(A,B,e_1) | -product(A,B,e_4). [resolve(14,c,17,a)].
% 0.40/0.97 Derived: -product(A,B,e_2) | -product(A,B,e_3). [resolve(14,c,19,a)].
% 0.40/0.97 Derived: -product(A,B,e_2) | -product(A,B,e_4). [resolve(14,c,20,a)].
% 0.40/0.97 Derived: -product(A,B,e_3) | -product(A,B,e_4). [resolve(14,c,23,a)].
% 0.40/0.97 27 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.40/0.97 Derived: -product(A,e_1,B) | -product(A,e_2,B). [resolve(27,c,15,a)].
% 0.40/0.97 Derived: -product(A,e_1,B) | -product(A,e_3,B). [resolve(27,c,16,a)].
% 0.40/0.97 Derived: -product(A,e_1,B) | -product(A,e_4,B). [resolve(27,c,17,a)].
% 0.40/0.97 Derived: -product(A,e_2,B) | -product(A,e_3,B). [resolve(27,c,19,a)].
% 0.40/0.97 Derived: -product(A,e_2,B) | -product(A,e_4,B). [resolve(27,c,20,a)].
% 0.40/0.97 Derived: -product(A,e_3,B) | -product(A,e_4,B). [resolve(27,c,23,a)].
% 0.40/0.97 28 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.40/0.97 Derived: -product(e_1,A,B) | -product(e_2,A,B). [resolve(28,c,15,a)].
% 0.40/0.97 Derived: -product(e_1,A,B) | -product(e_3,A,B). [resolve(28,c,16,a)].
% 0.40/0.97 Derived: -product(e_1,A,B) | -product(e_4,A,B). [resolve(28,c,17,a)].
% 0.40/0.97 Derived: -product(e_2,A,B) | -product(e_3,A,B). [resolve(28,c,19,a)].
% 0.40/0.97 Derived: -product(e_2,A,B) | -product(e_4,A,B). [resolve(28,c,20,a)].
% 0.40/0.97 Derived: -product(e_3,A,B) | -product(e_4,A,B). [resolve(28,c,23,a)].
% 0.40/0.97
% 0.40/0.97 ============================== end predicate elimination =============
% 0.40/0.97
% 0.40/0.97 Auto_denials: (non-Horn, no changes).
% 0.40/0.97
% 0.40/0.97 Term ordering decisions:
% 0.40/0.97 Function symbol KB weights: e_1=1. e_2=1. e_3=1. e_4=1.
% 0.40/0.97
% 0.40/0.97 ============================== end of process initial clauses ========
% 0.40/0.97
% 0.40/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.40/0.97
% 0.40/0.97 ============================== end of clauses for search =============
% 0.40/0.97
% 0.40/0.97 ============================== SEARCH ================================
% 0.40/0.97
% 0.40/0.97 % Starting search at 0.01 seconds.
% 0.40/0.97
% 0.40/0.97 ============================== PROOF =================================
% 0.40/0.97 % SZS status Unsatisfiable
% 0.40/0.97 % SZS output start Refutation
% 0.40/0.97
% 0.40/0.97 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.40/0.97 % Length of proof is 53.
% 0.40/0.97 % Level of proof is 8.
% 0.40/0.97 % Maximum clause weight is 20.000.
% 0.40/0.97 % Given clauses 56.
% 0.40/0.97
% 0.40/0.97 1 -product(A,e_1,B) | -next(A,C) | -greater(B,C) # label(no_redundancy) # label(axiom). [assumption].
% 0.40/0.97 2 next(e_1,e_2) # label(e_1_then_e_2) # label(axiom). [assumption].
% 0.40/0.97 3 next(e_2,e_3) # label(e_2_then_e_3) # label(axiom). [assumption].
% 0.40/0.97 5 -product(e_1,e_1,A) | -greater(A,e_2). [resolve(1,b,2,a)].
% 0.40/0.97 10 greater(e_4,e_2) # label(e_4_greater_e_2) # label(axiom). [assumption].
% 0.40/0.97 11 greater(e_4,e_3) # label(e_4_greater_e_3) # label(axiom). [assumption].
% 0.40/0.97 12 -product(e_2,e_1,A) | -greater(A,e_3). [resolve(1,b,3,a)].
% 0.40/0.97 15 -equalish(e_1,e_2) # label(e_1_is_not_e_2) # label(axiom). [assumption].
% 0.40/0.97 16 -equalish(e_1,e_3) # label(e_1_is_not_e_3) # label(axiom). [assumption].
% 0.40/0.97 17 -equalish(e_1,e_4) # label(e_1_is_not_e_4) # label(axiom). [assumption].
% 0.40/0.97 20 -equalish(e_2,e_4) # label(e_2_is_not_e_4) # label(axiom). [assumption].
% 0.40/0.97 23 -equalish(e_3,e_4) # label(e_3_is_not_e_4) # label(axiom). [assumption].
% 0.40/0.97 27 -product(A,B,C) | -product(A,D,C) | equalish(B,D) # label(product_right_cancellation) # label(axiom). [assumption].
% 0.40/0.97 28 -product(A,B,C) | -product(D,B,C) | equalish(A,D) # label(product_left_cancellation) # label(axiom). [assumption].
% 0.40/0.97 29 group_element(e_1) # label(element_1) # label(axiom). [assumption].
% 0.40/0.97 30 group_element(e_2) # label(element_2) # label(axiom). [assumption].
% 0.40/0.97 31 group_element(e_3) # label(element_3) # label(axiom). [assumption].
% 0.40/0.97 32 group_element(e_4) # label(element_4) # label(axiom). [assumption].
% 0.40/0.97 33 product(A,A,A) # label(product_idempotence) # label(axiom). [assumption].
% 0.40/0.97 34 -product(A,B,C) | -product(B,A,D) | product(C,D,B) # label(qg4) # label(negated_conjecture). [assumption].
% 0.40/0.97 35 -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].
% 0.40/0.97 37 -product(e_1,e_1,e_4). [resolve(5,b,10,a)].
% 0.40/0.97 38 -product(e_2,e_1,e_4). [resolve(12,b,11,a)].
% 0.40/0.97 45 -product(A,e_1,B) | -product(A,e_2,B). [resolve(27,c,15,a)].
% 0.40/0.97 46 -product(A,e_1,B) | -product(A,e_3,B). [resolve(27,c,16,a)].
% 0.40/0.97 47 -product(A,e_1,B) | -product(A,e_4,B). [resolve(27,c,17,a)].
% 0.40/0.97 50 -product(A,e_3,B) | -product(A,e_4,B). [resolve(27,c,23,a)].
% 0.40/0.97 51 -product(e_1,A,B) | -product(e_2,A,B). [resolve(28,c,15,a)].
% 0.40/0.97 53 -product(e_1,A,B) | -product(e_4,A,B). [resolve(28,c,17,a)].
% 0.40/0.97 55 -product(e_2,A,B) | -product(e_4,A,B). [resolve(28,c,20,a)].
% 0.40/0.97 56 -product(e_3,A,B) | -product(e_4,A,B). [resolve(28,c,23,a)].
% 0.40/0.97 61 -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(35,a,32,a)].
% 0.40/0.97 62 -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(35,a,31,a)].
% 0.40/0.97 63 -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(35,a,30,a)].
% 0.40/0.97 79 -product(e_2,e_1,e_2). [resolve(45,b,33,a)].
% 0.40/0.97 83 -product(e_4,e_1,e_4). [resolve(47,b,33,a)].
% 0.40/0.97 89 -product(e_4,e_3,e_4). [resolve(50,b,33,a)].
% 0.40/0.97 90 -product(e_3,e_4,e_3). [ur(50,a,33,a)].
% 0.40/0.97 92 -product(e_2,e_1,e_1). [ur(51,a,33,a)].
% 0.40/0.97 96 -product(e_4,e_1,e_1). [ur(53,a,33,a)].
% 0.40/0.97 101 -product(e_3,e_4,e_4). [resolve(56,b,33,a)].
% 0.40/0.97 102 -product(e_4,e_3,e_3). [ur(56,a,33,a)].
% 0.40/0.97 103 product(e_4,e_3,e_1) | product(e_4,e_3,e_2). [resolve(61,a,31,a),unit_del(c,102),unit_del(d,89)].
% 0.40/0.97 105 product(e_4,e_1,e_2) | product(e_4,e_1,e_3). [resolve(61,a,29,a),unit_del(a,96),unit_del(d,83)].
% 0.40/0.97 107 product(e_4,e_3,e_1) | -product(e_4,e_1,e_2). [resolve(103,b,46,b)].
% 0.40/0.97 114 product(e_3,e_4,e_1) | product(e_3,e_4,e_2). [resolve(62,a,32,a),unit_del(c,90),unit_del(d,101)].
% 0.40/0.97 117 product(e_4,e_1,e_2) | -product(e_2,e_1,e_3). [resolve(105,b,55,b)].
% 0.40/0.97 122 product(e_2,e_1,e_3). [resolve(63,a,29,a),unit_del(a,92),unit_del(b,79),unit_del(d,38)].
% 0.40/0.97 123 product(e_4,e_1,e_2). [back_unit_del(117),unit_del(b,122)].
% 0.40/0.97 124 product(e_4,e_3,e_1). [back_unit_del(107),unit_del(b,123)].
% 0.40/0.97 141 -product(e_3,e_4,e_2). [ur(34,b,124,a,c,38,a)].
% 0.40/0.97 142 -product(e_3,e_4,e_1). [ur(34,b,124,a,c,37,a)].
% 0.40/0.97 147 $F. [back_unit_del(114),unit_del(a,142),unit_del(b,141)].
% 0.40/0.97
% 0.40/0.97 % SZS output end Refutation
% 0.40/0.97 ============================== end of proof ==========================
% 0.40/0.97
% 0.40/0.97 ============================== STATISTICS ============================
% 0.40/0.97
% 0.40/0.97 Given=56. Generated=213. Kept=118. proofs=1.
% 0.40/0.97 Usable=50. Sos=44. Demods=0. Limbo=6, Disabled=74. Hints=0.
% 0.40/0.97 Megabytes=0.10.
% 0.40/0.97 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.40/0.97
% 0.40/0.97 ============================== end of statistics =====================
% 0.40/0.97
% 0.40/0.97 ============================== end of search =========================
% 0.40/0.97
% 0.40/0.97 THEOREM PROVED
% 0.40/0.97 % SZS status Unsatisfiable
% 0.40/0.97
% 0.40/0.97 Exiting with 1 proof.
% 0.40/0.97
% 0.40/0.97 Process 15808 exit (max_proofs) Mon Jun 13 23:05:55 2022
% 0.40/0.97 Prover9 interrupted
%------------------------------------------------------------------------------