TSTP Solution File: RNG010-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG010-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 : Mon Jul 18 20:39:11 EDT 2022
% Result : Unsatisfiable 0.74s 1.01s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG010-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 07:27:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.74/1.01 ============================== Prover9 ===============================
% 0.74/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.01 Process 29280 was started by sandbox on n023.cluster.edu,
% 0.74/1.01 Mon May 30 07:27:12 2022
% 0.74/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29126_n023.cluster.edu".
% 0.74/1.01 ============================== end of head ===========================
% 0.74/1.01
% 0.74/1.01 ============================== INPUT =================================
% 0.74/1.01
% 0.74/1.01 % Reading from file /tmp/Prover9_29126_n023.cluster.edu
% 0.74/1.01
% 0.74/1.01 set(prolog_style_variables).
% 0.74/1.01 set(auto2).
% 0.74/1.01 % set(auto2) -> set(auto).
% 0.74/1.01 % set(auto) -> set(auto_inference).
% 0.74/1.01 % set(auto) -> set(auto_setup).
% 0.74/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.01 % set(auto) -> set(auto_limits).
% 0.74/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.01 % set(auto) -> set(auto_denials).
% 0.74/1.01 % set(auto) -> set(auto_process).
% 0.74/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.01 % set(auto2) -> assign(stats, some).
% 0.74/1.01 % set(auto2) -> clear(echo_input).
% 0.74/1.01 % set(auto2) -> set(quiet).
% 0.74/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.01 % set(auto2) -> clear(print_given).
% 0.74/1.01 assign(lrs_ticks,-1).
% 0.74/1.01 assign(sos_limit,10000).
% 0.74/1.01 assign(order,kbo).
% 0.74/1.01 set(lex_order_vars).
% 0.74/1.01 clear(print_given).
% 0.74/1.01
% 0.74/1.01 % formulas(sos). % not echoed (24 formulas)
% 0.74/1.01
% 0.74/1.01 ============================== end of input ==========================
% 0.74/1.01
% 0.74/1.01 % From the command line: assign(max_seconds, 300).
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.01
% 0.74/1.01 % Formulas that are not ordinary clauses:
% 0.74/1.01
% 0.74/1.01 ============================== end of process non-clausal formulas ===
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.01
% 0.74/1.01 ============================== PREDICATE ELIMINATION =================
% 0.74/1.01
% 0.74/1.01 ============================== end predicate elimination =============
% 0.74/1.01
% 0.74/1.01 Auto_denials:
% 0.74/1.01 % copying label associator_skew_symmetry1 to answer in negative clause
% 0.74/1.01 % copying label associator_skew_symmetry2 to answer in negative clause
% 0.74/1.01 % copying label middle_law to answer in negative clause
% 0.74/1.01 % copying label prove_skew_symmetry to answer in negative clause
% 0.74/1.01 % assign(max_proofs, 4). % (Horn set with more than one neg. clause)
% 0.74/1.01
% 0.74/1.01 Term ordering decisions:
% 0.74/1.01
% 0.74/1.01 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (9).
% 0.74/1.01 Function symbol KB weights: additive_identity=1. cx=1. cy=1. cz=1. multiply=1. add=1. associator=1. additive_inverse=0.
% 0.74/1.01
% 0.74/1.01 ============================== PROOF =================================
% 0.74/1.01 % SZS status Unsatisfiable
% 0.74/1.01 % SZS output start Refutation
% 0.74/1.01
% 0.74/1.01 % Proof 1 at 0.01 (+ 0.00) seconds: middle_law.
% 0.74/1.01 % Length of proof is 3.
% 0.74/1.01 % Level of proof is 1.
% 0.74/1.01 % Maximum clause weight is 11.000.
% 0.74/1.01 % Given clauses 0.
% 0.74/1.01
% 0.74/1.01 14 multiply(multiply(A,A),B) = multiply(A,multiply(A,B)) # label(left_alternative) # label(axiom). [assumption].
% 0.74/1.01 30 multiply(multiply(A,B),A) != multiply(A,multiply(B,A)) # label(middle_law) # label(axiom) # answer(middle_law). [assumption].
% 0.74/1.01 31 $F # answer(middle_law). [resolve(30,a,14,a)].
% 0.74/1.01
% 0.74/1.01 % SZS output end Refutation
% 0.74/1.01 ============================== end of proof ==========================
% 0.74/1.01 % Redundant proof: 32 $F # answer(middle_law). [resolve(30,a,13,a)].
% 0.74/1.01
% 0.74/1.01 % Disable descendants (x means already disabled):
% 0.74/1.01 30
% 0.74/1.01
% 0.74/1.01 ============================== end of process initial clauses ========
% 0.74/1.01
% 0.74/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.01
% 0.74/1.01 ============================== end of clauses for search =============
% 0.74/1.01
% 0.74/1.01 ============================== SEARCH ================================
% 0.74/1.02
% 0.74/1.02 % Starting search at 0.01 seconds.
% 0.74/1.02
% 0.74/1.02 ============================== PROOF =================================
% 0.74/1.02 % SZS status Unsatisfiable
% 0.74/1.02 % SZS output start Refutation
% 0.74/1.02
% 0.74/1.02 % Proof 2 at 0.02 (+ 0.00) seconds: associator_skew_symmetry1.
% 0.74/1.02 % Length of proof is 16.
% 0.74/1.02 % Level of proof is 5.
% 0.74/1.02 % Maximum clause weight is 25.000.
% 0.74/1.02 % Given clauses 16.
% 0.74/1.02
% 0.74/1.02 1 additive_inverse(additive_identity) = additive_identity # label(inverse_additive_identity) # label(axiom). [assumption].
% 0.74/1.02 2 add(additive_identity,A) = A # label(left_additive_identity) # label(axiom). [assumption].
% 0.74/1.02 4 multiply(A,additive_identity) = additive_identity # label(right_multiplicative_zero) # label(axiom). [assumption].
% 0.74/1.02 5 additive_inverse(additive_inverse(A)) = A # label(additive_inverse_additive_inverse) # label(axiom). [assumption].
% 0.74/1.02 7 add(A,B) = add(B,A) # label(commutativity_for_addition) # label(axiom). [assumption].
% 0.74/1.02 8 multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)) # label(inverse_product1) # label(axiom). [assumption].
% 0.74/1.02 9 additive_inverse(multiply(A,B)) = multiply(additive_inverse(A),B). [copy(8),flip(a)].
% 0.74/1.02 10 multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)) # label(inverse_product2) # label(axiom). [assumption].
% 0.74/1.02 11 multiply(additive_inverse(A),B) = multiply(A,additive_inverse(B)). [copy(10),rewrite([9(4)]),flip(a)].
% 0.74/1.02 12 additive_inverse(add(A,B)) = add(additive_inverse(A),additive_inverse(B)) # label(sum_of_inverses) # label(axiom). [assumption].
% 0.74/1.02 24 associator(A,B,C) = add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))) # label(associator) # label(axiom). [assumption].
% 0.74/1.02 25 associator(A,B,C) = add(multiply(A,multiply(B,additive_inverse(C))),multiply(multiply(A,B),C)). [copy(24),rewrite([9(6),11(6),9(5),11(5),7(7)])].
% 0.74/1.02 26 associator(A,B,C) != additive_inverse(associator(B,A,C)) # label(associator_skew_symmetry1) # label(axiom) # answer(associator_skew_symmetry1). [assumption].
% 0.74/1.02 27 add(multiply(A,multiply(B,additive_inverse(C))),multiply(multiply(A,B),C)) != add(multiply(B,multiply(A,C)),multiply(multiply(B,additive_inverse(A)),C)) # answer(associator_skew_symmetry1). [copy(26),rewrite([25(1),25(7),12(13),9(10),11(10),9(9),11(9),5(8),9(11),9(10),11(10)])].
% 0.74/1.02 39 add(A,additive_identity) = A. [back_rewrite(2),rewrite([7(2)])].
% 0.74/1.02 91 $F # answer(associator_skew_symmetry1). [para(1(a,1),27(a,1,1,2,2)),rewrite([4(2),4(2),4(4),39(3),4(3),4(3),4(6),39(4)]),xx(a)].
% 0.74/1.02
% 0.74/1.02 % SZS output end Refutation
% 0.74/1.02 ============================== end of proof ==========================
% 0.74/1.02 % Redundant proof: 92 $F # answer(associator_skew_symmetry1). [para(1(a,1),27(a,2,2,1,2)),rewrite([3(4),3(3),3(3),39(3),3(3),4(3),4(4),3(4),39(4)]),xx(a)].
% 0.74/1.02 % Redundant proof: 93 $F # answer(associator_skew_symmetry1). [para(3(a,1),27(a,1,1,2)),rewrite([4(2),4(3),3(3),39(3),3(4),3(5),3(4),39(4)]),xx(a)].
% 0.74/1.02 % Redundant proof: 94 $F # answer(associator_skew_symmetry1). [para(3(a,1),27(a,1,1)),rewrite([3(3),3(3),39(3),3(3),4(3),1(4),4(4),3(4),39(4)]),xx(a)].
% 0.74/1.02 % Redundant proof: 95 $F # answer(associator_skew_symmetry1). [para(3(a,1),27(a,1,2,1)),rewrite([3(4),3(3),39(3),3(3),4(3),1(4),4(4),3(4),39(4)]),xx(a)].
% 0.74/1.02 % Redundant proof: 96 $F # answer(associator_skew_symmetry1). [para(3(a,1),27(a,2,1,2)),rewrite([3(4),3(3),3(3),39(3),4(3),1(4),4(4),3(4),39(4)]),xx(a)].
% 0.74/1.02 % Redundant proof: 97 $F # answer(associator_skew_symmetry1). [para(3(a,1),27(a,2,1)),rewrite([3(3),4(2),4(3),3(3),39(3),3(5),3(4),39(4)]),xx(a)].
% 0.74/1.02 % Redundant proof: 98 $F # answer(associator_skew_symmetry1). [para(3(a,1),27(a,2,2,1)),rewrite([3(3),4(2),4(3),3(3),39(3),3(4),3(4),39(4)]),xx(a)].
% 0.74/1.02 % Redundant proof: 99 $F # answer(associator_skew_symmetry1). [para(4(a,1),27(a,1,2,1)),rewrite([3(3),4(2),3(3),39(3),3(4),3(5),3(4),39(4)]),xx(a)].
% 0.74/1.02 % Redundant proof: 100 $F # answer(associator_skew_symmetry1). [para(4(a,1),27(a,1,2)),rewrite([1(2),4(2),4(2),39(3),4(3),4(3),4(6),39(4)]),xx(a)].
% 0.74/1.02 % Redundant proof: 101 $F # answer(associator_skew_symmetry1). [para(4(a,1),27(a,2,1,2)),rewrite([1(2),4(2),4(2),4(4),39(3),4(3),4(6),39(4)]),xx(a)].
% 0.74/1.02 % Redundant proof: 102 $F # answer(associator_skew_symmetry1). [para(4(a,1),27(a,2,2)),rewrite([1(2),4(2),4(2),4(4),39(3),4(3),4(3),39(4)]),xx(a)].
% 0.74/1.03 % Redundant proof: 116 $F # answer(associator_skew_symmetry1). [para(14(a,1),27(a,1,2)),rewrite([7(6),18(6),18(4),38(2),4(2),4(2),46(6),18(7),18(5),38(3),4(3),4(3)]),xx(a)].
% 0.74/1.03 % Redundant proof: 117 $F # answer(associator_skew_symmetry1). [para(14(a,1),27(a,2,2)),rewrite([11(3),5(2),46(5),18(6),18(4),38(2),4(2),4(2),11(4),40(3),11(7),11(8),40(7),5(6),7(7),18(7),18(5),38(3),4(3),4(3)]),xx(a)].
% 0.74/1.03
% 0.74/1.03 % Disable descendants (x means already disabled):
% 0.74/1.03 26x 27 103 104 105 106 107 108 109 110
% 0.74/1.03 111 112 113 114 115 118 119 120 121 122
% 0.74/1.03 123 124 125 126 127
% 0.74/1.03
% 0.74/1.03 ============================== PROOF =================================
% 0.74/1.03 % SZS status Unsatisfiable
% 0.74/1.03 % SZS output start Refutation
% 0.74/1.03
% 0.74/1.03 % Proof 3 at 0.03 (+ 0.00) seconds: associator_skew_symmetry2.
% 0.74/1.03 % Length of proof is 17.
% 0.74/1.03 % Level of proof is 5.
% 0.74/1.03 % Maximum clause weight is 25.000.
% 0.74/1.03 % Given clauses 17.
% 0.74/1.03
% 0.74/1.03 1 additive_inverse(additive_identity) = additive_identity # label(inverse_additive_identity) # label(axiom). [assumption].
% 0.74/1.03 2 add(additive_identity,A) = A # label(left_additive_identity) # label(axiom). [assumption].
% 0.74/1.03 3 multiply(additive_identity,A) = additive_identity # label(left_multiplicative_zero) # label(axiom). [assumption].
% 0.74/1.03 4 multiply(A,additive_identity) = additive_identity # label(right_multiplicative_zero) # label(axiom). [assumption].
% 0.74/1.03 5 additive_inverse(additive_inverse(A)) = A # label(additive_inverse_additive_inverse) # label(axiom). [assumption].
% 0.74/1.03 7 add(A,B) = add(B,A) # label(commutativity_for_addition) # label(axiom). [assumption].
% 0.74/1.03 8 multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)) # label(inverse_product1) # label(axiom). [assumption].
% 0.74/1.03 9 additive_inverse(multiply(A,B)) = multiply(additive_inverse(A),B). [copy(8),flip(a)].
% 0.74/1.03 10 multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)) # label(inverse_product2) # label(axiom). [assumption].
% 0.74/1.03 11 multiply(additive_inverse(A),B) = multiply(A,additive_inverse(B)). [copy(10),rewrite([9(4)]),flip(a)].
% 0.74/1.03 12 additive_inverse(add(A,B)) = add(additive_inverse(A),additive_inverse(B)) # label(sum_of_inverses) # label(axiom). [assumption].
% 0.74/1.03 24 associator(A,B,C) = add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))) # label(associator) # label(axiom). [assumption].
% 0.74/1.03 25 associator(A,B,C) = add(multiply(A,multiply(B,additive_inverse(C))),multiply(multiply(A,B),C)). [copy(24),rewrite([9(6),11(6),9(5),11(5),7(7)])].
% 0.74/1.03 28 associator(A,B,C) != additive_inverse(associator(C,B,A)) # label(associator_skew_symmetry2) # label(axiom) # answer(associator_skew_symmetry2). [assumption].
% 0.74/1.03 29 add(multiply(A,multiply(B,additive_inverse(C))),multiply(multiply(A,B),C)) != add(multiply(C,multiply(B,A)),multiply(multiply(C,additive_inverse(B)),A)) # answer(associator_skew_symmetry2). [copy(28),rewrite([25(1),25(7),12(13),9(10),11(10),9(9),11(9),5(8),9(11),9(10),11(10)])].
% 0.74/1.03 39 add(A,additive_identity) = A. [back_rewrite(2),rewrite([7(2)])].
% 0.74/1.03 128 $F # answer(associator_skew_symmetry2). [para(1(a,1),29(a,1,1,2,2)),rewrite([4(2),4(2),4(4),39(3),3(4),3(5),3(4),39(4)]),xx(a)].
% 0.74/1.03
% 0.74/1.03 % SZS output end Refutation
% 0.74/1.03 ============================== end of proof ==========================
% 0.74/1.03 % Redundant proof: 129 $F # answer(associator_skew_symmetry2). [para(1(a,1),29(a,2,2,1,2)),rewrite([3(3),4(2),4(3),3(3),39(3),3(3),4(3),4(4),3(4),39(4)]),xx(a)].
% 0.74/1.03 % Redundant proof: 130 $F # answer(associator_skew_symmetry2). [para(3(a,1),29(a,1,1,2)),rewrite([4(2),4(3),3(3),39(3),3(3),4(3),1(4),4(4),3(4),39(4)]),xx(a)].
% 0.74/1.03 % Redundant proof: 131 $F # answer(associator_skew_symmetry2). [para(3(a,1),29(a,1,1)),rewrite([3(3),3(3),39(3),4(3),4(3),4(6),39(4)]),xx(a)].
% 0.74/1.03 % Redundant proof: 132 $F # answer(associator_skew_symmetry2). [para(3(a,1),29(a,1,2,1)),rewrite([3(4),3(3),39(3),4(3),4(3),4(6),39(4)]),xx(a)].
% 0.74/1.03 % Redundant proof: 133 $F # answer(associator_skew_symmetry2). [para(3(a,1),29(a,2,1,2)),rewrite([3(3),4(2),4(3),3(3),39(3),4(3),1(4),4(4),3(4),39(4)]),xx(a)].
% 0.74/1.03 % Redundant proof: 134 $F # answer(associator_skew_symmetry2). [para(3(a,1),29(a,2,1)),rewrite([1(2),4(2),4(2)Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------