TSTP Solution File: RNG005-2 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : RNG005-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n012.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 : 300s
% DateTime : Thu Aug 31 13:47:38 EDT 2023
% Result : Unsatisfiable 0.19s 0.70s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG005-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.16/0.35 % Computer : n012.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sun Aug 27 02:38:25 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.19/0.60 start to proof:theBenchmark
% 0.19/0.68 %-------------------------------------------
% 0.19/0.68 % File :CSE---1.6
% 0.19/0.68 % Problem :theBenchmark
% 0.19/0.68 % Transform :cnf
% 0.19/0.68 % Format :tptp:raw
% 0.19/0.68 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.68
% 0.19/0.68 % Result :Theorem 0.020000s
% 0.19/0.68 % Output :CNFRefutation 0.020000s
% 0.19/0.68 %-------------------------------------------
% 0.19/0.69 %--------------------------------------------------------------------------
% 0.19/0.69 % File : RNG005-2 : TPTP v8.1.2. Released v1.0.0.
% 0.19/0.69 % Domain : Ring Theory
% 0.19/0.69 % Problem : (-X*Y) + (X*Y) = additive_identity
% 0.19/0.69 % Version : [Wos65] axioms : Reduced > Incomplete.
% 0.19/0.69 % English :
% 0.19/0.69
% 0.19/0.69 % Refs : [Wos65] Wos (1965), Unpublished Note
% 0.19/0.69 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.19/0.69 % Source : [SPRFN]
% 0.19/0.69 % Names : Problem 23 [Wos65]
% 0.19/0.69 % : wos23 [WM76]
% 0.19/0.69
% 0.19/0.69 % Status : Unsatisfiable
% 0.19/0.69 % Rating : 0.14 v8.1.0, 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v6.1.0, 0.07 v6.0.0, 0.11 v5.5.0, 0.06 v5.4.0, 0.11 v5.3.0, 0.20 v5.2.0, 0.08 v5.1.0, 0.06 v5.0.0, 0.07 v4.0.1, 0.14 v3.4.0, 0.20 v3.3.0, 0.00 v2.7.0, 0.12 v2.6.0, 0.14 v2.4.0, 0.14 v2.3.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.22 v2.1.0, 0.14 v2.0.0
% 0.19/0.69 % Syntax : Number of clauses : 31 ( 11 unt; 0 nHn; 21 RR)
% 0.19/0.69 % Number of literals : 79 ( 0 equ; 49 neg)
% 0.19/0.69 % Maximal clause size : 5 ( 2 avg)
% 0.19/0.69 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.69 % Number of predicates : 3 ( 3 usr; 0 prp; 2-3 aty)
% 0.19/0.69 % Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% 0.19/0.69 % Number of variables : 105 ( 2 sgn)
% 0.19/0.69 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.19/0.69
% 0.19/0.69 % Comments :
% 0.19/0.69 %--------------------------------------------------------------------------
% 0.19/0.69 %----Include ring theory axioms
% 0.19/0.69 %include('Axioms/RNG001-0.ax').
% 0.19/0.69 %--------------------------------------------------------------------------
% 0.19/0.69 cnf(additive_inverse_substitution,axiom,
% 0.19/0.69 ( ~ equalish(X,Y)
% 0.19/0.69 | equalish(additive_inverse(X),additive_inverse(Y)) ) ).
% 0.19/0.69
% 0.19/0.69 cnf(add_substitution1,axiom,
% 0.19/0.69 ( ~ equalish(X,Y)
% 0.19/0.69 | equalish(add(X,W),add(Y,W)) ) ).
% 0.19/0.69
% 0.19/0.69 %----This axiom omited in this version
% 0.19/0.69 %input_clause(add_substitution2,axiom,
% 0.19/0.69 % [--equalish(X,Y),
% 0.19/0.69 % ++equalish(add(W,X),add(W,Y))]).
% 0.19/0.69
% 0.19/0.69 cnf(sum_substitution1,axiom,
% 0.19/0.69 ( ~ equalish(X,Y)
% 0.19/0.69 | ~ sum(X,W,Z)
% 0.19/0.69 | sum(Y,W,Z) ) ).
% 0.19/0.69
% 0.19/0.69 cnf(sum_substitution2,axiom,
% 0.19/0.69 ( ~ equalish(X,Y)
% 0.19/0.69 | ~ sum(W,X,Z)
% 0.19/0.69 | sum(W,Y,Z) ) ).
% 0.19/0.69
% 0.19/0.69 cnf(sum_substitution3,axiom,
% 0.19/0.69 ( ~ equalish(X,Y)
% 0.19/0.69 | ~ sum(W,Z,X)
% 0.19/0.69 | sum(W,Z,Y) ) ).
% 0.19/0.69
% 0.19/0.69 %----Equality axioms for multiplicative operator
% 0.19/0.69 cnf(multiply_substitution1,axiom,
% 0.19/0.69 ( ~ equalish(X,Y)
% 0.19/0.69 | equalish(multiply(X,W),multiply(Y,W)) ) ).
% 0.19/0.69
% 0.19/0.69 %----This axiom omited in this version
% 0.19/0.69 %input_clause(multiply_substitution2,axiom,
% 0.19/0.69 % [--equalish(X,Y),
% 0.19/0.69 % ++equalish(multiply(W,X),multiply(W,Y))]).
% 0.19/0.69
% 0.19/0.69 cnf(product_substitution1,axiom,
% 0.19/0.69 ( ~ equalish(X,Y)
% 0.19/0.69 | ~ product(X,W,Z)
% 0.19/0.69 | product(Y,W,Z) ) ).
% 0.19/0.69
% 0.19/0.69 cnf(product_substitution2,axiom,
% 0.19/0.69 ( ~ equalish(X,Y)
% 0.19/0.69 | ~ product(W,X,Z)
% 0.19/0.69 | product(W,Y,Z) ) ).
% 0.19/0.69
% 0.19/0.69 cnf(product_substitution3,axiom,
% 0.19/0.69 ( ~ equalish(X,Y)
% 0.19/0.69 | ~ product(W,Z,X)
% 0.19/0.69 | product(W,Z,Y) ) ).
% 0.19/0.70
% 0.19/0.70 cnf(additive_identity1,axiom,
% 0.19/0.70 sum(additive_identity,X,X) ).
% 0.19/0.70
% 0.19/0.70 cnf(additive_identity2,axiom,
% 0.19/0.70 sum(X,additive_identity,X) ).
% 0.19/0.70
% 0.19/0.70 cnf(closure_of_multiplication,axiom,
% 0.19/0.70 product(X,Y,multiply(X,Y)) ).
% 0.19/0.70
% 0.19/0.70 cnf(closure_of_addition,axiom,
% 0.19/0.70 sum(X,Y,add(X,Y)) ).
% 0.19/0.70
% 0.19/0.70 cnf(left_inverse,axiom,
% 0.19/0.70 sum(additive_inverse(X),X,additive_identity) ).
% 0.19/0.70
% 0.19/0.70 cnf(right_inverse,axiom,
% 0.19/0.70 sum(X,additive_inverse(X),additive_identity) ).
% 0.19/0.70
% 0.19/0.70 cnf(associativity_of_addition1,axiom,
% 0.19/0.70 ( ~ sum(X,Y,U)
% 0.19/0.70 | ~ sum(Y,Z,V)
% 0.19/0.70 | ~ sum(U,Z,W)
% 0.19/0.70 | sum(X,V,W) ) ).
% 0.19/0.70
% 0.19/0.70 cnf(associativity_of_addition2,axiom,
% 0.19/0.70 ( ~ sum(X,Y,U)
% 0.19/0.70 | ~ sum(Y,Z,V)
% 0.19/0.70 | ~ sum(X,V,W)
% 0.19/0.70 | sum(U,Z,W) ) ).
% 0.19/0.70
% 0.19/0.70 cnf(commutativity_of_addition,axiom,
% 0.19/0.70 ( ~ sum(X,Y,Z)
% 0.19/0.70 | sum(Y,X,Z) ) ).
% 0.19/0.70
% 0.19/0.70 cnf(associativity_of_multiplication1,axiom,
% 0.19/0.70 ( ~ product(X,Y,U)
% 0.19/0.70 | ~ product(Y,Z,V)
% 0.19/0.70 | ~ product(U,Z,W)
% 0.19/0.70 | product(X,V,W) ) ).
% 0.19/0.70
% 0.19/0.70 cnf(associativity_of_multiplication2,axiom,
% 0.19/0.70 ( ~ product(X,Y,U)
% 0.19/0.70 | ~ product(Y,Z,V)
% 0.19/0.70 | ~ product(X,V,W)
% 0.19/0.70 | product(U,Z,W) ) ).
% 0.19/0.70
% 0.19/0.70 cnf(distributivity1,axiom,
% 0.19/0.70 ( ~ product(X,Y,V1)
% 0.19/0.70 | ~ product(X,Z,V2)
% 0.19/0.70 | ~ sum(Y,Z,V3)
% 0.19/0.70 | ~ product(X,V3,V4)
% 0.19/0.70 | sum(V1,V2,V4) ) ).
% 0.19/0.70
% 0.19/0.70 cnf(distributivity2,axiom,
% 0.19/0.70 ( ~ product(X,Y,V1)
% 0.19/0.70 | ~ product(X,Z,V2)
% 0.19/0.70 | ~ sum(Y,Z,V3)
% 0.19/0.70 | ~ sum(V1,V2,V4)
% 0.19/0.70 | product(X,V3,V4) ) ).
% 0.19/0.70
% 0.19/0.70 cnf(distributivity3,axiom,
% 0.19/0.70 ( ~ product(Y,X,V1)
% 0.19/0.70 | ~ product(Z,X,V2)
% 0.19/0.70 | ~ sum(Y,Z,V3)
% 0.19/0.70 | ~ product(V3,X,V4)
% 0.19/0.70 | sum(V1,V2,V4) ) ).
% 0.19/0.70
% 0.19/0.70 cnf(distributivity4,axiom,
% 0.19/0.70 ( ~ product(Y,X,V1)
% 0.19/0.70 | ~ product(Z,X,V2)
% 0.19/0.70 | ~ sum(Y,Z,V3)
% 0.19/0.70 | ~ sum(V1,V2,V4)
% 0.19/0.70 | product(V3,X,V4) ) ).
% 0.19/0.70
% 0.19/0.70 %-----Equality axioms for operators
% 0.19/0.70 cnf(addition_is_well_defined,axiom,
% 0.19/0.70 ( ~ sum(X,Y,U)
% 0.19/0.70 | ~ sum(X,Y,V)
% 0.19/0.70 | equalish(U,V) ) ).
% 0.19/0.70
% 0.19/0.70 cnf(multiplication_is_well_defined,axiom,
% 0.19/0.70 ( ~ product(X,Y,U)
% 0.19/0.70 | ~ product(X,Y,V)
% 0.19/0.70 | equalish(U,V) ) ).
% 0.19/0.70
% 0.19/0.70 cnf(multiplicative_identity1,axiom,
% 0.19/0.70 product(additive_identity,X,additive_identity) ).
% 0.19/0.70
% 0.19/0.70 cnf(multiplicative_identity2,axiom,
% 0.19/0.70 product(X,additive_identity,additive_identity) ).
% 0.19/0.70
% 0.19/0.70 cnf(a_times_b,hypothesis,
% 0.19/0.70 product(a,b,d) ).
% 0.19/0.70
% 0.19/0.70 cnf(a_inverse_times_b,hypothesis,
% 0.19/0.70 product(additive_inverse(a),b,c) ).
% 0.19/0.70
% 0.19/0.70 cnf(prove_sum_is_additive_identity,negated_conjecture,
% 0.19/0.70 ~ sum(c,d,additive_identity) ).
% 0.19/0.70
% 0.19/0.70 %--------------------------------------------------------------------------
% 0.19/0.70 %-------------------------------------------
% 0.19/0.70 % Proof found
% 0.19/0.70 % SZS status Theorem for theBenchmark
% 0.19/0.70 % SZS output start Proof
% 0.19/0.70 %ClaNum:31(EqnAxiom:0)
% 0.19/0.70 %VarNum:212(SingletonVarNum:105)
% 0.19/0.70 %MaxLitNum:5
% 0.19/0.70 %MaxfuncDepth:1
% 0.19/0.70 %SharedTerms:9
% 0.19/0.70 %goalClause: 11
% 0.19/0.70 %singleGoalClaCount:1
% 0.19/0.70 [1]P1(a1,a2,a6)
% 0.19/0.70 [11]~P3(a7,a6,a3)
% 0.19/0.70 [6]P1(f5(a1),a2,a7)
% 0.19/0.70 [2]P1(x21,a3,a3)
% 0.19/0.70 [3]P1(a3,x31,a3)
% 0.19/0.70 [4]P3(x41,a3,x41)
% 0.19/0.70 [5]P3(a3,x51,x51)
% 0.19/0.70 [7]P3(x71,f5(x71),a3)
% 0.19/0.70 [8]P3(f5(x81),x81,a3)
% 0.19/0.70 [9]P3(x91,x92,f4(x91,x92))
% 0.19/0.70 [10]P1(x101,x102,f8(x101,x102))
% 0.19/0.70 [12]~P2(x121,x122)+P2(f5(x121),f5(x122))
% 0.19/0.70 [15]~P3(x152,x151,x153)+P3(x151,x152,x153)
% 0.19/0.70 [13]~P2(x131,x133)+P2(f4(x131,x132),f4(x133,x132))
% 0.19/0.70 [14]~P2(x141,x143)+P2(f8(x141,x142),f8(x143,x142))
% 0.19/0.70 [16]~P3(x161,x162,x164)+P3(x161,x162,x163)+~P2(x164,x163)
% 0.19/0.70 [17]~P3(x171,x174,x173)+P3(x171,x172,x173)+~P2(x174,x172)
% 0.19/0.70 [18]~P3(x184,x182,x183)+P3(x181,x182,x183)+~P2(x184,x181)
% 0.19/0.70 [19]~P1(x191,x192,x194)+P1(x191,x192,x193)+~P2(x194,x193)
% 0.19/0.70 [20]~P1(x201,x204,x203)+P1(x201,x202,x203)+~P2(x204,x202)
% 0.19/0.70 [21]~P1(x214,x212,x213)+P1(x211,x212,x213)+~P2(x214,x211)
% 0.19/0.70 [22]~P3(x223,x224,x221)+P2(x221,x222)+~P3(x223,x224,x222)
% 0.19/0.70 [23]~P1(x233,x234,x231)+P2(x231,x232)+~P1(x233,x234,x232)
% 0.19/0.70 [24]~P3(x246,x244,x241)+P3(x241,x242,x243)+~P3(x244,x242,x245)+~P3(x246,x245,x243)
% 0.19/0.70 [25]~P3(x251,x256,x254)+P3(x251,x252,x253)+~P3(x254,x255,x253)+~P3(x256,x255,x252)
% 0.19/0.70 [26]~P1(x266,x264,x261)+P1(x261,x262,x263)+~P1(x264,x262,x265)+~P1(x266,x265,x263)
% 0.19/0.70 [27]~P1(x271,x276,x274)+P1(x271,x272,x273)+~P1(x274,x275,x273)+~P1(x276,x275,x272)
% 0.19/0.70 [28]~P1(x287,x285,x282)+~P1(x287,x284,x281)+P3(x281,x282,x283)+~P3(x284,x285,x286)+~P1(x287,x286,x283)
% 0.19/0.70 [29]~P1(x295,x297,x292)+~P1(x294,x297,x291)+P3(x291,x292,x293)+~P3(x294,x295,x296)+~P1(x296,x297,x293)
% 0.19/0.70 [30]~P1(x307,x302,x305)+~P1(x306,x302,x304)+P1(x301,x302,x303)+~P3(x304,x305,x303)+~P3(x306,x307,x301)
% 0.19/0.70 [31]~P1(x311,x317,x315)+~P1(x311,x316,x314)+P1(x311,x312,x313)+~P3(x314,x315,x313)+~P3(x316,x317,x312)
% 0.19/0.70 %EqnAxiom
% 0.19/0.70
% 0.19/0.70 %-------------------------------------------
% 0.19/0.70 cnf(32,plain,
% 0.19/0.70 (~P3(a6,a7,a3)),
% 0.19/0.70 inference(scs_inference,[],[11,15])).
% 0.19/0.70 cnf(43,plain,
% 0.19/0.70 (~P3(a3,a6,f5(a7))),
% 0.19/0.70 inference(scs_inference,[],[11,4,2,3,1,9,10,7,15,23,22,27,25,24])).
% 0.19/0.70 cnf(77,plain,
% 0.19/0.70 (P1(a3,x771,a3)),
% 0.19/0.70 inference(rename_variables,[],[3])).
% 0.19/0.70 cnf(78,plain,
% 0.19/0.70 (P1(x781,x782,f8(x781,x782))),
% 0.19/0.70 inference(rename_variables,[],[10])).
% 0.19/0.71 cnf(81,plain,
% 0.19/0.71 (P3(x811,x812,f4(x811,x812))),
% 0.19/0.71 inference(rename_variables,[],[9])).
% 0.19/0.71 cnf(82,plain,
% 0.19/0.71 (P1(x821,x822,f8(x821,x822))),
% 0.19/0.71 inference(rename_variables,[],[10])).
% 0.19/0.71 cnf(85,plain,
% 0.19/0.71 (P1(a3,x851,a3)),
% 0.19/0.71 inference(rename_variables,[],[3])).
% 0.19/0.71 cnf(86,plain,
% 0.19/0.71 (P3(x861,x862,f4(x861,x862))),
% 0.19/0.71 inference(rename_variables,[],[9])).
% 0.19/0.71 cnf(89,plain,
% 0.19/0.71 (~P3(x891,f4(f5(x891),a6),f5(a7))),
% 0.19/0.71 inference(scs_inference,[],[6,3,77,9,81,86,10,78,7,1,4,43,26,29,30,24])).
% 0.19/0.71 cnf(90,plain,
% 0.19/0.71 (P3(x901,x902,f4(x901,x902))),
% 0.19/0.71 inference(rename_variables,[],[9])).
% 0.19/0.71 cnf(93,plain,
% 0.19/0.71 (P3(x931,f5(x931),a3)),
% 0.19/0.71 inference(rename_variables,[],[7])).
% 0.19/0.71 cnf(94,plain,
% 0.19/0.71 (P1(a3,x941,a3)),
% 0.19/0.71 inference(rename_variables,[],[3])).
% 0.19/0.71 cnf(95,plain,
% 0.19/0.71 (P1(x951,x952,f8(x951,x952))),
% 0.19/0.71 inference(rename_variables,[],[10])).
% 0.19/0.71 cnf(96,plain,
% 0.19/0.71 (P3(x961,x962,f4(x961,x962))),
% 0.19/0.71 inference(rename_variables,[],[9])).
% 0.19/0.71 cnf(101,plain,
% 0.19/0.71 (P1(x1011,x1012,f8(x1011,x1012))),
% 0.19/0.71 inference(rename_variables,[],[10])).
% 0.19/0.71 cnf(103,plain,
% 0.19/0.71 (P2(a3,f4(x1031,f5(x1031)))),
% 0.19/0.71 inference(scs_inference,[],[6,3,77,85,9,81,86,90,96,10,78,82,95,7,93,1,4,43,26,29,30,24,31,15,23,22])).
% 0.19/0.71 cnf(104,plain,
% 0.19/0.71 (P3(x1041,f5(x1041),a3)),
% 0.19/0.71 inference(rename_variables,[],[7])).
% 0.19/0.71 cnf(105,plain,
% 0.19/0.71 (P3(x1051,x1052,f4(x1051,x1052))),
% 0.19/0.71 inference(rename_variables,[],[9])).
% 0.19/0.71 cnf(108,plain,
% 0.19/0.71 (P3(x1081,x1082,f4(x1081,x1082))),
% 0.19/0.71 inference(rename_variables,[],[9])).
% 0.19/0.71 cnf(109,plain,
% 0.19/0.71 (P1(x1091,x1092,f8(x1091,x1092))),
% 0.19/0.71 inference(rename_variables,[],[10])).
% 0.19/0.71 cnf(119,plain,
% 0.19/0.71 (~P3(f8(f5(a1),a2),a6,a3)),
% 0.19/0.71 inference(scs_inference,[],[11,6,3,77,85,9,81,86,90,96,105,108,10,78,82,95,101,109,7,93,104,1,4,2,43,26,29,30,24,31,15,23,22,28,27,25,18])).
% 0.19/0.71 cnf(123,plain,
% 0.19/0.71 (P1(f4(x1231,f5(x1231)),x1232,a3)),
% 0.19/0.71 inference(scs_inference,[],[11,6,3,77,85,94,9,81,86,90,96,105,108,10,78,82,95,101,109,7,93,104,1,4,2,43,32,26,29,30,24,31,15,23,22,28,27,25,18,17,21])).
% 0.19/0.71 cnf(138,plain,
% 0.19/0.71 ($false),
% 0.19/0.71 inference(scs_inference,[],[1,32,8,3,9,10,6,2,89,123,103,119,19,18,26,15,29]),
% 0.19/0.71 ['proof']).
% 0.19/0.71 % SZS output end Proof
% 0.19/0.71 % Total time :0.020000s
%------------------------------------------------------------------------------