TSTP Solution File: RNG038-2 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : RNG038-2 : 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 : n013.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 13:47:51 EDT 2023
% Result : Unsatisfiable 0.20s 0.72s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG038-2 : 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
% 0.17/0.34 % Computer : n013.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sun Aug 27 02:48:02 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.62 start to proof:theBenchmark
% 0.20/0.70 %-------------------------------------------
% 0.20/0.70 % File :CSE---1.6
% 0.20/0.70 % Problem :theBenchmark
% 0.20/0.70 % Transform :cnf
% 0.20/0.70 % Format :tptp:raw
% 0.20/0.70 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.70
% 0.20/0.70 % Result :Theorem 0.030000s
% 0.20/0.70 % Output :CNFRefutation 0.030000s
% 0.20/0.70 %-------------------------------------------
% 0.20/0.71 %--------------------------------------------------------------------------
% 0.20/0.71 % File : RNG038-2 : TPTP v8.1.2. Released v1.0.0.
% 0.20/0.71 % Domain : Ring Theory
% 0.20/0.71 % Problem : Ring property 1
% 0.20/0.71 % Version : [Wos65] axioms : Reduced > Incomplete.
% 0.20/0.71 % English :
% 0.20/0.71
% 0.20/0.71 % Refs : [Wos65] Wos (1965), Unpublished Note
% 0.20/0.71 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.20/0.71 % Source : [SPRFN]
% 0.20/0.71 % Names : Problem 27 [Wos65]
% 0.20/0.71 % : wos27 [WM76]
% 0.20/0.71
% 0.20/0.71 % Status : Unsatisfiable
% 0.20/0.71 % Rating : 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.00 v2.6.0, 0.14 v2.5.0, 0.00 v2.4.0, 0.00 v2.3.0, 0.14 v2.2.1, 0.11 v2.1.0, 0.00 v2.0.0
% 0.20/0.71 % Syntax : Number of clauses : 30 ( 9 unt; 0 nHn; 21 RR)
% 0.20/0.71 % Number of literals : 79 ( 0 equ; 51 neg)
% 0.20/0.71 % Maximal clause size : 5 ( 2 avg)
% 0.20/0.71 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.71 % Number of predicates : 3 ( 3 usr; 0 prp; 2-3 aty)
% 0.20/0.71 % Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% 0.20/0.71 % Number of variables : 105 ( 2 sgn)
% 0.20/0.71 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.20/0.71
% 0.20/0.71 % Comments :
% 0.20/0.71 %--------------------------------------------------------------------------
% 0.20/0.71 %----Don't Include ring theory axioms
% 0.20/0.71 %include('Axioms/RNG001-0.ax').
% 0.20/0.71 %--------------------------------------------------------------------------
% 0.20/0.71 %----Equality axioms for additive operator
% 0.20/0.71 cnf(additive_inverse_substitution,axiom,
% 0.20/0.71 ( ~ equalish(X,Y)
% 0.20/0.71 | equalish(additive_inverse(X),additive_inverse(Y)) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(add_substitution1,axiom,
% 0.20/0.71 ( ~ equalish(X,Y)
% 0.20/0.71 | equalish(add(X,W),add(Y,W)) ) ).
% 0.20/0.71
% 0.20/0.71 %----This axiom omited in this version
% 0.20/0.71 %input_clause(add_substitution2,axiom,
% 0.20/0.71 % [--equalish(X,Y),
% 0.20/0.71 % ++equalish(add(W,X),add(W,Y))]).
% 0.20/0.71
% 0.20/0.71 cnf(sum_substitution1,axiom,
% 0.20/0.71 ( ~ equalish(X,Y)
% 0.20/0.71 | ~ sum(X,W,Z)
% 0.20/0.71 | sum(Y,W,Z) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(sum_substitution2,axiom,
% 0.20/0.71 ( ~ equalish(X,Y)
% 0.20/0.71 | ~ sum(W,X,Z)
% 0.20/0.71 | sum(W,Y,Z) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(sum_substitution3,axiom,
% 0.20/0.71 ( ~ equalish(X,Y)
% 0.20/0.71 | ~ sum(W,Z,X)
% 0.20/0.71 | sum(W,Z,Y) ) ).
% 0.20/0.71
% 0.20/0.71 %----Equality axioms for multiplicative operator
% 0.20/0.71 cnf(multiply_substitution1,axiom,
% 0.20/0.71 ( ~ equalish(X,Y)
% 0.20/0.71 | equalish(multiply(X,W),multiply(Y,W)) ) ).
% 0.20/0.71
% 0.20/0.71 %----This axiom omited in this version
% 0.20/0.71 %input_clause(multiply_substitution2,axiom,
% 0.20/0.71 % [--equalish(X,Y),
% 0.20/0.71 % ++equalish(multiply(W,X),multiply(W,Y))]).
% 0.20/0.71
% 0.20/0.71 cnf(product_substitution1,axiom,
% 0.20/0.71 ( ~ equalish(X,Y)
% 0.20/0.71 | ~ product(X,W,Z)
% 0.20/0.71 | product(Y,W,Z) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(product_substitution2,axiom,
% 0.20/0.71 ( ~ equalish(X,Y)
% 0.20/0.71 | ~ product(W,X,Z)
% 0.20/0.71 | product(W,Y,Z) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(product_substitution3,axiom,
% 0.20/0.71 ( ~ equalish(X,Y)
% 0.20/0.71 | ~ product(W,Z,X)
% 0.20/0.71 | product(W,Z,Y) ) ).
% 0.20/0.71
% 0.20/0.71 %----Not used in this version
% 0.20/0.71 %input_clause(additive_identity1,axiom,
% 0.20/0.71 % [++sum(additive_identity,X,X)]).
% 0.20/0.71
% 0.20/0.71 cnf(additive_identity2,axiom,
% 0.20/0.71 sum(X,additive_identity,X) ).
% 0.20/0.71
% 0.20/0.71 cnf(closure_of_multiplication,axiom,
% 0.20/0.71 product(X,Y,multiply(X,Y)) ).
% 0.20/0.71
% 0.20/0.71 cnf(closure_of_addition,axiom,
% 0.20/0.71 sum(X,Y,add(X,Y)) ).
% 0.20/0.71
% 0.20/0.71 %----Not used in this version
% 0.20/0.71 %input_clause(additive_inverse1,axiom,
% 0.20/0.71 % [++sum(additive_inverse(X),X,additive_identity)]).
% 0.20/0.71
% 0.20/0.71 cnf(additive_inverse2,axiom,
% 0.20/0.71 sum(X,additive_inverse(X),additive_identity) ).
% 0.20/0.71
% 0.20/0.71 cnf(associativity_of_addition1,axiom,
% 0.20/0.71 ( ~ sum(X,Y,U)
% 0.20/0.71 | ~ sum(Y,Z,V)
% 0.20/0.71 | ~ sum(U,Z,W)
% 0.20/0.71 | sum(X,V,W) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(associativity_of_addition2,axiom,
% 0.20/0.71 ( ~ sum(X,Y,U)
% 0.20/0.71 | ~ sum(Y,Z,V)
% 0.20/0.71 | ~ sum(X,V,W)
% 0.20/0.71 | sum(U,Z,W) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(commutativity_of_addition,axiom,
% 0.20/0.71 ( ~ sum(X,Y,Z)
% 0.20/0.71 | sum(Y,X,Z) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(associativity_of_multiplication1,axiom,
% 0.20/0.71 ( ~ product(X,Y,U)
% 0.20/0.71 | ~ product(Y,Z,V)
% 0.20/0.71 | ~ product(U,Z,W)
% 0.20/0.71 | product(X,V,W) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(associativity_of_multiplication2,axiom,
% 0.20/0.71 ( ~ product(X,Y,U)
% 0.20/0.71 | ~ product(Y,Z,V)
% 0.20/0.71 | ~ product(X,V,W)
% 0.20/0.71 | product(U,Z,W) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(distributivity1,axiom,
% 0.20/0.71 ( ~ product(X,Y,V1)
% 0.20/0.71 | ~ product(X,Z,V2)
% 0.20/0.71 | ~ sum(Y,Z,V3)
% 0.20/0.71 | ~ product(X,V3,V4)
% 0.20/0.71 | sum(V1,V2,V4) ) ).
% 0.20/0.71
% 0.20/0.71 cnf(distributivity2,axiom,
% 0.20/0.71 ( ~ product(X,Y,V1)
% 0.20/0.72 | ~ product(X,Z,V2)
% 0.20/0.72 | ~ sum(Y,Z,V3)
% 0.20/0.72 | ~ sum(V1,V2,V4)
% 0.20/0.72 | product(X,V3,V4) ) ).
% 0.20/0.72
% 0.20/0.72 cnf(distributivity3,axiom,
% 0.20/0.72 ( ~ product(Y,X,V1)
% 0.20/0.72 | ~ product(Z,X,V2)
% 0.20/0.72 | ~ sum(Y,Z,V3)
% 0.20/0.72 | ~ product(V3,X,V4)
% 0.20/0.72 | sum(V1,V2,V4) ) ).
% 0.20/0.72
% 0.20/0.72 cnf(distributivity4,axiom,
% 0.20/0.72 ( ~ product(Y,X,V1)
% 0.20/0.72 | ~ product(Z,X,V2)
% 0.20/0.72 | ~ sum(Y,Z,V3)
% 0.20/0.72 | ~ sum(V1,V2,V4)
% 0.20/0.72 | product(V3,X,V4) ) ).
% 0.20/0.72
% 0.20/0.72 %-----Equality axioms for operators
% 0.20/0.72 cnf(addition_is_well_defined,axiom,
% 0.20/0.72 ( ~ sum(X,Y,U)
% 0.20/0.72 | ~ sum(X,Y,V)
% 0.20/0.72 | equalish(U,V) ) ).
% 0.20/0.72
% 0.20/0.72 cnf(multiplication_is_well_defined,axiom,
% 0.20/0.72 ( ~ product(X,Y,U)
% 0.20/0.72 | ~ product(X,Y,V)
% 0.20/0.72 | equalish(U,V) ) ).
% 0.20/0.72
% 0.20/0.72 cnf(multiplicative_identity1,axiom,
% 0.20/0.72 product(additive_identity,X,additive_identity) ).
% 0.20/0.72
% 0.20/0.72 cnf(multiplicative_identity2,axiom,
% 0.20/0.72 product(X,additive_identity,additive_identity) ).
% 0.20/0.72
% 0.20/0.72 cnf(some_property,hypothesis,
% 0.20/0.72 ( ~ equalish(X,additive_identity)
% 0.20/0.72 | product(X,h(X,Y),Y) ) ).
% 0.20/0.72
% 0.20/0.72 cnf(a_times_b,hypothesis,
% 0.20/0.72 product(a,b,additive_identity) ).
% 0.20/0.72
% 0.20/0.72 %----Proving either a or b is the additive_identity. Either clause will
% 0.20/0.72 %----do.
% 0.20/0.72 cnf(a_not_additive_identity,negated_conjecture,
% 0.20/0.72 ~ equalish(a,additive_identity) ).
% 0.20/0.72
% 0.20/0.72 cnf(prove_b_is_additive_identity,negated_conjecture,
% 0.20/0.72 ~ equalish(b,additive_identity) ).
% 0.20/0.72
% 0.20/0.72 %--------------------------------------------------------------------------
% 0.20/0.72 %-------------------------------------------
% 0.20/0.72 % Proof found
% 0.20/0.72 % SZS status Theorem for theBenchmark
% 0.20/0.72 % SZS output start Proof
% 0.20/0.72 %ClaNum:30(EqnAxiom:0)
% 0.20/0.72 %VarNum:213(SingletonVarNum:105)
% 0.20/0.72 %MaxLitNum:5
% 0.20/0.72 %MaxfuncDepth:1
% 0.20/0.72 %SharedTerms:6
% 0.20/0.72 %goalClause: 8 9
% 0.20/0.72 %singleGoalClaCount:2
% 0.20/0.72 [1]P1(a1,a2,a3)
% 0.20/0.72 [8]~P2(a1,a3)
% 0.20/0.72 [9]~P2(a2,a3)
% 0.20/0.72 [2]P1(x21,a3,a3)
% 0.20/0.72 [3]P1(a3,x31,a3)
% 0.20/0.72 [4]P3(x41,a3,x41)
% 0.20/0.72 [5]P3(x51,f5(x51),a3)
% 0.20/0.72 [6]P3(x61,x62,f4(x61,x62))
% 0.20/0.72 [7]P1(x71,x72,f6(x71,x72))
% 0.20/0.72 [10]~P2(x101,x102)+P2(f5(x101),f5(x102))
% 0.20/0.72 [13]P1(x131,f7(x131,x132),x132)+~P2(x131,a3)
% 0.20/0.72 [14]~P3(x142,x141,x143)+P3(x141,x142,x143)
% 0.20/0.72 [11]~P2(x111,x113)+P2(f4(x111,x112),f4(x113,x112))
% 0.20/0.72 [12]~P2(x121,x123)+P2(f6(x121,x122),f6(x123,x122))
% 0.20/0.72 [15]~P3(x151,x152,x154)+P3(x151,x152,x153)+~P2(x154,x153)
% 0.20/0.72 [16]~P3(x161,x164,x163)+P3(x161,x162,x163)+~P2(x164,x162)
% 0.20/0.72 [17]~P3(x174,x172,x173)+P3(x171,x172,x173)+~P2(x174,x171)
% 0.20/0.72 [18]~P1(x181,x182,x184)+P1(x181,x182,x183)+~P2(x184,x183)
% 0.20/0.72 [19]~P1(x191,x194,x193)+P1(x191,x192,x193)+~P2(x194,x192)
% 0.20/0.72 [20]~P1(x204,x202,x203)+P1(x201,x202,x203)+~P2(x204,x201)
% 0.20/0.72 [21]~P3(x213,x214,x211)+P2(x211,x212)+~P3(x213,x214,x212)
% 0.20/0.72 [22]~P1(x223,x224,x221)+P2(x221,x222)+~P1(x223,x224,x222)
% 0.20/0.72 [23]~P3(x236,x234,x231)+P3(x231,x232,x233)+~P3(x234,x232,x235)+~P3(x236,x235,x233)
% 0.20/0.72 [24]~P3(x241,x246,x244)+P3(x241,x242,x243)+~P3(x244,x245,x243)+~P3(x246,x245,x242)
% 0.20/0.72 [25]~P1(x256,x254,x251)+P1(x251,x252,x253)+~P1(x254,x252,x255)+~P1(x256,x255,x253)
% 0.20/0.72 [26]~P1(x261,x266,x264)+P1(x261,x262,x263)+~P1(x264,x265,x263)+~P1(x266,x265,x262)
% 0.20/0.72 [27]~P1(x277,x275,x272)+~P1(x277,x274,x271)+P3(x271,x272,x273)+~P3(x274,x275,x276)+~P1(x277,x276,x273)
% 0.20/0.72 [28]~P1(x285,x287,x282)+~P1(x284,x287,x281)+P3(x281,x282,x283)+~P3(x284,x285,x286)+~P1(x286,x287,x283)
% 0.20/0.72 [29]~P1(x297,x292,x295)+~P1(x296,x292,x294)+P1(x291,x292,x293)+~P3(x294,x295,x293)+~P3(x296,x297,x291)
% 0.20/0.72 [30]~P1(x301,x307,x305)+~P1(x301,x306,x304)+P1(x301,x302,x303)+~P3(x304,x305,x303)+~P3(x306,x307,x302)
% 0.20/0.72 %EqnAxiom
% 0.20/0.72
% 0.20/0.72 %-------------------------------------------
% 0.20/0.72 cnf(35,plain,
% 0.20/0.72 (P1(x351,x352,f6(x351,x352))),
% 0.20/0.72 inference(rename_variables,[],[7])).
% 0.20/0.72 cnf(37,plain,
% 0.20/0.72 (P1(f6(a3,a2),a3,f6(a3,a2))),
% 0.20/0.72 inference(scs_inference,[],[4,2,3,1,7,22,21,26,25])).
% 0.20/0.72 cnf(38,plain,
% 0.20/0.72 (P1(x381,a3,a3)),
% 0.20/0.72 inference(rename_variables,[],[2])).
% 0.20/0.72 cnf(41,plain,
% 0.20/0.72 (P3(x411,x412,f4(x411,x412))),
% 0.20/0.72 inference(rename_variables,[],[6])).
% 0.20/0.72 cnf(44,plain,
% 0.20/0.72 (P3(x441,x442,f4(x441,x442))),
% 0.20/0.72 inference(rename_variables,[],[6])).
% 0.20/0.72 cnf(45,plain,
% 0.20/0.72 (P3(x451,a3,x451)),
% 0.20/0.72 inference(rename_variables,[],[4])).
% 0.20/0.72 cnf(48,plain,
% 0.20/0.72 (P1(x481,x482,f6(x481,x482))),
% 0.20/0.72 inference(rename_variables,[],[7])).
% 0.20/0.72 cnf(50,plain,
% 0.20/0.72 (P1(x501,a3,a3)),
% 0.20/0.72 inference(rename_variables,[],[2])).
% 0.20/0.72 cnf(51,plain,
% 0.20/0.72 (P3(x511,a3,x511)),
% 0.20/0.72 inference(rename_variables,[],[4])).
% 0.20/0.72 cnf(55,plain,
% 0.20/0.72 (P3(x551,a3,x551)),
% 0.20/0.72 inference(rename_variables,[],[4])).
% 0.20/0.72 cnf(70,plain,
% 0.20/0.72 (P1(a3,f7(a3,x701),x701)),
% 0.20/0.72 inference(scs_inference,[],[4,45,51,55,2,38,50,3,1,6,41,44,7,35,48,22,21,26,25,24,30,28,27,14,20,23,29,13])).
% 0.20/0.72 cnf(72,plain,
% 0.20/0.72 (P2(f6(a3,x721),a3)),
% 0.20/0.72 inference(scs_inference,[],[3,7,22])).
% 0.20/0.72 cnf(73,plain,
% 0.20/0.72 (P1(x731,x732,f6(x731,x732))),
% 0.20/0.72 inference(rename_variables,[],[7])).
% 0.20/0.72 cnf(77,plain,
% 0.20/0.72 (P3(x771,x772,f4(x771,x772))),
% 0.20/0.72 inference(rename_variables,[],[6])).
% 0.20/0.72 cnf(80,plain,
% 0.20/0.72 (P1(a3,x801,a3)),
% 0.20/0.72 inference(rename_variables,[],[3])).
% 0.20/0.72 cnf(81,plain,
% 0.20/0.72 (P1(x811,x812,f6(x811,x812))),
% 0.20/0.72 inference(rename_variables,[],[7])).
% 0.20/0.72 cnf(86,plain,
% 0.20/0.72 (P3(x861,x862,f4(x861,x862))),
% 0.20/0.72 inference(rename_variables,[],[6])).
% 0.20/0.72 cnf(89,plain,
% 0.20/0.72 (P3(x891,f5(x891),a3)),
% 0.20/0.72 inference(rename_variables,[],[5])).
% 0.20/0.72 cnf(90,plain,
% 0.20/0.72 (P1(a3,x901,a3)),
% 0.20/0.72 inference(rename_variables,[],[3])).
% 0.20/0.72 cnf(91,plain,
% 0.20/0.72 (P1(x911,x912,f6(x911,x912))),
% 0.20/0.72 inference(rename_variables,[],[7])).
% 0.20/0.72 cnf(92,plain,
% 0.20/0.72 (P3(x921,x922,f4(x921,x922))),
% 0.20/0.72 inference(rename_variables,[],[6])).
% 0.20/0.72 cnf(96,plain,
% 0.20/0.72 (P1(a3,x961,a3)),
% 0.20/0.72 inference(rename_variables,[],[3])).
% 0.20/0.72 cnf(97,plain,
% 0.20/0.72 (P3(x971,x972,f4(x971,x972))),
% 0.20/0.72 inference(rename_variables,[],[6])).
% 0.20/0.72 cnf(98,plain,
% 0.20/0.72 (P1(x981,x982,f6(x981,x982))),
% 0.20/0.72 inference(rename_variables,[],[7])).
% 0.20/0.72 cnf(101,plain,
% 0.68/0.72 (P1(x1011,x1012,f6(x1011,x1012))),
% 0.68/0.72 inference(rename_variables,[],[7])).
% 0.68/0.72 cnf(103,plain,
% 0.68/0.72 (P3(x1031,f5(x1031),a3)),
% 0.68/0.72 inference(rename_variables,[],[5])).
% 0.68/0.72 cnf(107,plain,
% 0.68/0.72 (P3(x1071,f5(x1071),a3)),
% 0.68/0.72 inference(rename_variables,[],[5])).
% 0.68/0.72 cnf(108,plain,
% 0.68/0.72 (P3(x1081,f5(x1081),a3)),
% 0.68/0.72 inference(rename_variables,[],[5])).
% 0.68/0.72 cnf(109,plain,
% 0.68/0.72 (P3(x1091,x1092,f4(x1091,x1092))),
% 0.68/0.72 inference(rename_variables,[],[6])).
% 0.68/0.72 cnf(117,plain,
% 0.68/0.72 (P2(f6(f6(a3,x1171),x1172),f6(a3,x1172))),
% 0.68/0.72 inference(scs_inference,[],[5,89,103,108,107,3,80,90,96,6,77,86,92,97,109,7,73,81,91,98,101,1,37,22,29,26,25,21,30,28,27,24,23,20,12])).
% 0.68/0.72 cnf(121,plain,
% 0.68/0.72 (P2(f5(f6(a3,x1211)),f5(a3))),
% 0.68/0.72 inference(scs_inference,[],[5,89,103,108,107,3,80,90,96,6,77,86,92,97,109,7,73,81,91,98,101,1,37,22,29,26,25,21,30,28,27,24,23,20,12,11,10])).
% 0.68/0.72 cnf(124,plain,
% 0.68/0.72 (P3(x1241,f5(x1241),a3)),
% 0.68/0.72 inference(rename_variables,[],[5])).
% 0.68/0.72 cnf(133,plain,
% 0.68/0.72 (P1(x1331,x1332,f6(x1331,x1332))),
% 0.68/0.72 inference(rename_variables,[],[7])).
% 0.68/0.72 cnf(141,plain,
% 0.68/0.72 ($false),
% 0.68/0.72 inference(scs_inference,[],[9,7,133,5,124,2,4,3,117,121,70,72,17,16,15,19,18,22,26]),
% 0.68/0.72 ['proof']).
% 0.68/0.72 % SZS output end Proof
% 0.68/0.72 % Total time :0.030000s
%------------------------------------------------------------------------------