TSTP Solution File: RNG010-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : RNG010-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n011.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 13:47:41 EDT 2023
% Result : Unsatisfiable 0.21s 0.63s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG010-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 01:42:39 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.58 start to proof:theBenchmark
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 % File :CSE---1.6
% 0.21/0.62 % Problem :theBenchmark
% 0.21/0.62 % Transform :cnf
% 0.21/0.62 % Format :tptp:raw
% 0.21/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.62
% 0.21/0.62 % Result :Theorem 0.000000s
% 0.21/0.62 % Output :CNFRefutation 0.000000s
% 0.21/0.62 %-------------------------------------------
% 0.21/0.63 %--------------------------------------------------------------------------
% 0.21/0.63 % File : RNG010-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.21/0.63 % Domain : Ring Theory (Alternative)
% 0.21/0.63 % Problem : Skew symmetry of the auxilliary function
% 0.21/0.63 % Version : [AH90] (equality) axioms : Augmented.
% 0.21/0.63 % Theorem formulation : In terms of the associator
% 0.21/0.63 % English : The left and right Moufang identities imply the skew symmetry
% 0.21/0.63 % of s(W,X,Y,Z) = (W*X,Y,Z) - X*(W,Y,Z) - (X,Y,Z)*W.
% 0.21/0.63 % Recall that skew symmetry means that the function sign
% 0.21/0.63 % changes when any two arguments are swapped. This problem
% 0.21/0.63 % proves the case for swapping the first two arguments.
% 0.21/0.63
% 0.21/0.63 % Refs : [AH90] Anantharaman & Hsiang (1990), Automated Proofs of the
% 0.21/0.63 % Source : [AH90]
% 0.21/0.63 % Names : PROOF VI [AH90]
% 0.21/0.63
% 0.21/0.63 % Status : Unsatisfiable
% 0.21/0.63 % Rating : 0.00 v8.1.0, 0.05 v7.5.0, 0.06 v7.3.0, 0.08 v7.1.0, 0.09 v7.0.0, 0.08 v6.4.0, 0.07 v6.3.0, 0.10 v6.2.0, 0.20 v6.1.0, 0.18 v6.0.0, 0.14 v5.5.0, 0.12 v5.4.0, 0.11 v5.3.0, 0.20 v5.2.0, 0.12 v5.1.0, 0.11 v5.0.0, 0.10 v4.1.0, 0.11 v4.0.1, 0.12 v4.0.0, 0.14 v3.4.0, 0.17 v3.3.0, 0.00 v2.0.0
% 0.21/0.63 % Syntax : Number of clauses : 24 ( 22 unt; 0 nHn; 7 RR)
% 0.21/0.63 % Number of literals : 26 ( 26 equ; 6 neg)
% 0.21/0.63 % Maximal clause size : 2 ( 1 avg)
% 0.21/0.63 % Maximal term depth : 5 ( 2 avg)
% 0.21/0.63 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.21/0.63 % Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% 0.21/0.63 % Number of variables : 49 ( 2 sgn)
% 0.21/0.63 % SPC : CNF_UNS_RFO_PEQ_NUE
% 0.21/0.63
% 0.21/0.63 % Comments : This how the problem appears in [AH90].
% 0.21/0.63 % Bugfixes : v1.2.1 - Clause left_moufang fixed.
% 0.21/0.63 %--------------------------------------------------------------------------
% 0.21/0.63 %----Include Ring theory (equality) axioms
% 0.21/0.63 include('Axioms/RNG004-0.ax').
% 0.21/0.63 %--------------------------------------------------------------------------
% 0.21/0.63 %----Associator
% 0.21/0.63 cnf(associator,axiom,
% 0.21/0.63 associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ).
% 0.21/0.63
% 0.21/0.63 %----The next three clauses are previously proved lemmas
% 0.21/0.63 cnf(middle_law,axiom,
% 0.21/0.63 multiply(multiply(Y,X),Y) != multiply(Y,multiply(X,Y)) ).
% 0.21/0.63
% 0.21/0.63 cnf(associator_skew_symmetry1,axiom,
% 0.21/0.63 associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)) ).
% 0.21/0.63
% 0.21/0.63 cnf(associator_skew_symmetry2,axiom,
% 0.21/0.63 associator(Z,Y,X) != additive_inverse(associator(X,Y,Z)) ).
% 0.21/0.63
% 0.21/0.63 cnf(right_moufang,hypothesis,
% 0.21/0.63 multiply(Z,multiply(X,multiply(Y,X))) = multiply(multiply(multiply(Z,X),Y),X) ).
% 0.21/0.63
% 0.21/0.63 cnf(left_moufang,hypothesis,
% 0.21/0.63 multiply(multiply(X,multiply(Y,X)),Z) = multiply(X,multiply(Y,multiply(X,Z))) ).
% 0.21/0.63
% 0.21/0.63 cnf(prove_skew_symmetry,negated_conjecture,
% 0.21/0.63 associator(multiply(cx,cx),cy,cz) != add(multiply(associator(cx,cy,cz),cx),multiply(cx,associator(cx,cy,cz))) ).
% 0.21/0.63
% 0.21/0.63 %--------------------------------------------------------------------------
% 0.21/0.63 %-------------------------------------------
% 0.21/0.63 % Proof found
% 0.21/0.63 % SZS status Theorem for theBenchmark
% 0.21/0.63 % SZS output start Proof
% 0.21/0.63 %ClaNum:31(EqnAxiom:8)
% 0.21/0.63 %VarNum:114(SingletonVarNum:46)
% 0.21/0.63 %MaxLitNum:2
% 0.21/0.63 %MaxfuncDepth:6
% 0.21/0.63 %SharedTerms:22
% 0.21/0.63 %goalClause: 29
% 0.21/0.63 %singleGoalClaCount:1
% 0.21/0.63 [9]E(f3(a1),a1)
% 0.21/0.63 [29]~E(f2(f4(f2(f4(f4(a5,a6),a7),f3(f4(a5,f4(a6,a7)))),a5),f4(a5,f2(f4(f4(a5,a6),a7),f3(f4(a5,f4(a6,a7)))))),f2(f4(f4(f4(a5,a5),a6),a7),f3(f4(f4(a5,a5),f4(a6,a7)))))
% 0.21/0.63 [11]E(f4(x111,a1),a1)
% 0.21/0.63 [12]E(f4(a1,x121),a1)
% 0.21/0.63 [13]E(f2(a1,x131),x131)
% 0.21/0.63 [10]E(f3(f3(x101)),x101)
% 0.21/0.63 [14]E(f2(f3(x141),x141),a1)
% 0.21/0.63 [15]E(f2(x151,x152),f2(x152,x151))
% 0.21/0.63 [16]E(f3(f4(x161,x162)),f4(x161,f3(x162)))
% 0.21/0.63 [17]E(f3(f4(x171,x172)),f4(f3(x171),x172))
% 0.21/0.63 [18]E(f3(f2(x181,x182)),f2(f3(x181),f3(x182)))
% 0.21/0.63 [20]E(f4(f4(x201,x202),x202),f4(x201,f4(x202,x202)))
% 0.21/0.63 [21]E(f4(f4(x211,x211),x212),f4(x211,f4(x211,x212)))
% 0.21/0.63 [26]~E(f4(f4(x261,x262),x261),f4(x261,f4(x262,x261)))
% 0.21/0.63 [19]E(f2(f2(x191,x192),x193),f2(x191,f2(x192,x193)))
% 0.21/0.63 [22]E(f2(f4(x221,x222),f4(x221,x223)),f4(x221,f2(x222,x223)))
% 0.21/0.63 [23]E(f2(f4(x231,x232),f4(x233,x232)),f4(f2(x231,x233),x232))
% 0.21/0.63 [24]E(f4(f4(f4(x241,x242),x243),x242),f4(x241,f4(x242,f4(x243,x242))))
% 0.21/0.63 [25]E(f4(f4(x251,f4(x252,x251)),x253),f4(x251,f4(x252,f4(x251,x253))))
% 0.21/0.63 [27]~E(f3(f2(f4(f4(x271,x272),x273),f3(f4(x271,f4(x272,x273))))),f2(f4(f4(x273,x272),x271),f3(f4(x273,f4(x272,x271)))))
% 0.21/0.63 [28]~E(f3(f2(f4(f4(x281,x282),x283),f3(f4(x281,f4(x282,x283))))),f2(f4(f4(x282,x281),x283),f3(f4(x282,f4(x281,x283)))))
% 0.21/0.63 [30]E(x301,x302)+~E(f2(x303,x301),f2(x303,x302))
% 0.21/0.63 [31]E(x311,x312)+~E(f2(x311,x313),f2(x312,x313))
% 0.21/0.63 %EqnAxiom
% 0.21/0.63 [1]E(x11,x11)
% 0.21/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.63 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 0.21/0.63 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53))
% 0.21/0.63 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62))
% 0.21/0.63 [7]~E(x71,x72)+E(f4(x71,x73),f4(x72,x73))
% 0.21/0.63 [8]~E(x81,x82)+E(f4(x83,x81),f4(x83,x82))
% 0.21/0.63
% 0.21/0.63 %-------------------------------------------
% 0.21/0.64 cnf(32,plain,
% 0.21/0.64 ($false),
% 0.21/0.64 inference(scs_inference,[],[20,26]),
% 0.21/0.64 ['proof']).
% 0.21/0.64 % SZS output end Proof
% 0.21/0.64 % Total time :0.000000s
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