TSTP Solution File: RNG024-7 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : RNG024-7 : 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 : n001.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 13:47:45 EDT 2023
% Result : Unsatisfiable 1.60s 1.66s
% Output : CNFRefutation 1.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG024-7 : 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
% 0.13/0.34 % Computer : n001.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 : 300
% 0.13/0.34 % DateTime : Sun Aug 27 02:46:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 1.60/1.65 %-------------------------------------------
% 1.60/1.65 % File :CSE---1.6
% 1.60/1.65 % Problem :theBenchmark
% 1.60/1.65 % Transform :cnf
% 1.60/1.65 % Format :tptp:raw
% 1.60/1.65 % Command :java -jar mcs_scs.jar %d %s
% 1.60/1.65
% 1.60/1.65 % Result :Theorem 1.050000s
% 1.60/1.65 % Output :CNFRefutation 1.050000s
% 1.60/1.65 %-------------------------------------------
% 1.60/1.66 %--------------------------------------------------------------------------
% 1.60/1.66 % File : RNG024-7 : TPTP v8.1.2. Released v1.0.0.
% 1.60/1.66 % Domain : Ring Theory (Alternative)
% 1.60/1.66 % Problem : Right alternative
% 1.60/1.66 % Version : [Ste87] (equality) axioms : Augmented.
% 1.60/1.66 % Theorem formulation : In terms of associators
% 1.60/1.66 % English :
% 1.60/1.66
% 1.60/1.66 % Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin
% 1.60/1.66 % : [Ste92] Stevens (1992), Unpublished Note
% 1.60/1.66 % Source : [TPTP]
% 1.60/1.66 % Names :
% 1.60/1.66
% 1.60/1.66 % Status : Unsatisfiable
% 1.60/1.66 % Rating : 0.04 v8.1.0, 0.05 v7.5.0, 0.04 v7.4.0, 0.09 v7.3.0, 0.05 v7.1.0, 0.11 v6.4.0, 0.05 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.12 v6.0.0, 0.14 v5.5.0, 0.11 v5.4.0, 0.13 v5.3.0, 0.08 v5.2.0, 0.07 v4.1.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.13 v2.0.0
% 1.60/1.66 % Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 1 RR)
% 1.60/1.66 % Number of literals : 23 ( 23 equ; 1 neg)
% 1.60/1.66 % Maximal clause size : 1 ( 1 avg)
% 1.60/1.66 % Maximal term depth : 5 ( 2 avg)
% 1.60/1.66 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 1.60/1.66 % Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% 1.60/1.66 % Number of variables : 45 ( 2 sgn)
% 1.60/1.66 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 1.60/1.66
% 1.60/1.66 % Comments :
% 1.60/1.66 %--------------------------------------------------------------------------
% 1.60/1.66 %----Include nonassociative ring axioms
% 1.60/1.66 include('Axioms/RNG003-0.ax').
% 1.60/1.66 %--------------------------------------------------------------------------
% 1.60/1.66 %----The next 7 clause are extra lemmas which Stevens found useful
% 1.60/1.66 cnf(product_of_inverses,axiom,
% 1.60/1.66 multiply(additive_inverse(X),additive_inverse(Y)) = multiply(X,Y) ).
% 1.60/1.66
% 1.60/1.66 cnf(inverse_product1,axiom,
% 1.60/1.66 multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ).
% 1.60/1.66
% 1.60/1.66 cnf(inverse_product2,axiom,
% 1.60/1.66 multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ).
% 1.60/1.66
% 1.60/1.66 cnf(distributivity_of_difference1,axiom,
% 1.60/1.66 multiply(X,add(Y,additive_inverse(Z))) = add(multiply(X,Y),additive_inverse(multiply(X,Z))) ).
% 1.60/1.66
% 1.60/1.66 cnf(distributivity_of_difference2,axiom,
% 1.60/1.66 multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) ).
% 1.60/1.66
% 1.60/1.66 cnf(distributivity_of_difference3,axiom,
% 1.60/1.66 multiply(additive_inverse(X),add(Y,Z)) = add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))) ).
% 1.60/1.66
% 1.60/1.66 cnf(distributivity_of_difference4,axiom,
% 1.60/1.66 multiply(add(X,Y),additive_inverse(Z)) = add(additive_inverse(multiply(X,Z)),additive_inverse(multiply(Y,Z))) ).
% 1.60/1.66
% 1.60/1.66 cnf(prove_right_alternative,negated_conjecture,
% 1.60/1.66 associator(x,y,y) != additive_identity ).
% 1.60/1.66
% 1.60/1.66 %--------------------------------------------------------------------------
% 1.60/1.66 %-------------------------------------------
% 1.60/1.66 % Proof found
% 1.60/1.66 % SZS status Theorem for theBenchmark
% 1.60/1.66 % SZS output start Proof
% 1.60/1.66 %ClaNum:29(EqnAxiom:8)
% 1.60/1.66 %VarNum:88(SingletonVarNum:40)
% 1.60/1.66 %MaxLitNum:1
% 1.60/1.66 %MaxfuncDepth:4
% 1.60/1.66 %SharedTerms:10
% 1.60/1.66 %goalClause: 29
% 1.60/1.66 %singleGoalClaCount:1
% 1.60/1.66 [29]~E(f3(f4(f4(a5,a6),a6),f1(f4(a5,f4(a6,a6)))),a2)
% 1.60/1.66 [10]E(f4(x101,a2),a2)
% 1.60/1.66 [11]E(f4(a2,x111),a2)
% 1.60/1.66 [12]E(f3(x121,a2),x121)
% 1.60/1.66 [13]E(f3(a2,x131),x131)
% 1.60/1.66 [9]E(f1(f1(x91)),x91)
% 1.60/1.66 [14]E(f3(x141,f1(x141)),a2)
% 1.60/1.66 [15]E(f3(f1(x151),x151),a2)
% 1.60/1.66 [16]E(f3(x161,x162),f3(x162,x161))
% 1.60/1.66 [17]E(f4(f1(x171),f1(x172)),f4(x171,x172))
% 1.60/1.66 [18]E(f1(f4(x181,x182)),f4(x181,f1(x182)))
% 1.60/1.66 [19]E(f1(f4(x191,x192)),f4(f1(x191),x192))
% 1.60/1.66 [21]E(f4(f4(x211,x212),x212),f4(x211,f4(x212,x212)))
% 1.60/1.66 [22]E(f4(f4(x221,x221),x222),f4(x221,f4(x221,x222)))
% 1.60/1.66 [20]E(f3(f3(x201,x202),x203),f3(x201,f3(x202,x203)))
% 1.60/1.66 [23]E(f3(f4(x231,x232),f4(x231,x233)),f4(x231,f3(x232,x233)))
% 1.60/1.66 [24]E(f3(f4(x241,x242),f4(x243,x242)),f4(f3(x241,x243),x242))
% 1.60/1.66 [25]E(f3(f4(x251,x252),f1(f4(x251,x253))),f4(x251,f3(x252,f1(x253))))
% 1.60/1.66 [26]E(f3(f4(x261,x262),f1(f4(x263,x262))),f4(f3(x261,f1(x263)),x262))
% 1.60/1.66 [27]E(f3(f1(f4(x271,x272)),f1(f4(x271,x273))),f4(f1(x271),f3(x272,x273)))
% 1.60/1.66 [28]E(f3(f1(f4(x281,x282)),f1(f4(x283,x282))),f4(f3(x281,x283),f1(x282)))
% 1.60/1.66 %EqnAxiom
% 1.60/1.66 [1]E(x11,x11)
% 1.60/1.66 [2]E(x22,x21)+~E(x21,x22)
% 1.60/1.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.60/1.66 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 1.60/1.66 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53))
% 1.60/1.66 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62))
% 1.60/1.66 [7]~E(x71,x72)+E(f4(x71,x73),f4(x72,x73))
% 1.60/1.66 [8]~E(x81,x82)+E(f4(x83,x81),f4(x83,x82))
% 1.60/1.66
% 1.60/1.66 %-------------------------------------------
% 1.60/1.66 cnf(30,plain,
% 1.60/1.66 (E(x301,f3(x301,a2))),
% 1.60/1.66 inference(scs_inference,[],[12,2])).
% 1.60/1.66 cnf(31,plain,
% 1.60/1.66 (~E(f3(f4(f4(a5,a6),a6),f1(f4(a5,f4(a6,a6)))),f3(a2,a2))),
% 1.60/1.66 inference(scs_inference,[],[29,12,2,3])).
% 1.60/1.66 cnf(32,plain,
% 1.60/1.66 (E(f3(x321,a2),x321)),
% 1.60/1.66 inference(rename_variables,[],[12])).
% 1.60/1.66 cnf(35,plain,
% 1.60/1.66 (E(f3(x351,f3(x352,a2)),f3(x351,x352))),
% 1.60/1.66 inference(scs_inference,[],[29,12,32,2,3,8,7,6])).
% 1.60/1.66 cnf(37,plain,
% 1.60/1.66 (E(f1(f3(x371,a2)),f1(x371))),
% 1.60/1.66 inference(scs_inference,[],[29,12,32,2,3,8,7,6,5,4])).
% 1.60/1.66 cnf(38,plain,
% 1.60/1.66 (~E(f3(f1(f4(a5,f4(a6,a6))),f4(f4(a5,a6),a6)),a2)),
% 1.60/1.66 inference(scs_inference,[],[29,16,3])).
% 1.60/1.66 cnf(40,plain,
% 1.60/1.66 (~E(a2,f3(f4(f4(a5,a6),a6),f1(f4(a5,f4(a6,a6)))))),
% 1.60/1.66 inference(scs_inference,[],[29,16,3,2])).
% 1.60/1.66 cnf(44,plain,
% 1.60/1.66 (~E(f3(f1(f4(a5,f4(a6,a6))),f4(f4(a5,a6),a6)),f4(x441,a2))),
% 1.60/1.66 inference(scs_inference,[],[10,38,3])).
% 1.60/1.66 cnf(65,plain,
% 1.60/1.66 (~E(f3(f4(f4(a5,a6),a6),f1(f4(a5,f4(a6,a6)))),f3(f3(a2,a2),a2))),
% 1.60/1.66 inference(scs_inference,[],[12,31,3])).
% 1.60/1.66 cnf(81,plain,
% 1.60/1.66 (~E(f3(a2,f4(x811,a2)),f3(f1(f4(a5,f4(a6,a6))),f4(f4(a5,a6),a6)))),
% 1.60/1.66 inference(scs_inference,[],[13,44,3,2])).
% 1.60/1.66 cnf(82,plain,
% 1.60/1.66 (E(a2,f3(x821,f1(x821)))),
% 1.60/1.66 inference(scs_inference,[],[14,2])).
% 1.60/1.66 cnf(84,plain,
% 1.60/1.66 (E(f3(x841,f1(x841)),a2)),
% 1.60/1.66 inference(rename_variables,[],[14])).
% 1.60/1.66 cnf(87,plain,
% 1.60/1.66 (E(f3(f3(x871,f1(x871)),x872),f3(a2,x872))),
% 1.60/1.66 inference(scs_inference,[],[14,84,35,2,3,4,5])).
% 1.60/1.66 cnf(91,plain,
% 1.60/1.66 (E(f3(f1(x911),x911),f3(a2,a2))),
% 1.60/1.66 inference(scs_inference,[],[15,30,3])).
% 1.60/1.66 cnf(106,plain,
% 1.60/1.66 (E(f4(f3(x1061,x1062),x1063),f4(f3(x1062,x1061),x1063))),
% 1.60/1.66 inference(scs_inference,[],[16,37,18,3,4,6,5,8,7])).
% 1.60/1.67 cnf(116,plain,
% 1.60/1.67 (E(f4(x1161,f4(x1162,x1162)),f4(f4(x1161,x1162),x1162))),
% 1.60/1.67 inference(scs_inference,[],[17,21,3,2])).
% 1.60/1.67 cnf(121,plain,
% 1.60/1.67 (E(f3(f1(f4(x1211,x1212)),x1213),f3(f4(x1211,f1(x1212)),x1213))),
% 1.60/1.67 inference(scs_inference,[],[18,35,65,3,4,6,5])).
% 1.60/1.67 cnf(407,plain,
% 1.60/1.67 (~E(f3(x4071,f1(x4071)),f3(f4(f4(a5,a6),a6),f1(f4(a5,f4(a6,a6)))))),
% 1.60/1.67 inference(scs_inference,[],[91,82,40,2,3])).
% 1.60/1.67 cnf(471,plain,
% 1.60/1.67 (E(f3(f4(x4711,f1(x4712)),x4713),f3(f1(f4(x4711,x4712)),x4713))),
% 1.60/1.67 inference(scs_inference,[],[121,2])).
% 1.60/1.67 cnf(474,plain,
% 1.60/1.67 (~E(f3(a2,f4(x4741,a2)),f3(f4(a5,f1(f4(a6,a6))),f4(f4(a5,a6),a6)))),
% 1.60/1.67 inference(scs_inference,[],[81,471,3])).
% 1.60/1.67 cnf(476,plain,
% 1.60/1.67 (~E(f3(f4(a5,f1(f4(a6,a6))),f4(f4(a5,a6),a6)),f3(a2,f4(x4761,a2)))),
% 1.60/1.67 inference(scs_inference,[],[474,2])).
% 1.60/1.67 cnf(527,plain,
% 1.60/1.67 (~E(f3(f4(a5,f1(f4(a6,a6))),f4(f4(a5,a6),a6)),f3(f3(x5271,f1(x5271)),f4(x5272,a2)))),
% 1.60/1.67 inference(scs_inference,[],[87,476,3])).
% 1.60/1.67 cnf(531,plain,
% 1.60/1.67 (E(f4(x5311,f4(x5312,x5312)),f4(f4(x5311,x5312),x5312))),
% 1.60/1.67 inference(rename_variables,[],[116])).
% 1.60/1.67 cnf(534,plain,
% 1.60/1.67 ($false),
% 1.60/1.67 inference(scs_inference,[],[116,531,106,527,407,2,3,7,5]),
% 1.60/1.67 ['proof']).
% 1.60/1.67 % SZS output end Proof
% 1.60/1.67 % Total time :1.050000s
%------------------------------------------------------------------------------