TSTP Solution File: RNG011-5 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : RNG011-5 : 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 : n025.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 13:47:42 EDT 2023
% Result : Unsatisfiable 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG011-5 : 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
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 03:09:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.19/0.59 %-------------------------------------------
% 0.19/0.59 % File :CSE---1.6
% 0.19/0.59 % Problem :theBenchmark
% 0.19/0.59 % Transform :cnf
% 0.19/0.59 % Format :tptp:raw
% 0.19/0.59 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.59
% 0.19/0.59 % Result :Theorem 0.000000s
% 0.19/0.59 % Output :CNFRefutation 0.000000s
% 0.19/0.59 %-------------------------------------------
% 0.19/0.59 %--------------------------------------------------------------------------
% 0.19/0.59 % File : RNG011-5 : TPTP v8.1.2. Released v1.0.0.
% 0.19/0.59 % Domain : Ring Theory
% 0.19/0.59 % Problem : In a right alternative ring (((X,X,Y)*X)*(X,X,Y)) = Add Id
% 0.19/0.59 % Version : [Ove90] (equality) axioms :
% 0.19/0.59 % Incomplete > Augmented > Incomplete.
% 0.19/0.59 % English :
% 0.19/0.59
% 0.19/0.59 % Refs : [Ove90] Overbeek (1990), ATP competition announced at CADE-10
% 0.19/0.59 % : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal
% 0.19/0.59 % : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11
% 0.19/0.60 % : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in
% 0.19/0.60 % Source : [Ove90]
% 0.19/0.60 % Names : CADE-11 Competition Eq-10 [Ove90]
% 0.19/0.60 % : THEOREM EQ-10 [LM93]
% 0.19/0.60 % : PROBLEM 10 [Zha93]
% 0.19/0.60
% 0.19/0.60 % Status : Unsatisfiable
% 0.19/0.60 % Rating : 0.04 v8.1.0, 0.05 v7.5.0, 0.04 v7.4.0, 0.09 v7.3.0, 0.00 v7.0.0, 0.05 v6.3.0, 0.00 v2.0.0
% 0.19/0.60 % Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 2 RR)
% 0.19/0.60 % Number of literals : 22 ( 22 equ; 1 neg)
% 0.19/0.60 % Maximal clause size : 1 ( 1 avg)
% 0.19/0.60 % Maximal term depth : 5 ( 2 avg)
% 0.19/0.60 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.19/0.60 % Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% 0.19/0.60 % Number of variables : 37 ( 2 sgn)
% 0.19/0.60 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.19/0.60
% 0.19/0.60 % Comments :
% 0.19/0.60 %--------------------------------------------------------------------------
% 0.19/0.60 %----Commutativity of addition
% 0.19/0.60 cnf(commutative_addition,axiom,
% 0.19/0.60 add(X,Y) = add(Y,X) ).
% 0.19/0.60
% 0.19/0.60 %----Associativity of addition
% 0.19/0.60 cnf(associative_addition,axiom,
% 0.19/0.60 add(add(X,Y),Z) = add(X,add(Y,Z)) ).
% 0.19/0.60
% 0.19/0.60 %----Additive identity
% 0.19/0.60 cnf(right_identity,axiom,
% 0.19/0.60 add(X,additive_identity) = X ).
% 0.19/0.60
% 0.19/0.60 cnf(left_identity,axiom,
% 0.19/0.60 add(additive_identity,X) = X ).
% 0.19/0.60
% 0.19/0.60 %----Additive inverse
% 0.19/0.60 cnf(right_additive_inverse,axiom,
% 0.19/0.60 add(X,additive_inverse(X)) = additive_identity ).
% 0.19/0.60
% 0.19/0.60 cnf(left_additive_inverse,axiom,
% 0.19/0.60 add(additive_inverse(X),X) = additive_identity ).
% 0.19/0.60
% 0.19/0.60 %----Inverse of identity is identity, stupid
% 0.19/0.60 cnf(additive_inverse_identity,axiom,
% 0.19/0.60 additive_inverse(additive_identity) = additive_identity ).
% 0.19/0.60
% 0.19/0.60 %----Axiom of Overbeek
% 0.19/0.60 cnf(property_of_inverse_and_add,axiom,
% 0.19/0.60 add(X,add(additive_inverse(X),Y)) = Y ).
% 0.19/0.60
% 0.19/0.60 %----Inverse of (x + y) is additive_inverse(x) + additive_inverse(y),
% 0.19/0.60 cnf(distribute_additive_inverse,axiom,
% 0.19/0.60 additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)) ).
% 0.19/0.60
% 0.19/0.60 %----Inverse of additive_inverse of X is X
% 0.19/0.60 cnf(additive_inverse_additive_inverse,axiom,
% 0.19/0.60 additive_inverse(additive_inverse(X)) = X ).
% 0.19/0.60
% 0.19/0.60 %----Behavior of 0 and the multiplication operation
% 0.19/0.60 cnf(multiply_additive_id1,axiom,
% 0.19/0.60 multiply(X,additive_identity) = additive_identity ).
% 0.19/0.60
% 0.19/0.60 cnf(multiply_additive_id2,axiom,
% 0.19/0.60 multiply(additive_identity,X) = additive_identity ).
% 0.19/0.60
% 0.19/0.60 %----Axiom of Overbeek
% 0.19/0.60 cnf(product_of_inverse,axiom,
% 0.19/0.60 multiply(additive_inverse(X),additive_inverse(Y)) = multiply(X,Y) ).
% 0.19/0.60
% 0.19/0.60 %----x * additive_inverse(y) = additive_inverse (x * y),
% 0.19/0.60 cnf(multiply_additive_inverse1,axiom,
% 0.19/0.60 multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ).
% 0.19/0.60
% 0.19/0.60 cnf(multiply_additive_inverse2,axiom,
% 0.19/0.60 multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ).
% 0.19/0.60
% 0.19/0.60 %----Distributive property of product over sum
% 0.19/0.60 cnf(distribute1,axiom,
% 0.19/0.60 multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ).
% 0.19/0.60
% 0.19/0.60 cnf(distribute2,axiom,
% 0.19/0.60 multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ).
% 0.19/0.60
% 0.19/0.60 %----Right alternative law
% 0.19/0.60 cnf(right_alternative,axiom,
% 0.19/0.60 multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) ).
% 0.19/0.60
% 0.19/0.60 %----Associator
% 0.19/0.60 cnf(associator,axiom,
% 0.19/0.60 associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ).
% 0.19/0.60
% 0.19/0.60 %----Commutator
% 0.19/0.60 cnf(commutator,axiom,
% 0.19/0.60 commutator(X,Y) = add(multiply(Y,X),additive_inverse(multiply(X,Y))) ).
% 0.19/0.60
% 0.19/0.60 %----Middle associator identity
% 0.19/0.60 cnf(middle_associator,axiom,
% 0.19/0.60 multiply(multiply(associator(X,X,Y),X),associator(X,X,Y)) = additive_identity ).
% 0.19/0.60
% 0.19/0.60 cnf(prove_equality,negated_conjecture,
% 0.19/0.60 multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity ).
% 0.19/0.60
% 0.19/0.60 %--------------------------------------------------------------------------
% 0.19/0.60 %-------------------------------------------
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark
% 0.19/0.60 % SZS output start Proof
% 0.19/0.60 %ClaNum:28(EqnAxiom:8)
% 0.19/0.60 %VarNum:75(SingletonVarNum:32)
% 0.19/0.60 %MaxLitNum:1
% 0.19/0.60 %MaxfuncDepth:5
% 0.19/0.60 %SharedTerms:14
% 0.19/0.60 %goalClause: 28
% 0.19/0.60 %singleGoalClaCount:1
% 0.19/0.60 [9]E(f4(a1),a1)
% 0.19/0.60 [28]~E(f5(f5(f2(f5(f5(a3,a3),a6),f4(f5(a3,f5(a3,a6)))),a3),f2(f5(f5(a3,a3),a6),f4(f5(a3,f5(a3,a6))))),a1)
% 0.19/0.60 [11]E(f5(x111,a1),a1)
% 0.19/0.60 [12]E(f5(a1,x121),a1)
% 0.19/0.60 [13]E(f2(x131,a1),x131)
% 0.19/0.60 [14]E(f2(a1,x141),x141)
% 0.19/0.60 [10]E(f4(f4(x101)),x101)
% 0.19/0.60 [15]E(f2(x151,f4(x151)),a1)
% 0.19/0.60 [16]E(f2(f4(x161),x161),a1)
% 0.19/0.60 [17]E(f2(x171,x172),f2(x172,x171))
% 0.19/0.60 [18]E(f5(f4(x181),f4(x182)),f5(x181,x182))
% 0.19/0.60 [19]E(f4(f5(x191,x192)),f5(x191,f4(x192)))
% 0.19/0.60 [20]E(f4(f5(x201,x202)),f5(f4(x201),x202))
% 0.19/0.60 [22]E(f4(f2(x221,x222)),f2(f4(x221),f4(x222)))
% 0.19/0.60 [24]E(f5(f5(x241,x242),x242),f5(x241,f5(x242,x242)))
% 0.19/0.60 [21]E(f2(x211,f2(f4(x211),x212)),x212)
% 0.19/0.60 [27]E(f5(f5(f2(f5(f5(x271,x271),x272),f4(f5(x271,f5(x271,x272)))),x271),f2(f5(f5(x271,x271),x272),f4(f5(x271,f5(x271,x272))))),a1)
% 0.19/0.60 [23]E(f2(f2(x231,x232),x233),f2(x231,f2(x232,x233)))
% 0.19/0.60 [25]E(f2(f5(x251,x252),f5(x251,x253)),f5(x251,f2(x252,x253)))
% 0.19/0.60 [26]E(f2(f5(x261,x262),f5(x263,x262)),f5(f2(x261,x263),x262))
% 0.19/0.60 %EqnAxiom
% 0.19/0.60 [1]E(x11,x11)
% 0.19/0.60 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.60 [4]~E(x41,x42)+E(f4(x41),f4(x42))
% 0.19/0.60 [5]~E(x51,x52)+E(f5(x51,x53),f5(x52,x53))
% 0.19/0.60 [6]~E(x61,x62)+E(f5(x63,x61),f5(x63,x62))
% 0.19/0.60 [7]~E(x71,x72)+E(f2(x71,x73),f2(x72,x73))
% 0.19/0.60 [8]~E(x81,x82)+E(f2(x83,x81),f2(x83,x82))
% 0.19/0.60
% 0.19/0.60 %-------------------------------------------
% 0.19/0.60 cnf(29,plain,
% 0.19/0.60 ($false),
% 0.19/0.60 inference(scs_inference,[],[28,27]),
% 0.19/0.60 ['proof']).
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time :0.000000s
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