TSTP Solution File: ROB021-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ROB021-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 14:07:11 EDT 2023
% Result : Unsatisfiable 0.21s 0.73s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ROB021-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 06:47:54 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.59 start to proof:theBenchmark
% 0.21/0.72 %-------------------------------------------
% 0.21/0.72 % File :CSE---1.6
% 0.21/0.72 % Problem :theBenchmark
% 0.21/0.72 % Transform :cnf
% 0.21/0.72 % Format :tptp:raw
% 0.21/0.72 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.72
% 0.21/0.72 % Result :Theorem 0.080000s
% 0.21/0.72 % Output :CNFRefutation 0.080000s
% 0.21/0.72 %-------------------------------------------
% 0.21/0.72 %--------------------------------------------------------------------------
% 0.21/0.72 % File : ROB021-1 : TPTP v8.1.2. Released v1.0.0.
% 0.21/0.72 % Domain : Robbins Algebra
% 0.21/0.72 % Problem : (-X = -Y)=>(X = Y) => Boolean
% 0.21/0.72 % Version : [Win90] (equality) axioms.
% 0.21/0.72 % English : If (-X = -Y) => (X = Y) then the algebra is Boolean.
% 0.21/0.72
% 0.21/0.72 % Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras
% 0.21/0.72 % : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
% 0.21/0.73 % : [McC92] McCune (1992), Email to G. Sutcliffe
% 0.21/0.73 % Source : [McC92]
% 0.21/0.73 % Names : - [McC92]
% 0.21/0.73
% 0.21/0.73 % Status : Unsatisfiable
% 0.21/0.73 % Rating : 0.00 v6.3.0, 0.10 v6.2.0, 0.30 v6.1.0, 0.18 v6.0.0, 0.14 v5.5.0, 0.25 v5.4.0, 0.11 v5.3.0, 0.20 v5.2.0, 0.12 v5.1.0, 0.22 v5.0.0, 0.10 v4.1.0, 0.11 v4.0.1, 0.12 v4.0.0, 0.14 v3.7.0, 0.00 v2.2.1, 0.17 v2.2.0, 0.00 v2.0.0
% 0.21/0.73 % Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 2 RR)
% 0.21/0.73 % Number of literals : 6 ( 6 equ; 2 neg)
% 0.21/0.73 % Maximal clause size : 2 ( 1 avg)
% 0.21/0.73 % Maximal term depth : 6 ( 2 avg)
% 0.21/0.73 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.21/0.73 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.21/0.73 % Number of variables : 9 ( 0 sgn)
% 0.21/0.73 % SPC : CNF_UNS_RFO_PEQ_NUE
% 0.21/0.73
% 0.21/0.73 % Comments : Commutativity, associativity, and Huntington's axiom
% 0.21/0.73 % axiomatize Boolean algebra.
% 0.21/0.73 %--------------------------------------------------------------------------
% 0.21/0.73 %----Include axioms for Robbins algebra
% 0.21/0.73 include('Axioms/ROB001-0.ax').
% 0.21/0.73 %--------------------------------------------------------------------------
% 0.21/0.73 cnf(negative_equality_implies_positive_equality,hypothesis,
% 0.21/0.73 ( negate(X) != negate(Y)
% 0.21/0.73 | X = Y ) ).
% 0.21/0.73
% 0.21/0.73 cnf(prove_huntingtons_axiom,negated_conjecture,
% 0.21/0.73 add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b ).
% 0.21/0.73
% 0.21/0.73 %--------------------------------------------------------------------------
% 0.21/0.73 %-------------------------------------------
% 0.21/0.73 % Proof found
% 0.21/0.73 % SZS status Theorem for theBenchmark
% 0.21/0.73 % SZS output start Proof
% 0.21/0.73 %ClaNum:11(EqnAxiom:6)
% 0.21/0.73 %VarNum:19(SingletonVarNum:9)
% 0.21/0.73 %MaxLitNum:2
% 0.21/0.73 %MaxfuncDepth:5
% 0.21/0.73 %SharedTerms:10
% 0.21/0.73 %goalClause: 10
% 0.21/0.73 %singleGoalClaCount:1
% 0.21/0.73 [10]~E(f1(f3(f1(a2,f3(a4))),f3(f1(f3(a2),f3(a4)))),a4)
% 0.21/0.73 [7]E(f1(x71,x72),f1(x72,x71))
% 0.21/0.73 [9]E(f3(f1(f3(f1(x91,x92)),f3(f1(x91,f3(x92))))),x91)
% 0.21/0.73 [8]E(f1(f1(x81,x82),x83),f1(x81,f1(x82,x83)))
% 0.21/0.73 [11]E(x111,x112)+~E(f3(x111),f3(x112))
% 0.21/0.73 %EqnAxiom
% 0.21/0.73 [1]E(x11,x11)
% 0.21/0.73 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.73 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.73 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.21/0.73 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.21/0.73 [6]~E(x61,x62)+E(f3(x61),f3(x62))
% 0.21/0.73
% 0.21/0.73 %-------------------------------------------
% 0.21/0.73 cnf(12,plain,
% 0.21/0.73 (E(f1(x121,f1(x122,x123)),f1(f1(x121,x122),x123))),
% 0.21/0.73 inference(scs_inference,[],[8,2])).
% 0.21/0.73 cnf(16,plain,
% 0.21/0.73 (E(f1(x161,f1(x162,x163)),f1(x162,f1(x163,x161)))),
% 0.21/0.73 inference(scs_inference,[],[7,8,9,2,11,3])).
% 0.21/0.73 cnf(18,plain,
% 0.21/0.73 (E(f1(x181,x182),f1(x182,x181))),
% 0.21/0.73 inference(rename_variables,[],[7])).
% 0.21/0.73 cnf(19,plain,
% 0.21/0.73 (E(f3(f1(x191,x192)),f3(f1(x192,x191)))),
% 0.21/0.73 inference(scs_inference,[],[7,18,8,9,2,11,3,6])).
% 0.21/0.73 cnf(20,plain,
% 0.21/0.73 (E(f1(x201,f1(x202,x203)),f1(x201,f1(x203,x202)))),
% 0.21/0.73 inference(scs_inference,[],[7,18,8,9,2,11,3,6,5])).
% 0.21/0.73 cnf(23,plain,
% 0.21/0.73 (~E(f1(f3(f1(f3(a2),f3(a4))),f3(f1(a2,f3(a4)))),a4)),
% 0.21/0.73 inference(scs_inference,[],[10,7,2,3])).
% 0.21/0.73 cnf(25,plain,
% 0.21/0.73 (E(x251,f3(f1(f3(f1(x251,x252)),f3(f1(x251,f3(x252))))))),
% 0.21/0.73 inference(scs_inference,[],[9,2])).
% 0.21/0.73 cnf(30,plain,
% 0.21/0.73 (E(f1(f1(x301,x302),x303),f1(f1(x303,x301),x302))),
% 0.21/0.73 inference(scs_inference,[],[7,12,23,2,3])).
% 0.21/0.73 cnf(45,plain,
% 0.21/0.73 (E(x451,f3(f1(f3(f1(x451,f3(x452))),f3(f1(x451,x452)))))),
% 0.21/0.73 inference(scs_inference,[],[16,19,25,30,5,6,2,4,3])).
% 0.21/0.73 cnf(48,plain,
% 0.21/0.73 (E(x481,f1(f3(f1(f3(x481),f3(x482))),f3(f1(f3(x481),x482))))),
% 0.21/0.73 inference(scs_inference,[],[45,11])).
% 0.21/0.73 cnf(56,plain,
% 0.21/0.73 (E(f1(x561,f3(f1(x562,x563))),f1(x561,f3(f1(x563,x562))))),
% 0.21/0.73 inference(scs_inference,[],[19,2,5])).
% 0.21/0.73 cnf(57,plain,
% 0.21/0.73 (E(f1(f3(f1(x571,x572)),x573),f1(f3(f1(x572,x571)),x573))),
% 0.21/0.73 inference(scs_inference,[],[19,4])).
% 0.21/0.73 cnf(59,plain,
% 0.21/0.73 (E(f1(f3(f1(f3(x591),f3(x592))),f3(f1(f3(x591),x592))),x591)),
% 0.21/0.73 inference(scs_inference,[],[19,20,48,4,5,2])).
% 0.21/0.73 cnf(76,plain,
% 0.21/0.73 (~E(f1(f3(f1(f3(a2),f3(a4))),f3(f1(f3(a4),a2))),a4)),
% 0.21/0.73 inference(scs_inference,[],[23,56,3])).
% 0.21/0.73 cnf(80,plain,
% 0.21/0.73 ($false),
% 0.21/0.73 inference(scs_inference,[],[59,57,76,2,3]),
% 0.21/0.73 ['proof']).
% 0.21/0.73 % SZS output end Proof
% 0.21/0.73 % Total time :0.080000s
%------------------------------------------------------------------------------