TSTP Solution File: BOO021-1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : BOO021-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n008.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 : Wed Aug 30 18:05:27 EDT 2023
% Result : Unsatisfiable 1.07s 1.12s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO021-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.17/0.34 % Computer : n008.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 08:39:02 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 1.02/1.12 %-------------------------------------------
% 1.02/1.12 % File :CSE---1.6
% 1.02/1.12 % Problem :theBenchmark
% 1.02/1.12 % Transform :cnf
% 1.02/1.12 % Format :tptp:raw
% 1.02/1.12 % Command :java -jar mcs_scs.jar %d %s
% 1.02/1.12
% 1.02/1.12 % Result :Theorem 0.510000s
% 1.02/1.12 % Output :CNFRefutation 0.510000s
% 1.02/1.12 %-------------------------------------------
% 1.02/1.12 %--------------------------------------------------------------------------
% 1.02/1.12 % File : BOO021-1 : TPTP v8.1.2. Released v2.2.0.
% 1.02/1.12 % Domain : Boolean Algebra
% 1.02/1.12 % Problem : A Basis for Boolean Algebra
% 1.02/1.12 % Version : [MP96] (equality) axioms.
% 1.02/1.12 % English : This theorem starts with a (self-dual independent) basis_
% 1.02/1.12 % for Boolean algebra and derives commutativity of product.
% 1.02/1.12
% 1.02/1.12 % Refs : [McC98] McCune (1998), Email to G. Sutcliffe
% 1.02/1.12 % : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq
% 1.02/1.12 % Source : [McC98]
% 1.02/1.12 % Names : DUAL-BA-1 [MP96]
% 1.02/1.12
% 1.02/1.12 % Status : Unsatisfiable
% 1.02/1.12 % Rating : 0.00 v7.5.0, 0.04 v7.3.0, 0.05 v7.1.0, 0.06 v7.0.0, 0.05 v6.4.0, 0.11 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.06 v6.0.0, 0.10 v5.5.0, 0.16 v5.4.0, 0.13 v5.3.0, 0.08 v5.2.0, 0.07 v5.1.0, 0.20 v5.0.0, 0.14 v4.1.0, 0.09 v4.0.1, 0.14 v4.0.0, 0.15 v3.7.0, 0.00 v3.3.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1
% 1.02/1.12 % Syntax : Number of clauses : 7 ( 7 unt; 0 nHn; 1 RR)
% 1.02/1.12 % Number of literals : 7 ( 7 equ; 1 neg)
% 1.02/1.12 % Maximal clause size : 1 ( 1 avg)
% 1.02/1.12 % Maximal term depth : 3 ( 2 avg)
% 1.02/1.12 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 1.02/1.12 % Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% 1.02/1.12 % Number of variables : 12 ( 2 sgn)
% 1.02/1.12 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 1.02/1.12
% 1.02/1.12 % Comments : The other part of this problem is to prove associativity.
% 1.02/1.12 %--------------------------------------------------------------------------
% 1.02/1.12 %----Boolean Algebra:
% 1.02/1.12 cnf(multiply_add,axiom,
% 1.02/1.12 multiply(add(X,Y),Y) = Y ).
% 1.02/1.12
% 1.02/1.12 cnf(multiply_add_property,axiom,
% 1.02/1.12 multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) ).
% 1.02/1.12
% 1.02/1.12 cnf(additive_inverse,axiom,
% 1.02/1.12 add(X,inverse(X)) = n1 ).
% 1.02/1.12
% 1.02/1.12 cnf(add_multiply,axiom,
% 1.02/1.12 add(multiply(X,Y),Y) = Y ).
% 1.02/1.12
% 1.02/1.12 cnf(add_multiply_property,axiom,
% 1.02/1.12 add(X,multiply(Y,Z)) = multiply(add(Y,X),add(Z,X)) ).
% 1.02/1.12
% 1.02/1.12 cnf(multiplicative_inverse,axiom,
% 1.02/1.12 multiply(X,inverse(X)) = n0 ).
% 1.02/1.12
% 1.02/1.12 %----Denial of conclusion:
% 1.02/1.12 cnf(prove_commutativity_of_multiply,negated_conjecture,
% 1.02/1.12 multiply(b,a) != multiply(a,b) ).
% 1.02/1.12
% 1.02/1.12 %--------------------------------------------------------------------------
% 1.07/1.12 %-------------------------------------------
% 1.07/1.12 % Proof found
% 1.07/1.12 % SZS status Theorem for theBenchmark
% 1.07/1.12 % SZS output start Proof
% 1.07/1.12 %ClaNum:15(EqnAxiom:8)
% 1.07/1.12 %VarNum:26(SingletonVarNum:12)
% 1.07/1.12 %MaxLitNum:1
% 1.07/1.12 %MaxfuncDepth:2
% 1.07/1.12 %SharedTerms:7
% 1.07/1.12 %goalClause: 15
% 1.07/1.12 %singleGoalClaCount:1
% 1.07/1.12 [15]~E(f6(a4,a3),f6(a3,a4))
% 1.07/1.12 [9]E(f2(x91,f1(x91)),a5)
% 1.07/1.12 [10]E(f6(x101,f1(x101)),a7)
% 1.07/1.12 [11]E(f2(f6(x111,x112),x112),x112)
% 1.07/1.12 [12]E(f6(f2(x121,x122),x122),x122)
% 1.07/1.12 [13]E(f6(f2(x131,x132),f2(x133,x132)),f2(x132,f6(x131,x133)))
% 1.07/1.12 [14]E(f2(f6(x141,x142),f6(x143,x142)),f6(x142,f2(x141,x143)))
% 1.07/1.12 %EqnAxiom
% 1.07/1.12 [1]E(x11,x11)
% 1.07/1.12 [2]E(x22,x21)+~E(x21,x22)
% 1.07/1.12 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.07/1.12 [4]~E(x41,x42)+E(f1(x41),f1(x42))
% 1.07/1.12 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53))
% 1.07/1.12 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62))
% 1.07/1.12 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 1.07/1.12 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 1.07/1.13
% 1.07/1.13 %-------------------------------------------
% 1.07/1.13 cnf(16,plain,
% 1.07/1.13 (E(x161,f2(f6(x162,x161),x161))),
% 1.07/1.13 inference(scs_inference,[],[11,2])).
% 1.07/1.13 cnf(17,plain,
% 1.07/1.13 (~E(f6(a4,a3),f2(f6(x171,f6(a3,a4)),f6(a3,a4)))),
% 1.07/1.13 inference(scs_inference,[],[15,11,2,3])).
% 1.07/1.13 cnf(18,plain,
% 1.07/1.13 (E(f2(f6(x181,x182),x182),x182)),
% 1.07/1.13 inference(rename_variables,[],[11])).
% 1.07/1.13 cnf(19,plain,
% 1.07/1.13 (E(f6(x191,f2(f6(x192,x193),x193)),f6(x191,x193))),
% 1.07/1.13 inference(scs_inference,[],[15,11,18,2,3,8])).
% 1.07/1.13 cnf(20,plain,
% 1.07/1.13 (E(f6(f2(f6(x201,x202),x202),x203),f6(x202,x203))),
% 1.07/1.13 inference(scs_inference,[],[15,11,18,2,3,8,7])).
% 1.07/1.13 cnf(24,plain,
% 1.07/1.13 (~E(f6(a3,a4),f6(a4,a3))),
% 1.07/1.13 inference(scs_inference,[],[15,2])).
% 1.07/1.13 cnf(25,plain,
% 1.07/1.13 (~E(f2(f6(x251,f6(a4,a3)),f6(a4,a3)),f6(a3,a4))),
% 1.07/1.13 inference(scs_inference,[],[15,16,2,3])).
% 1.07/1.13 cnf(27,plain,
% 1.07/1.13 (E(a5,f2(x271,f1(x271)))),
% 1.07/1.13 inference(scs_inference,[],[9,2])).
% 1.07/1.13 cnf(30,plain,
% 1.07/1.13 (~E(f2(f6(x301,f6(a3,a4)),f6(a3,a4)),f6(a4,a3))),
% 1.07/1.13 inference(scs_inference,[],[17,2])).
% 1.07/1.13 cnf(31,plain,
% 1.07/1.13 (E(f2(x311,f1(x311)),f2(x312,f1(x312)))),
% 1.07/1.13 inference(scs_inference,[],[9,17,27,2,3])).
% 1.07/1.13 cnf(40,plain,
% 1.07/1.13 (~E(f6(a3,a4),f2(f6(x401,f6(a4,a3)),f6(a4,a3)))),
% 1.07/1.13 inference(scs_inference,[],[25,2])).
% 1.07/1.13 cnf(41,plain,
% 1.07/1.13 (~E(f6(a3,a4),f6(f2(x411,f6(a4,a3)),f6(a4,a3)))),
% 1.07/1.13 inference(scs_inference,[],[12,25,24,2,3])).
% 1.07/1.13 cnf(47,plain,
% 1.07/1.13 (~E(f6(f6(a4,a3),f6(a4,a3)),f6(a3,a4))),
% 1.07/1.13 inference(scs_inference,[],[20,41,2,3])).
% 1.07/1.13 cnf(49,plain,
% 1.07/1.13 (E(x491,f6(f2(x492,x491),x491))),
% 1.07/1.13 inference(scs_inference,[],[12,2])).
% 1.07/1.13 cnf(50,plain,
% 1.07/1.13 (~E(f6(f6(a4,a3),f6(a4,a3)),f6(f2(x501,f6(a3,a4)),f6(a3,a4)))),
% 1.07/1.13 inference(scs_inference,[],[12,47,2,3])).
% 1.07/1.13 cnf(51,plain,
% 1.07/1.13 (E(f6(f2(x511,x512),x512),x512)),
% 1.07/1.13 inference(rename_variables,[],[12])).
% 1.07/1.13 cnf(52,plain,
% 1.07/1.13 (E(f6(x521,f6(f2(x522,x523),x523)),f6(x521,x523))),
% 1.07/1.13 inference(scs_inference,[],[12,51,47,2,3,8])).
% 1.07/1.13 cnf(55,plain,
% 1.07/1.13 (E(f2(f6(f2(x551,x552),x552),x553),f2(x552,x553))),
% 1.07/1.13 inference(scs_inference,[],[12,51,47,2,3,8,7,6,5])).
% 1.07/1.13 cnf(57,plain,
% 1.07/1.13 (~E(f6(f2(x571,f6(a3,a4)),f6(a3,a4)),f6(f6(a4,a3),f6(a4,a3)))),
% 1.07/1.13 inference(scs_inference,[],[50,2])).
% 1.07/1.13 cnf(61,plain,
% 1.07/1.13 (~E(f6(f6(a3,a4),f6(a3,a4)),f6(f6(a4,a3),f6(a4,a3)))),
% 1.07/1.13 inference(scs_inference,[],[13,20,57,2,3])).
% 1.07/1.13 cnf(65,plain,
% 1.07/1.13 (~E(f6(a3,a4),f6(a4,f2(f6(x651,a3),a3)))),
% 1.07/1.13 inference(scs_inference,[],[19,61,24,2,3])).
% 1.07/1.13 cnf(67,plain,
% 1.07/1.13 (E(f6(x671,f2(x672,x673)),f2(f6(x672,x671),f6(x673,x671)))),
% 1.07/1.13 inference(scs_inference,[],[14,2])).
% 1.07/1.13 cnf(77,plain,
% 1.07/1.13 (~E(f2(f6(f6(x771,a3),a4),f6(a3,a4)),f6(a3,a4))),
% 1.07/1.13 inference(scs_inference,[],[67,65,2,3])).
% 1.07/1.13 cnf(83,plain,
% 1.07/1.13 (E(x831,f2(x831,x831))),
% 1.07/1.13 inference(scs_inference,[],[16,55,77,2,3])).
% 1.07/1.13 cnf(86,plain,
% 1.07/1.13 (E(f2(x861,x861),x861)),
% 1.07/1.13 inference(scs_inference,[],[83,2])).
% 1.07/1.13 cnf(88,plain,
% 1.07/1.13 (E(x881,f2(x881,x881))),
% 1.07/1.13 inference(rename_variables,[],[83])).
% 1.07/1.13 cnf(89,plain,
% 1.07/1.13 (E(f6(x891,x892),f6(x891,f2(x892,x892)))),
% 1.07/1.13 inference(scs_inference,[],[17,83,88,2,3,8])).
% 1.07/1.13 cnf(90,plain,
% 1.07/1.13 (E(f6(x901,x902),f6(f2(x901,x901),x902))),
% 1.07/1.13 inference(scs_inference,[],[17,83,88,2,3,8,7])).
% 1.07/1.13 cnf(92,plain,
% 1.07/1.13 (E(f2(x921,x922),f2(f2(x921,x921),x922))),
% 1.07/1.13 inference(scs_inference,[],[17,83,88,2,3,8,7,6,5])).
% 1.07/1.13 cnf(104,plain,
% 1.07/1.13 (E(f6(f2(x1041,x1041),x1042),f6(x1041,x1042))),
% 1.07/1.13 inference(scs_inference,[],[90,2])).
% 1.07/1.13 cnf(120,plain,
% 1.07/1.13 (E(f2(f2(x1201,x1201),x1202),f2(x1201,x1202))),
% 1.07/1.13 inference(scs_inference,[],[92,2])).
% 1.07/1.13 cnf(127,plain,
% 1.07/1.13 (~E(f2(f6(x1271,f6(a3,a4)),f6(a3,a4)),f6(f2(a4,a4),a3))),
% 1.07/1.13 inference(scs_inference,[],[30,104,3])).
% 1.07/1.13 cnf(131,plain,
% 1.07/1.13 (E(f2(f2(x1311,x1311),f1(x1311)),f2(x1312,f1(x1312)))),
% 1.07/1.13 inference(scs_inference,[],[31,120,127,2,3])).
% 1.07/1.13 cnf(139,plain,
% 1.07/1.13 (E(f2(x1391,x1392),f2(f6(f2(x1393,x1391),x1391),x1392))),
% 1.07/1.13 inference(scs_inference,[],[24,131,52,86,49,3,2,8,7,6,5])).
% 1.07/1.13 cnf(196,plain,
% 1.07/1.13 (~E(f6(a3,f2(a4,a4)),f2(f6(x1961,f6(a4,a3)),f6(a4,a3)))),
% 1.07/1.13 inference(scs_inference,[],[40,89,3])).
% 1.07/1.13 cnf(204,plain,
% 1.07/1.13 ($false),
% 1.07/1.13 inference(scs_inference,[],[196,67,139,2,3]),
% 1.07/1.13 ['proof']).
% 1.07/1.13 % SZS output end Proof
% 1.07/1.13 % Total time :0.510000s
%------------------------------------------------------------------------------