TSTP Solution File: COL027-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COL027-1 : 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 : n020.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 18:21:22 EDT 2023
% Result : Unsatisfiable 77.36s 77.75s
% Output : CNFRefutation 77.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COL027-1 : 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
% 0.14/0.35 % Computer : n020.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 05:19:44 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 77.36/77.74 %-------------------------------------------
% 77.36/77.74 % File :CSE---1.6
% 77.36/77.74 % Problem :theBenchmark
% 77.36/77.74 % Transform :cnf
% 77.36/77.74 % Format :tptp:raw
% 77.36/77.74 % Command :java -jar mcs_scs.jar %d %s
% 77.36/77.74
% 77.36/77.74 % Result :Theorem 76.790000s
% 77.36/77.74 % Output :CNFRefutation 76.790000s
% 77.36/77.74 %-------------------------------------------
% 77.36/77.75 %--------------------------------------------------------------------------
% 77.36/77.75 % File : COL027-1 : TPTP v8.1.2. Released v1.0.0.
% 77.36/77.75 % Domain : Combinatory Logic
% 77.36/77.75 % Problem : Weak fixed point for B and H
% 77.36/77.75 % Version : [WM88] (equality) axioms.
% 77.36/77.75 % English : The weak fixed point property holds for the set P consisting
% 77.36/77.75 % of the combinators B and H, where ((Bx)y)z = x(yz), ((Hx)y)z
% 77.36/77.75 % = ((xy)z)y.
% 77.36/77.75
% 77.36/77.75 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
% 77.36/77.75 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
% 77.36/77.75 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% 77.36/77.75 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb
% 77.36/77.75 % Source : [MW88]
% 77.36/77.75 % Names : - [MW88]
% 77.36/77.75
% 77.36/77.75 % Status : Unsatisfiable
% 77.36/77.75 % Rating : 0.21 v8.1.0, 0.25 v7.5.0, 0.21 v7.4.0, 0.30 v7.3.0, 0.21 v7.1.0, 0.11 v6.4.0, 0.16 v6.3.0, 0.12 v6.2.0, 0.07 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.05 v5.4.0, 0.00 v5.1.0, 0.13 v5.0.0, 0.14 v4.1.0, 0.09 v4.0.1, 0.14 v4.0.0, 0.23 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v2.0.0
% 77.36/77.75 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR)
% 77.36/77.75 % Number of literals : 3 ( 3 equ; 1 neg)
% 77.36/77.75 % Maximal clause size : 1 ( 1 avg)
% 77.36/77.75 % Maximal term depth : 4 ( 2 avg)
% 77.36/77.75 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 77.36/77.75 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 77.36/77.75 % Number of variables : 7 ( 0 sgn)
% 77.36/77.75 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 77.36/77.75
% 77.36/77.75 % Comments :
% 77.36/77.75 %--------------------------------------------------------------------------
% 77.36/77.75 cnf(b_definition,axiom,
% 77.36/77.75 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
% 77.36/77.75
% 77.36/77.75 cnf(h_definition,axiom,
% 77.36/77.75 apply(apply(apply(h,X),Y),Z) = apply(apply(apply(X,Y),Z),Y) ).
% 77.36/77.75
% 77.36/77.75 cnf(prove_fixed_point,negated_conjecture,
% 77.36/77.75 Y != apply(combinator,Y) ).
% 77.36/77.75
% 77.36/77.75 %--------------------------------------------------------------------------
% 77.36/77.75 %-------------------------------------------
% 77.36/77.75 % Proof found
% 77.36/77.75 % SZS status Theorem for theBenchmark
% 77.36/77.75 % SZS output start Proof
% 77.36/77.75 %ClaNum:8(EqnAxiom:5)
% 77.36/77.75 %VarNum:15(SingletonVarNum:7)
% 77.36/77.75 %MaxLitNum:1
% 77.36/77.75 %MaxfuncDepth:3
% 77.36/77.75 %SharedTerms:3
% 77.36/77.75 %goalClause: 8
% 77.36/77.75 %singleGoalClaCount:1
% 77.36/77.75 [8]~E(f2(a4,x81),x81)
% 77.36/77.75 [6]E(f2(f2(f2(a1,x61),x62),x63),f2(x61,f2(x62,x63)))
% 77.36/77.75 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(f2(f2(x71,x72),x73),x72))
% 77.36/77.75 %EqnAxiom
% 77.36/77.75 [1]E(x11,x11)
% 77.36/77.75 [2]E(x22,x21)+~E(x21,x22)
% 77.36/77.75 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 77.36/77.75 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 77.36/77.75 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 77.36/77.75
% 77.36/77.75 %-------------------------------------------
% 77.36/77.76 cnf(9,plain,
% 77.36/77.76 (E(f2(x91,f2(x92,x93)),f2(f2(f2(a1,x91),x92),x93))),
% 77.36/77.76 inference(scs_inference,[],[6,2])).
% 77.36/77.76 cnf(10,plain,
% 77.36/77.76 (~E(f2(a4,f2(x101,f2(x102,x103))),f2(f2(f2(a1,x101),x102),x103))),
% 77.36/77.76 inference(scs_inference,[],[8,6,2,3])).
% 77.36/77.76 cnf(13,plain,
% 77.36/77.76 (~E(f2(f2(f2(a1,a4),x131),x132),f2(x131,x132))),
% 77.36/77.76 inference(scs_inference,[],[8,9,2,3])).
% 77.36/77.76 cnf(16,plain,
% 77.36/77.76 (~E(f2(f2(a1,a4),x161),x161)),
% 77.36/77.76 inference(scs_inference,[],[8,9,2,3,4])).
% 77.36/77.76 cnf(17,plain,
% 77.36/77.76 (E(f2(f2(f2(x171,x172),x173),x172),f2(f2(f2(a3,x171),x172),x173))),
% 77.36/77.76 inference(scs_inference,[],[7,2])).
% 77.36/77.76 cnf(18,plain,
% 77.36/77.76 (~E(f2(x181,x182),f2(f2(f2(a1,a4),x181),x182))),
% 77.36/77.76 inference(scs_inference,[],[13,2])).
% 77.36/77.76 cnf(19,plain,
% 77.36/77.76 (E(f2(x191,f2(x192,x191)),f2(f2(f2(a3,a1),x191),x192))),
% 77.36/77.76 inference(scs_inference,[],[9,17,3])).
% 77.36/77.76 cnf(22,plain,
% 77.36/77.76 (E(f2(f2(f2(a3,a1),x221),x222),f2(x221,f2(x222,x221)))),
% 77.36/77.76 inference(scs_inference,[],[9,17,3,2])).
% 77.36/77.76 cnf(25,plain,
% 77.36/77.76 (~E(f2(a4,f2(x251,f2(x252,x253))),f2(f2(f2(a1,x251),x252),x253))),
% 77.36/77.76 inference(rename_variables,[],[10])).
% 77.36/77.76 cnf(27,plain,
% 77.36/77.76 (~E(x271,f2(f2(a1,a4),x271))),
% 77.36/77.76 inference(scs_inference,[],[7,10,25,18,3,2,4])).
% 77.36/77.76 cnf(40,plain,
% 77.36/77.76 (E(f2(x401,f2(a1,x401)),f2(f2(f2(a3,a3),a1),x401))),
% 77.36/77.76 inference(scs_inference,[],[17,19,3])).
% 77.36/77.76 cnf(43,plain,
% 77.36/77.76 (E(f2(f2(f2(a3,a3),a1),x431),f2(x431,f2(a1,x431)))),
% 77.36/77.76 inference(scs_inference,[],[17,19,3,2])).
% 77.36/77.76 cnf(55,plain,
% 77.36/77.76 (E(f2(f2(f2(a3,a3),a3),a1),f2(a3,f2(a1,a3)))),
% 77.36/77.76 inference(scs_inference,[],[17,40,3,2])).
% 77.36/77.76 cnf(155,plain,
% 77.36/77.76 (E(f2(x1551,f2(a3,f2(a1,a3))),f2(x1551,f2(f2(f2(a3,a3),a3),a1)))),
% 77.36/77.76 inference(scs_inference,[],[55,2,5])).
% 77.36/77.76 cnf(429,plain,
% 77.36/77.76 (~E(f2(f2(a1,a4),f2(f2(f2(a3,a1),x4291),x4292)),f2(x4291,f2(x4292,x4291)))),
% 77.36/77.76 inference(scs_inference,[],[16,19,3])).
% 77.36/77.76 cnf(431,plain,
% 77.36/77.76 (~E(f2(f2(f2(a3,a1),f2(a1,a4)),x4311),f2(x4311,f2(a1,a4)))),
% 77.36/77.76 inference(scs_inference,[],[16,19,3,5])).
% 77.36/77.76 cnf(434,plain,
% 77.36/77.76 (~E(f2(f2(f2(a1,f2(a1,a4)),x4341),f2(a1,a4)),f2(x4341,f2(a1,a4)))),
% 77.36/77.76 inference(scs_inference,[],[431,7,3])).
% 77.36/77.76 cnf(443,plain,
% 77.36/77.76 (~E(f2(f2(f2(a3,a1),f2(a1,a4)),f2(f2(a3,a1),x4431)),f2(x4431,f2(f2(a1,a4),x4431)))),
% 77.36/77.76 inference(scs_inference,[],[429,19,2,3])).
% 77.36/77.76 cnf(447,plain,
% 77.36/77.76 (~E(f2(f2(a1,f2(a1,a4)),x4471),x4471)),
% 77.36/77.76 inference(scs_inference,[],[429,434,19,2,3,5,4])).
% 77.36/77.76 cnf(458,plain,
% 77.36/77.76 (~E(f2(x4581,f2(f2(a1,a4),x4581)),f2(f2(f2(a3,a1),f2(a1,a4)),f2(f2(a3,a1),x4581)))),
% 77.36/77.76 inference(scs_inference,[],[443,447,55,3,2])).
% 77.36/77.76 cnf(460,plain,
% 77.36/77.76 (~E(f2(x4601,f2(a1,x4601)),f2(f2(a1,a4),f2(f2(f2(a3,a3),a1),x4601)))),
% 77.36/77.76 inference(scs_inference,[],[27,43,3])).
% 77.36/77.76 cnf(493,plain,
% 77.36/77.76 (~E(f2(f2(a1,a4),f2(f2(f2(a3,a3),a1),x4931)),f2(x4931,f2(a1,x4931)))),
% 77.36/77.76 inference(scs_inference,[],[460,2])).
% 77.36/77.76 cnf(825,plain,
% 77.36/77.76 (~E(f2(x8251,x8252),f2(f2(f2(a1,f2(a1,a4)),x8251),x8252))),
% 77.36/77.76 inference(scs_inference,[],[27,6,3])).
% 77.36/77.76 cnf(830,plain,
% 77.36/77.76 (~E(f2(x8301,f2(x8302,x8303)),f2(f2(a1,a4),f2(f2(f2(a1,x8301),x8302),x8303)))),
% 77.36/77.76 inference(scs_inference,[],[27,825,6,2,3])).
% 77.36/77.76 cnf(833,plain,
% 77.36/77.76 (~E(f2(x8331,f2(x8332,f2(a1,a4))),f2(f2(f2(a3,a1),f2(a1,a4)),f2(f2(a1,x8331),x8332)))),
% 77.36/77.76 inference(scs_inference,[],[830,22,3])).
% 77.36/77.76 cnf(1107,plain,
% 77.36/77.76 (E(f2(x11071,f2(f2(f2(a3,a3),a3),a1)),f2(x11071,f2(a3,f2(a1,a3))))),
% 77.36/77.76 inference(scs_inference,[],[155,458,19,5,4,2])).
% 77.36/77.76 cnf(1114,plain,
% 77.36/77.76 (E(f2(x11141,f2(f2(f2(a3,a3),a1),x11142)),f2(x11141,f2(x11142,f2(a1,x11142))))),
% 77.36/77.76 inference(scs_inference,[],[43,5])).
% 77.36/77.76 cnf(1127,plain,
% 77.36/77.76 (E(f2(f2(f2(a3,a1),a1),f2(f2(a3,a3),a3)),f2(a1,f2(a3,f2(a1,a3))))),
% 77.36/77.76 inference(scs_inference,[],[1107,1114,833,40,22,5,4,2,3])).
% 77.36/77.76 cnf(1167,plain,
% 77.36/77.76 (E(f2(f2(f2(f2(a1,x11671),x11672),x11673),x11674),f2(f2(x11671,f2(x11672,x11673)),x11674))),
% 77.36/77.76 inference(scs_inference,[],[6,1127,2,4])).
% 77.36/77.76 cnf(1383,plain,
% 77.36/77.76 (~E(f2(f2(f2(a1,f2(a1,a4)),f2(f2(a3,a3),a1)),x13831),f2(x13831,f2(a1,x13831)))),
% 77.36/77.76 inference(scs_inference,[],[9,493,3])).
% 77.36/77.76 cnf(1397,plain,
% 77.36/77.76 ($false),
% 77.36/77.76 inference(scs_inference,[],[7,18,1167,1383,2,3]),
% 77.36/77.76 ['proof']).
% 77.36/77.76 % SZS output end Proof
% 77.36/77.76 % Total time :76.790000s
%------------------------------------------------------------------------------