TSTP Solution File: COL044-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COL044-1 : 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 : n028.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 18:21:26 EDT 2023
% Result : Unsatisfiable 61.57s 61.63s
% Output : CNFRefutation 61.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL044-1 : 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
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sun Aug 27 04:54:08 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.53 start to proof:theBenchmark
% 61.50/61.61 %-------------------------------------------
% 61.50/61.61 % File :CSE---1.6
% 61.50/61.61 % Problem :theBenchmark
% 61.50/61.62 % Transform :cnf
% 61.50/61.62 % Format :tptp:raw
% 61.50/61.62 % Command :java -jar mcs_scs.jar %d %s
% 61.50/61.62
% 61.50/61.62 % Result :Theorem 61.030000s
% 61.50/61.62 % Output :CNFRefutation 61.030000s
% 61.50/61.62 %-------------------------------------------
% 61.57/61.63 %--------------------------------------------------------------------------
% 61.57/61.63 % File : COL044-1 : TPTP v8.1.2. Released v1.0.0.
% 61.57/61.63 % Domain : Combinatory Logic
% 61.57/61.63 % Problem : Strong fixed point for B and N
% 61.57/61.63 % Version : [WM88] (equality) axioms.
% 61.57/61.63 % English : The strong fixed point property holds for the set
% 61.57/61.63 % P consisting of the combinators B and N, where ((Bx)y)z
% 61.57/61.63 % = x(yz), ((Nx)y)z = ((xz)y)z.
% 61.57/61.63
% 61.57/61.63 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
% 61.57/61.63 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
% 61.57/61.63 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% 61.57/61.63 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb
% 61.57/61.63 % : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit
% 61.57/61.63 % : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St
% 61.57/61.63 % Source : [MW88]
% 61.57/61.63 % Names : - [MW88]
% 61.57/61.63 % : CL3 [LW92]
% 61.57/61.63 % : Question 5 [Wos93]
% 61.57/61.63
% 61.57/61.63 % Status : Unsatisfiable
% 61.57/61.63 % Rating : 0.29 v8.1.0, 0.35 v7.5.0, 0.33 v7.4.0, 0.39 v7.3.0, 0.37 v7.1.0, 0.28 v7.0.0, 0.26 v6.4.0, 0.32 v6.3.0, 0.29 v6.1.0, 0.31 v6.0.0, 0.38 v5.5.0, 0.32 v5.4.0, 0.33 v5.3.0, 0.42 v5.2.0, 0.36 v5.1.0, 0.47 v5.0.0, 0.43 v4.1.0, 0.36 v4.0.1, 0.43 v4.0.0, 0.46 v3.7.0, 0.22 v3.4.0, 0.25 v3.3.0, 0.29 v3.2.0, 0.21 v3.1.0, 0.22 v2.7.0, 0.18 v2.6.0, 0.33 v2.5.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.25 v2.0.0
% 61.57/61.63 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR)
% 61.57/61.63 % Number of literals : 3 ( 3 equ; 1 neg)
% 61.57/61.63 % Maximal clause size : 1 ( 1 avg)
% 61.57/61.63 % Maximal term depth : 4 ( 2 avg)
% 61.57/61.63 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 61.57/61.63 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 61.57/61.63 % Number of variables : 7 ( 0 sgn)
% 61.57/61.63 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 61.57/61.63
% 61.57/61.63 % Comments :
% 61.57/61.63 %--------------------------------------------------------------------------
% 61.57/61.63 cnf(b_definition,axiom,
% 61.57/61.63 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
% 61.57/61.63
% 61.57/61.63 cnf(n_definition,axiom,
% 61.57/61.63 apply(apply(apply(n,X),Y),Z) = apply(apply(apply(X,Z),Y),Z) ).
% 61.57/61.63
% 61.57/61.63 cnf(prove_fixed_point,negated_conjecture,
% 61.57/61.63 apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).
% 61.57/61.63
% 61.57/61.63 %--------------------------------------------------------------------------
% 61.57/61.63 %-------------------------------------------
% 61.57/61.63 % Proof found
% 61.57/61.63 % SZS status Theorem for theBenchmark
% 61.57/61.63 % SZS output start Proof
% 61.57/61.64 %ClaNum:9(EqnAxiom:6)
% 61.57/61.64 %VarNum:18(SingletonVarNum:7)
% 61.57/61.64 %MaxLitNum:1
% 61.57/61.64 %MaxfuncDepth:3
% 61.57/61.64 %SharedTerms:2
% 61.57/61.64 %goalClause: 9
% 61.57/61.64 %singleGoalClaCount:1
% 61.57/61.64 [9]~E(f2(f4(x91),f2(x91,f4(x91))),f2(x91,f4(x91)))
% 61.57/61.64 [7]E(f2(f2(f2(a1,x71),x72),x73),f2(x71,f2(x72,x73)))
% 61.57/61.64 [8]E(f2(f2(f2(a3,x81),x82),x83),f2(f2(f2(x81,x83),x82),x83))
% 61.57/61.64 %EqnAxiom
% 61.57/61.64 [1]E(x11,x11)
% 61.57/61.64 [2]E(x22,x21)+~E(x21,x22)
% 61.57/61.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 61.57/61.64 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 61.57/61.64 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 61.57/61.64 [6]~E(x61,x62)+E(f4(x61),f4(x62))
% 61.57/61.64
% 61.57/61.64 %-------------------------------------------
% 61.57/61.65 cnf(10,plain,
% 61.57/61.65 (E(f2(x101,f2(x102,x103)),f2(f2(f2(a1,x101),x102),x103))),
% 61.57/61.65 inference(scs_inference,[],[7,2])).
% 61.57/61.65 cnf(11,plain,
% 61.57/61.65 (E(f2(f2(f2(a3,a1),x111),x112),f2(x112,f2(x111,x112)))),
% 61.57/61.65 inference(scs_inference,[],[7,8,2,3])).
% 61.57/61.65 cnf(15,plain,
% 61.57/61.65 (~E(f2(f2(f2(a1,f4(x151)),x151),f4(x151)),f2(x151,f4(x151)))),
% 61.57/61.65 inference(scs_inference,[],[9,10,2,3])).
% 61.57/61.65 cnf(19,plain,
% 61.57/61.65 (E(f2(f2(f2(x191,x192),x193),x192),f2(f2(f2(a3,x191),x193),x192))),
% 61.57/61.65 inference(scs_inference,[],[8,2])).
% 61.57/61.65 cnf(20,plain,
% 61.57/61.65 (~E(f2(x201,f4(x201)),f2(f2(f2(a1,f4(x201)),x201),f4(x201)))),
% 61.57/61.65 inference(scs_inference,[],[15,2])).
% 61.57/61.65 cnf(21,plain,
% 61.57/61.65 (E(f2(x211,f2(x212,x211)),f2(f2(f2(a3,a1),x212),x211))),
% 61.57/61.65 inference(scs_inference,[],[10,19,3])).
% 61.57/61.65 cnf(27,plain,
% 61.57/61.65 (~E(x271,f2(f2(a3,a1),x271))),
% 61.57/61.65 inference(scs_inference,[],[8,20,3,4])).
% 61.57/61.65 cnf(28,plain,
% 61.57/61.65 (~E(f2(f2(f2(a1,x281),x282),x283),f2(f2(a3,a1),f2(x281,f2(x282,x283))))),
% 61.57/61.65 inference(scs_inference,[],[10,27,3])).
% 61.57/61.65 cnf(36,plain,
% 61.57/61.65 (E(f2(a1,f2(x361,a1)),f2(f2(f2(a3,a3),x361),a1))),
% 61.57/61.65 inference(scs_inference,[],[21,19,3])).
% 61.57/61.65 cnf(45,plain,
% 61.57/61.65 (E(f2(f2(f2(a1,a1),x451),a1),f2(f2(f2(a3,a3),x451),a1))),
% 61.57/61.65 inference(scs_inference,[],[36,7,3])).
% 61.57/61.65 cnf(52,plain,
% 61.57/61.65 (~E(f2(f2(f2(a1,x521),x522),x523),f2(f2(a3,a1),f2(x521,f2(x522,x523))))),
% 61.57/61.65 inference(rename_variables,[],[28])).
% 61.57/61.65 cnf(53,plain,
% 61.57/61.65 (~E(f2(f2(a3,a1),f2(x531,f2(x532,x533))),f2(f2(f2(a1,x531),x532),x533))),
% 61.57/61.65 inference(scs_inference,[],[28,52,45,3,2])).
% 61.57/61.65 cnf(54,plain,
% 61.57/61.65 (~E(f2(x541,x542),f2(f2(f2(a1,f2(a3,a1)),x541),x542))),
% 61.57/61.65 inference(scs_inference,[],[27,7,3])).
% 61.57/61.65 cnf(93,plain,
% 61.57/61.65 (~E(f2(f2(f2(a1,f2(a3,a1)),x931),x932),f2(x931,x932))),
% 61.57/61.65 inference(scs_inference,[],[53,54,10,3,2])).
% 61.57/61.65 cnf(165,plain,
% 61.57/61.65 (E(f2(f2(f2(f2(a1,x1651),x1652),x1653),x1654),f2(f2(x1651,f2(x1652,x1653)),x1654))),
% 61.57/61.65 inference(scs_inference,[],[7,4])).
% 61.57/61.65 cnf(177,plain,
% 61.57/61.65 (E(f2(f2(x1771,f2(x1772,x1773)),x1774),f2(f2(f2(f2(a1,x1771),x1772),x1773),x1774))),
% 61.57/61.65 inference(scs_inference,[],[165,11,4,2])).
% 61.57/61.65 cnf(343,plain,
% 61.57/61.65 ($false),
% 61.57/61.65 inference(scs_inference,[],[19,177,93,3]),
% 61.57/61.65 ['proof']).
% 61.57/61.66 % SZS output end Proof
% 61.57/61.66 % Total time :61.030000s
%------------------------------------------------------------------------------