TSTP Solution File: COL057-1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COL057-1 : 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 : n023.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 18:21:30 EDT 2023
% Result : Unsatisfiable 2.26s 2.34s
% Output : CNFRefutation 2.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL057-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.33 % Computer : n023.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 04:51:26 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.56 start to proof:theBenchmark
% 2.26/2.34 %-------------------------------------------
% 2.26/2.34 % File :CSE---1.6
% 2.26/2.34 % Problem :theBenchmark
% 2.26/2.34 % Transform :cnf
% 2.26/2.34 % Format :tptp:raw
% 2.26/2.34 % Command :java -jar mcs_scs.jar %d %s
% 2.26/2.34
% 2.26/2.34 % Result :Theorem 1.730000s
% 2.26/2.34 % Output :CNFRefutation 1.730000s
% 2.26/2.34 %-------------------------------------------
% 2.26/2.34 %--------------------------------------------------------------------------
% 2.26/2.34 % File : COL057-1 : TPTP v8.1.2. Released v1.0.0.
% 2.26/2.34 % Domain : Combinatory Logic
% 2.26/2.34 % Problem : Strong fixed point for S, B, C, and I
% 2.26/2.34 % Version : [WM88] (equality) axioms.
% 2.26/2.34 % English : The strong fixed point property holds for the set
% 2.26/2.34 % P consisting of the combinators S, B, C, and I, where
% 2.26/2.34 % ((Sx)y)z = (xz)(yz), ((Bx)y)z = x(yz), ((Cx)y)z = (xz)y, and
% 2.26/2.34 % Ix = x.
% 2.26/2.34
% 2.26/2.34 % Refs : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit
% 2.26/2.34 % Source : [LW92]
% 2.26/2.34 % Names : CL5 [LW92]
% 2.26/2.34
% 2.26/2.34 % Status : Unsatisfiable
% 2.26/2.34 % Rating : 0.38 v8.1.0, 0.35 v7.5.0, 0.42 v7.4.0, 0.48 v7.3.0, 0.47 v7.1.0, 0.39 v7.0.0, 0.37 v6.4.0, 0.42 v6.3.0, 0.41 v6.2.0, 0.43 v6.1.0, 0.44 v6.0.0, 0.48 v5.5.0, 0.47 v5.4.0, 0.53 v5.3.0, 0.58 v5.2.0, 0.50 v5.1.0, 0.47 v5.0.0, 0.43 v4.1.0, 0.36 v4.0.1, 0.50 v4.0.0, 0.54 v3.7.0, 0.22 v3.4.0, 0.25 v3.3.0, 0.36 v3.1.0, 0.56 v2.7.0, 0.27 v2.6.0, 0.17 v2.5.0, 0.00 v2.1.0, 0.25 v2.0.0
% 2.26/2.34 % Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 1 RR)
% 2.26/2.34 % Number of literals : 5 ( 5 equ; 1 neg)
% 2.26/2.34 % Maximal clause size : 1 ( 1 avg)
% 2.26/2.34 % Maximal term depth : 4 ( 2 avg)
% 2.26/2.34 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 2.26/2.34 % Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% 2.26/2.34 % Number of variables : 11 ( 0 sgn)
% 2.26/2.34 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 2.26/2.34
% 2.26/2.34 % Comments :
% 2.26/2.34 %--------------------------------------------------------------------------
% 2.26/2.34 cnf(s_definition,axiom,
% 2.26/2.34 apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ).
% 2.26/2.34
% 2.26/2.34 cnf(b_definition,axiom,
% 2.26/2.34 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
% 2.26/2.34
% 2.26/2.34 cnf(c_definition,axiom,
% 2.26/2.34 apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y) ).
% 2.26/2.34
% 2.26/2.34 cnf(i_definition,axiom,
% 2.26/2.34 apply(i,X) = X ).
% 2.26/2.34
% 2.26/2.34 cnf(prove_strong_fixed_point,negated_conjecture,
% 2.26/2.34 apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).
% 2.26/2.34
% 2.26/2.34 %--------------------------------------------------------------------------
% 2.26/2.34 %-------------------------------------------
% 2.26/2.34 % Proof found
% 2.26/2.34 % SZS status Theorem for theBenchmark
% 2.26/2.34 % SZS output start Proof
% 2.26/2.35 %ClaNum:11(EqnAxiom:6)
% 2.26/2.35 %VarNum:26(SingletonVarNum:11)
% 2.26/2.35 %MaxLitNum:1
% 2.26/2.35 %MaxfuncDepth:3
% 2.26/2.35 %SharedTerms:4
% 2.26/2.35 %goalClause: 11
% 2.26/2.35 %singleGoalClaCount:1
% 2.26/2.35 [7]E(f2(a1,x71),x71)
% 2.26/2.35 [11]~E(f2(f5(x111),f2(x111,f5(x111))),f2(x111,f5(x111)))
% 2.26/2.35 [8]E(f2(f2(f2(a3,x81),x82),x83),f2(x81,f2(x82,x83)))
% 2.26/2.35 [9]E(f2(f2(f2(a4,x91),x92),x93),f2(f2(x91,x93),x92))
% 2.26/2.35 [10]E(f2(f2(f2(a6,x101),x102),x103),f2(f2(x101,x103),f2(x102,x103)))
% 2.26/2.35 %EqnAxiom
% 2.26/2.35 [1]E(x11,x11)
% 2.26/2.35 [2]E(x22,x21)+~E(x21,x22)
% 2.26/2.35 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 2.26/2.35 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 2.26/2.35 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 2.26/2.35 [6]~E(x61,x62)+E(f5(x61),f5(x62))
% 2.26/2.35
% 2.26/2.35 %-------------------------------------------
% 2.26/2.35 cnf(12,plain,
% 2.26/2.35 (E(x121,f2(a1,x121))),
% 2.26/2.35 inference(scs_inference,[],[7,2])).
% 2.26/2.35 cnf(13,plain,
% 2.26/2.35 (~E(f2(f5(a1),f2(a1,f5(a1))),f5(a1))),
% 2.26/2.35 inference(scs_inference,[],[11,7,2,3])).
% 2.26/2.35 cnf(16,plain,
% 2.26/2.35 (E(f2(a1,x161),x161)),
% 2.26/2.35 inference(rename_variables,[],[7])).
% 2.26/2.35 cnf(17,plain,
% 2.26/2.35 (E(f2(x171,f2(a1,x172)),f2(x171,x172))),
% 2.26/2.35 inference(scs_inference,[],[11,7,16,2,3,6,5])).
% 2.26/2.35 cnf(18,plain,
% 2.26/2.35 (E(f2(f2(a1,x181),x182),f2(x181,x182))),
% 2.26/2.35 inference(scs_inference,[],[11,7,16,2,3,6,5,4])).
% 2.26/2.35 cnf(19,plain,
% 2.26/2.35 (~E(f2(x191,f5(x191)),f2(f5(x191),f2(x191,f5(x191))))),
% 2.26/2.35 inference(scs_inference,[],[11,2])).
% 2.26/2.35 cnf(20,plain,
% 2.26/2.35 (~E(f2(f5(a1),f5(a1)),f2(a1,f5(a1)))),
% 2.26/2.35 inference(scs_inference,[],[11,17,2,3])).
% 2.26/2.35 cnf(23,plain,
% 2.26/2.35 (~E(f5(a1),a1)),
% 2.26/2.35 inference(scs_inference,[],[11,17,2,3,4])).
% 2.26/2.35 cnf(24,plain,
% 2.26/2.35 (E(f2(x241,f2(x242,x243)),f2(f2(f2(a3,x241),x242),x243))),
% 2.26/2.35 inference(scs_inference,[],[8,2])).
% 2.26/2.35 cnf(25,plain,
% 2.26/2.35 (E(f2(x251,x252),f2(f2(a1,x251),x252))),
% 2.26/2.35 inference(scs_inference,[],[12,8,2,4])).
% 2.26/2.35 cnf(26,plain,
% 2.26/2.35 (E(f2(f2(f2(a3,a1),x261),x262),f2(x261,x262))),
% 2.26/2.35 inference(scs_inference,[],[7,12,8,2,4,3])).
% 2.26/2.35 cnf(29,plain,
% 2.26/2.35 (~E(f2(a1,f5(a1)),f2(f5(a1),f5(a1)))),
% 2.26/2.35 inference(scs_inference,[],[20,2])).
% 2.26/2.35 cnf(31,plain,
% 2.26/2.35 (~E(f2(f5(a1),f5(a1)),f5(a1))),
% 2.26/2.35 inference(scs_inference,[],[12,20,2,4,3])).
% 2.26/2.35 cnf(34,plain,
% 2.26/2.35 (E(f2(f2(f2(a1,x341),x342),x343),f2(f2(x341,x342),x343))),
% 2.26/2.35 inference(scs_inference,[],[9,18,2,4])).
% 2.26/2.35 cnf(35,plain,
% 2.26/2.35 (~E(f2(a1,f2(a1,f5(a1))),f2(f5(a1),f5(a1)))),
% 2.26/2.35 inference(scs_inference,[],[9,12,18,29,2,4,3])).
% 2.26/2.35 cnf(36,plain,
% 2.26/2.35 (E(x361,f2(a1,x361))),
% 2.26/2.35 inference(rename_variables,[],[12])).
% 2.26/2.35 cnf(37,plain,
% 2.26/2.35 (E(f2(x371,x372),f2(x371,f2(a1,x372)))),
% 2.26/2.35 inference(scs_inference,[],[9,12,36,18,29,2,4,3,5])).
% 2.26/2.35 cnf(38,plain,
% 2.26/2.35 (E(f5(x381),f5(f2(a1,x381)))),
% 2.26/2.35 inference(scs_inference,[],[9,12,36,18,29,2,4,3,5,6])).
% 2.26/2.35 cnf(40,plain,
% 2.26/2.35 (E(f2(x401,x402),f2(f2(f2(a3,a1),x401),x402))),
% 2.26/2.35 inference(scs_inference,[],[13,12,24,2,3])).
% 2.26/2.35 cnf(44,plain,
% 2.26/2.35 (~E(f2(x441,f5(x441)),f2(f2(f2(a3,a1),f5(x441)),f2(x441,f5(x441))))),
% 2.26/2.35 inference(scs_inference,[],[10,19,26,2,3])).
% 2.26/2.35 cnf(46,plain,
% 2.26/2.35 (~E(f2(f2(f2(a3,a1),f5(x461)),f2(x461,f5(x461))),f2(x461,f5(x461)))),
% 2.26/2.35 inference(scs_inference,[],[44,2])).
% 2.26/2.35 cnf(51,plain,
% 2.26/2.35 (E(f2(f2(f2(a6,x511),a1),x512),f2(f2(x511,x512),x512))),
% 2.26/2.35 inference(scs_inference,[],[10,17,34,4,2,3])).
% 2.26/2.35 cnf(53,plain,
% 2.26/2.35 (E(f2(x531,f2(a1,x532)),f2(x531,x532))),
% 2.26/2.35 inference(rename_variables,[],[17])).
% 2.26/2.35 cnf(55,plain,
% 2.26/2.35 (E(f5(f2(x551,f2(a1,x552))),f5(f2(x551,x552)))),
% 2.26/2.35 inference(scs_inference,[],[10,17,53,34,4,2,3,5,6])).
% 2.26/2.35 cnf(57,plain,
% 2.26/2.35 (~E(f2(x571,f5(x571)),f2(f2(f2(a6,f2(a3,a1)),x571),f5(x571)))),
% 2.26/2.35 inference(scs_inference,[],[10,31,44,2,3])).
% 2.26/2.35 cnf(65,plain,
% 2.26/2.35 (E(f2(f2(a1,x651),x652),f2(a1,f2(x651,x652)))),
% 2.26/2.35 inference(scs_inference,[],[12,18,57,2,3])).
% 2.26/2.35 cnf(67,plain,
% 2.26/2.35 (~E(f2(f2(a6,f2(a3,a1)),x671),x671)),
% 2.26/2.35 inference(scs_inference,[],[12,18,57,2,3,4])).
% 2.26/2.35 cnf(68,plain,
% 2.26/2.35 (E(f2(f5(x681),x682),f2(f5(f2(a1,x681)),x682))),
% 2.26/2.35 inference(scs_inference,[],[38,4])).
% 2.26/2.35 cnf(69,plain,
% 2.26/2.35 (E(f5(f2(x691,x692)),f5(f2(x691,f2(a1,x692))))),
% 2.26/2.35 inference(scs_inference,[],[55,38,4,2])).
% 2.26/2.35 cnf(70,plain,
% 2.26/2.35 (~E(f2(x701,f5(x701)),f2(f2(a1,f5(x701)),f2(x701,f5(x701))))),
% 2.26/2.35 inference(scs_inference,[],[19,18,55,38,4,2,3])).
% 2.26/2.35 cnf(71,plain,
% 2.26/2.35 (E(f2(f2(a1,x711),x712),f2(x711,x712))),
% 2.26/2.35 inference(rename_variables,[],[18])).
% 2.26/2.35 cnf(72,plain,
% 2.26/2.35 (E(f2(x721,f2(f2(a1,x722),x723)),f2(x721,f2(x722,x723)))),
% 2.26/2.35 inference(scs_inference,[],[19,18,71,55,38,4,2,3,5])).
% 2.26/2.35 cnf(75,plain,
% 2.26/2.35 (~E(f2(f2(f2(a3,a1),f5(a1)),f5(a1)),f2(a1,f5(a1)))),
% 2.26/2.35 inference(scs_inference,[],[17,46,70,2,3])).
% 2.26/2.35 cnf(79,plain,
% 2.26/2.35 (E(f2(x791,f2(x792,x793)),f2(x791,f2(f2(a1,x792),x793)))),
% 2.26/2.35 inference(scs_inference,[],[72,2])).
% 2.26/2.35 cnf(80,plain,
% 2.26/2.35 (E(f2(f2(a1,x801),f2(a1,x802)),f2(x801,x802))),
% 2.26/2.35 inference(scs_inference,[],[18,17,72,2,3])).
% 2.26/2.35 cnf(86,plain,
% 2.26/2.35 (~E(a1,f2(f2(a3,a1),f5(a1)))),
% 2.26/2.35 inference(scs_inference,[],[67,75,65,2,3,4])).
% 2.26/2.35 cnf(90,plain,
% 2.26/2.35 (E(f2(x901,f2(f2(a1,x902),f2(a1,x903))),f2(x901,f2(x902,x903)))),
% 2.26/2.35 inference(scs_inference,[],[23,68,80,38,2,3,5])).
% 2.26/2.35 cnf(91,plain,
% 2.26/2.35 (E(f5(f2(x911,x912)),f5(f2(f2(a1,x911),x912)))),
% 2.26/2.35 inference(scs_inference,[],[23,68,25,80,38,2,3,5,6])).
% 2.26/2.35 cnf(109,plain,
% 2.26/2.35 (E(f2(x1091,f2(x1092,x1093)),f2(f2(f2(a3,x1091),f2(a1,x1092)),x1093))),
% 2.26/2.35 inference(scs_inference,[],[24,79,90,38,5,2,3])).
% 2.26/2.35 cnf(134,plain,
% 2.26/2.35 (E(f5(f2(x1341,x1342)),f5(f2(f2(a1,x1341),f2(a1,x1342))))),
% 2.26/2.35 inference(scs_inference,[],[69,91,109,2,3])).
% 2.26/2.35 cnf(162,plain,
% 2.26/2.35 (E(f2(f2(x1621,x1622),x1622),f2(f2(f2(a6,x1621),a1),x1622))),
% 2.26/2.35 inference(scs_inference,[],[51,2])).
% 2.26/2.35 cnf(163,plain,
% 2.26/2.35 (~E(f2(a1,a1),f2(f2(a3,a1),f5(a1)))),
% 2.26/2.35 inference(scs_inference,[],[86,51,12,2,3])).
% 2.26/2.35 cnf(166,plain,
% 2.26/2.35 (E(f2(f2(f2(a1,x1661),x1662),x1663),f2(f2(x1661,x1662),f2(a1,x1663)))),
% 2.26/2.35 inference(scs_inference,[],[34,37,163,2,3])).
% 2.26/2.35 cnf(177,plain,
% 2.26/2.35 (E(f5(x1771),f5(f2(f2(a1,a1),f2(a1,x1771))))),
% 2.26/2.35 inference(scs_inference,[],[38,134,166,2,3])).
% 2.26/2.35 cnf(185,plain,
% 2.26/2.35 (~E(f2(f2(f2(a3,a1),a1),f2(a1,f5(a1))),f2(f5(a1),f5(a1)))),
% 2.26/2.35 inference(scs_inference,[],[35,40,177,2,3])).
% 2.26/2.35 cnf(192,plain,
% 2.26/2.35 (E(f2(f2(x1921,x1922),x1923),f2(f2(f2(f2(a3,a1),x1921),f2(a1,x1922)),x1923))),
% 2.26/2.35 inference(scs_inference,[],[40,37,185,2,3,5,4])).
% 2.26/2.35 cnf(201,plain,
% 2.26/2.35 (E(f2(f2(f2(f2(a3,a1),x2011),f2(a1,x2012)),x2013),f2(f2(x2011,x2012),x2013))),
% 2.26/2.35 inference(scs_inference,[],[192,2])).
% 2.26/2.35 cnf(267,plain,
% 2.26/2.35 (E(f2(f2(f2(f2(a3,a1),f2(a6,x2671)),f2(a1,a1)),x2672),f2(f2(x2671,x2672),x2672))),
% 2.26/2.35 inference(scs_inference,[],[51,201,80,2,3])).
% 2.26/2.35 cnf(274,plain,
% 2.26/2.35 (E(f2(f2(x2741,x2742),x2742),f2(f2(f2(f2(a3,a1),f2(a6,x2741)),f2(a1,a1)),x2742))),
% 2.26/2.35 inference(scs_inference,[],[267,2])).
% 2.26/2.35 cnf(342,plain,
% 2.26/2.35 (~E(f2(f2(f2(f2(a3,a1),f2(a6,a6)),f2(a1,a1)),f2(a3,a1)),f2(a3,a1))),
% 2.26/2.35 inference(scs_inference,[],[67,274,3])).
% 2.26/2.35 cnf(349,plain,
% 2.26/2.35 ($false),
% 2.26/2.35 inference(scs_inference,[],[67,342,162,109,2,3]),
% 2.26/2.35 ['proof']).
% 2.26/2.35 % SZS output end Proof
% 2.26/2.35 % Total time :1.730000s
%------------------------------------------------------------------------------