TSTP Solution File: COL001-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COL001-2 : 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 : n009.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 18:21:13 EDT 2023
% Result : Unsatisfiable 1.11s 1.20s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : COL001-2 : TPTP v8.1.2. Released v1.0.0.
% 0.02/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.10/0.30 % Computer : n009.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sun Aug 27 04:37:20 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.16/0.53 start to proof:theBenchmark
% 1.11/1.19 %-------------------------------------------
% 1.11/1.19 % File :CSE---1.6
% 1.11/1.19 % Problem :theBenchmark
% 1.11/1.19 % Transform :cnf
% 1.11/1.19 % Format :tptp:raw
% 1.11/1.19 % Command :java -jar mcs_scs.jar %d %s
% 1.11/1.19
% 1.11/1.19 % Result :Theorem 0.610000s
% 1.11/1.19 % Output :CNFRefutation 0.610000s
% 1.11/1.19 %-------------------------------------------
% 1.11/1.19 %--------------------------------------------------------------------------
% 1.11/1.19 % File : COL001-2 : TPTP v8.1.2. Released v1.0.0.
% 1.11/1.19 % Domain : Combinatory Logic
% 1.11/1.19 % Problem : Weak fixed point for S and K
% 1.11/1.19 % Version : [WM88] (equality) axioms : Augmented.
% 1.11/1.19 % English : The weak fixed point property holds for the set P consisting
% 1.11/1.19 % of the combinators S and K alone, where ((Sx)y)z = (xz)(yz)
% 1.11/1.19 % and (Kx)y = x.
% 1.11/1.19
% 1.11/1.19 % Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% 1.11/1.19 % Source : [TPTP]
% 1.11/1.19 % Names :
% 1.11/1.19
% 1.11/1.19 % Status : Unsatisfiable
% 1.11/1.19 % Rating : 0.21 v8.1.0, 0.20 v7.5.0, 0.25 v7.4.0, 0.30 v7.3.0, 0.26 v7.1.0, 0.17 v7.0.0, 0.16 v6.4.0, 0.21 v6.3.0, 0.18 v6.2.0, 0.21 v6.1.0, 0.12 v6.0.0, 0.24 v5.5.0, 0.21 v5.4.0, 0.13 v5.3.0, 0.17 v5.2.0, 0.21 v5.1.0, 0.27 v5.0.0, 0.29 v4.1.0, 0.18 v4.0.1, 0.21 v4.0.0, 0.31 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.1.0, 0.13 v2.0.0
% 1.11/1.19 % Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 1 RR)
% 1.11/1.19 % Number of literals : 6 ( 6 equ; 1 neg)
% 1.11/1.19 % Maximal clause size : 1 ( 1 avg)
% 1.11/1.19 % Maximal term depth : 6 ( 2 avg)
% 1.11/1.20 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 1.11/1.20 % Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% 1.11/1.20 % Number of variables : 11 ( 1 sgn)
% 1.11/1.20 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 1.11/1.20
% 1.11/1.20 % Comments : This allows the use of B and I in the proof, as done in the
% 1.11/1.20 % "Proof of Theorem C1" in [WM88].
% 1.11/1.20 %--------------------------------------------------------------------------
% 1.11/1.20 cnf(s_definition,axiom,
% 1.11/1.20 apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ).
% 1.11/1.20
% 1.11/1.20 cnf(k_definition,axiom,
% 1.11/1.20 apply(apply(k,X),Y) = X ).
% 1.11/1.20
% 1.11/1.20 cnf(b_definition,axiom,
% 1.11/1.20 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
% 1.11/1.20
% 1.11/1.20 cnf(i_definition,axiom,
% 1.11/1.20 apply(i,X) = X ).
% 1.11/1.20
% 1.11/1.20 cnf(sb_property,axiom,
% 1.11/1.20 apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)) = apply(x,apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))) ).
% 1.11/1.20
% 1.11/1.20 cnf(prove_fixed_point,negated_conjecture,
% 1.11/1.20 Y != apply(combinator,Y) ).
% 1.11/1.20
% 1.11/1.20 %--------------------------------------------------------------------------
% 1.11/1.20 %-------------------------------------------
% 1.11/1.20 % Proof found
% 1.11/1.20 % SZS status Theorem for theBenchmark
% 1.11/1.20 % SZS output start Proof
% 1.11/1.20 %ClaNum:11(EqnAxiom:5)
% 1.11/1.20 %VarNum:24(SingletonVarNum:11)
% 1.11/1.20 %MaxLitNum:1
% 1.11/1.20 %MaxfuncDepth:5
% 1.11/1.20 %SharedTerms:6
% 1.11/1.20 %goalClause: 11
% 1.11/1.20 %singleGoalClaCount:1
% 1.11/1.20 [6]E(f2(a1,x61),x61)
% 1.11/1.20 [11]~E(f2(a4,x111),x111)
% 1.11/1.20 [10]E(f2(a7,f2(f2(f2(a6,f2(a3,x101)),a1),f2(f2(a6,f2(a3,x101)),a1))),f2(f2(f2(a6,f2(a3,x101)),a1),f2(f2(a6,f2(a3,x101)),a1)))
% 1.11/1.20 [7]E(f2(f2(a5,x71),x72),x71)
% 1.11/1.20 [8]E(f2(f2(f2(a3,x81),x82),x83),f2(x81,f2(x82,x83)))
% 1.11/1.20 [9]E(f2(f2(f2(a6,x91),x92),x93),f2(f2(x91,x93),f2(x92,x93)))
% 1.11/1.20 %EqnAxiom
% 1.11/1.20 [1]E(x11,x11)
% 1.11/1.20 [2]E(x22,x21)+~E(x21,x22)
% 1.11/1.20 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.11/1.20 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 1.11/1.20 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 1.11/1.20
% 1.11/1.20 %-------------------------------------------
% 1.11/1.20 cnf(12,plain,
% 1.11/1.20 (E(x121,f2(a1,x121))),
% 1.11/1.20 inference(scs_inference,[],[6,2])).
% 1.11/1.20 cnf(13,plain,
% 1.11/1.20 (~E(f2(a4,x131),f2(a1,x131))),
% 1.11/1.20 inference(scs_inference,[],[11,6,2,3])).
% 1.11/1.20 cnf(14,plain,
% 1.11/1.20 (E(f2(a1,x141),x141)),
% 1.11/1.20 inference(rename_variables,[],[6])).
% 1.11/1.20 cnf(15,plain,
% 1.11/1.20 (E(f2(x151,f2(a1,x152)),f2(x151,x152))),
% 1.11/1.20 inference(scs_inference,[],[11,6,14,2,3,5])).
% 1.11/1.20 cnf(16,plain,
% 1.11/1.20 (E(f2(f2(a1,x161),x162),f2(x161,x162))),
% 1.11/1.20 inference(scs_inference,[],[11,6,14,2,3,5,4])).
% 1.11/1.20 cnf(17,plain,
% 1.11/1.20 (~E(x171,f2(a4,x171))),
% 1.11/1.20 inference(scs_inference,[],[11,2])).
% 1.11/1.20 cnf(18,plain,
% 1.11/1.20 (~E(f2(a4,x181),f2(a1,f2(a1,x181)))),
% 1.11/1.20 inference(scs_inference,[],[11,15,13,2,3])).
% 1.11/1.20 cnf(22,plain,
% 1.11/1.20 (E(x221,f2(f2(a5,x221),x222))),
% 1.11/1.20 inference(scs_inference,[],[7,2])).
% 1.11/1.20 cnf(25,plain,
% 1.11/1.20 (E(f2(x251,x252),f2(f2(a1,x251),x252))),
% 1.11/1.20 inference(scs_inference,[],[6,12,7,2,3,4])).
% 1.11/1.20 cnf(28,plain,
% 1.11/1.20 (~E(f2(a1,f2(a1,x281)),f2(a4,x281))),
% 1.11/1.20 inference(scs_inference,[],[6,17,18,3,2])).
% 1.11/1.20 cnf(29,plain,
% 1.11/1.20 (~E(x291,f2(a4,f2(a1,x291)))),
% 1.11/1.20 inference(scs_inference,[],[6,17,18,3,2,5])).
% 1.11/1.20 cnf(30,plain,
% 1.11/1.20 (E(f2(x301,f2(f2(a5,x302),x303)),f2(x301,x302))),
% 1.11/1.20 inference(scs_inference,[],[7,5])).
% 1.11/1.20 cnf(33,plain,
% 1.11/1.20 (E(f2(x331,f2(x332,x333)),f2(f2(f2(a3,x331),x332),x333))),
% 1.11/1.20 inference(scs_inference,[],[7,8,12,13,5,3,2])).
% 1.11/1.20 cnf(34,plain,
% 1.11/1.20 (E(f2(f2(a5,f2(f2(f2(a6,x341),x342),x343)),x344),f2(f2(x341,x343),f2(x342,x343)))),
% 1.11/1.20 inference(scs_inference,[],[7,9,3])).
% 1.11/1.20 cnf(47,plain,
% 1.11/1.20 (E(f2(f2(f2(f2(a6,x471),x472),x473),x474),f2(f2(f2(x471,x473),f2(x472,x473)),x474))),
% 1.11/1.20 inference(scs_inference,[],[9,4])).
% 1.11/1.20 cnf(48,plain,
% 1.11/1.20 (E(f2(f2(f2(a6,a1),x481),x482),f2(x482,f2(x481,x482)))),
% 1.11/1.20 inference(scs_inference,[],[9,16,4,3])).
% 1.11/1.20 cnf(57,plain,
% 1.11/1.20 (E(f2(x571,f2(x572,f2(a1,x573))),f2(x571,f2(x572,x573)))),
% 1.11/1.20 inference(scs_inference,[],[15,5])).
% 1.11/1.20 cnf(65,plain,
% 1.11/1.20 (~E(x651,f2(f2(a1,a4),x651))),
% 1.11/1.20 inference(scs_inference,[],[17,16,5,3])).
% 1.11/1.20 cnf(67,plain,
% 1.11/1.20 (E(f2(f2(f2(x671,x672),f2(x673,x672)),x674),f2(f2(f2(f2(a6,x671),x673),x672),x674))),
% 1.11/1.20 inference(scs_inference,[],[17,16,47,5,3,2])).
% 1.11/1.20 cnf(71,plain,
% 1.11/1.20 (~E(f2(f2(a1,a4),x711),x711)),
% 1.11/1.20 inference(scs_inference,[],[12,18,65,3,2])).
% 1.11/1.20 cnf(91,plain,
% 1.11/1.20 (~E(f2(x911,x912),f2(a4,f2(f2(a1,x911),x912)))),
% 1.11/1.20 inference(scs_inference,[],[16,17,3])).
% 1.11/1.20 cnf(100,plain,
% 1.11/1.20 (~E(f2(a4,f2(f2(a1,x1001),x1002)),f2(x1001,x1002))),
% 1.11/1.20 inference(scs_inference,[],[25,71,91,3,2])).
% 1.11/1.20 cnf(101,plain,
% 1.11/1.20 (~E(f2(f2(a1,f2(a1,a4)),x1011),x1011)),
% 1.11/1.20 inference(scs_inference,[],[25,71,91,3,2,5])).
% 1.11/1.20 cnf(113,plain,
% 1.11/1.20 (~E(f2(f2(a1,f2(a1,a4)),f2(f2(a5,x1131),x1132)),x1131)),
% 1.11/1.20 inference(scs_inference,[],[22,67,101,5,3])).
% 1.11/1.20 cnf(116,plain,
% 1.11/1.20 (~E(f2(f2(a5,f2(f2(a1,f2(a1,a4)),x1161)),x1162),x1161)),
% 1.11/1.20 inference(scs_inference,[],[113,5])).
% 1.11/1.20 cnf(117,plain,
% 1.11/1.20 (~E(f2(f2(a1,f2(a1,a4)),f2(f2(a5,x1171),x1172)),x1171)),
% 1.11/1.20 inference(rename_variables,[],[113])).
% 1.11/1.20 cnf(120,plain,
% 1.11/1.20 (~E(x1201,f2(f2(a1,f2(a1,a4)),f2(f2(a5,x1201),x1202)))),
% 1.11/1.20 inference(scs_inference,[],[28,25,113,117,5,3,2])).
% 1.11/1.20 cnf(121,plain,
% 1.11/1.20 (~E(f2(a5,f2(f2(a1,f2(a1,a4)),f2(x1211,x1212))),x1211)),
% 1.11/1.20 inference(scs_inference,[],[28,25,113,117,5,3,2,4])).
% 1.11/1.20 cnf(132,plain,
% 1.11/1.20 (~E(f2(a5,f2(f2(a1,f2(a1,a4)),f2(f2(a5,f2(x1321,x1322)),x1323))),x1321)),
% 1.11/1.20 inference(scs_inference,[],[22,120,116,121,5,3,2,4])).
% 1.11/1.20 cnf(134,plain,
% 1.11/1.20 (E(f2(x1341,f2(x1342,f2(f2(a5,x1343),x1344))),f2(x1341,f2(x1342,x1343)))),
% 1.11/1.20 inference(scs_inference,[],[30,4,5])).
% 1.11/1.20 cnf(138,plain,
% 1.11/1.20 (~E(f2(f2(a1,f2(a1,a4)),f2(f2(a5,f2(f2(a5,x1381),x1382)),x1383)),x1381)),
% 1.11/1.20 inference(scs_inference,[],[132,5])).
% 1.11/1.20 cnf(150,plain,
% 1.11/1.20 (~E(f2(f2(a1,f2(a1,a4)),f2(f2(a5,f2(f2(a5,x1501),x1502)),x1503)),x1501)),
% 1.11/1.20 inference(rename_variables,[],[138])).
% 1.11/1.20 cnf(153,plain,
% 1.11/1.20 (~E(x1531,f2(f2(a1,f2(a1,a4)),f2(f2(a5,f2(f2(a5,x1531),x1532)),x1533)))),
% 1.11/1.20 inference(scs_inference,[],[25,29,138,150,5,3,2])).
% 1.11/1.20 cnf(165,plain,
% 1.11/1.20 (~E(f2(a4,f2(f2(a1,f2(f2(a3,x1651),x1652)),x1653)),f2(x1651,f2(x1652,x1653)))),
% 1.11/1.20 inference(scs_inference,[],[33,134,153,100,5,4,3])).
% 1.11/1.20 cnf(176,plain,
% 1.11/1.20 (~E(f2(a4,f2(f2(a1,f2(f2(a3,x1761),x1762)),x1763)),f2(x1761,f2(x1762,x1763)))),
% 1.11/1.20 inference(rename_variables,[],[165])).
% 1.11/1.20 cnf(181,plain,
% 1.11/1.20 (~E(f2(x1811,f2(x1812,x1813)),f2(a4,f2(f2(a1,f2(f2(a3,x1811),x1812)),x1813)))),
% 1.11/1.20 inference(scs_inference,[],[34,33,165,176,5,4,3,2])).
% 1.11/1.20 cnf(188,plain,
% 1.11/1.20 (~E(f2(x1881,x1882),f2(f2(a1,f2(f2(a3,a4),x1881)),x1882))),
% 1.11/1.20 inference(scs_inference,[],[181,5])).
% 1.11/1.20 cnf(354,plain,
% 1.11/1.21 ($false),
% 1.11/1.21 inference(scs_inference,[],[48,57,188,3]),
% 1.11/1.21 ['proof']).
% 1.11/1.21 % SZS output end Proof
% 1.11/1.21 % Total time :0.610000s
%------------------------------------------------------------------------------