TSTP Solution File: COL009-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COL009-1 : 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 : n026.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 18:21:18 EDT 2023
% Result : Unsatisfiable 0.80s 0.83s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL009-1 : 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
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 05:32:34 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.62 start to proof:theBenchmark
% 0.67/0.82 %-------------------------------------------
% 0.67/0.82 % File :CSE---1.6
% 0.67/0.82 % Problem :theBenchmark
% 0.67/0.82 % Transform :cnf
% 0.67/0.82 % Format :tptp:raw
% 0.67/0.82 % Command :java -jar mcs_scs.jar %d %s
% 0.67/0.82
% 0.67/0.82 % Result :Theorem 0.160000s
% 0.67/0.82 % Output :CNFRefutation 0.160000s
% 0.67/0.82 %-------------------------------------------
% 0.67/0.83 %--------------------------------------------------------------------------
% 0.67/0.83 % File : COL009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.67/0.83 % Domain : Combinatory Logic
% 0.67/0.83 % Problem : Weak fixed point for B and L2
% 0.67/0.83 % Version : [WM88] (equality) axioms.
% 0.67/0.83 % English : The weak fixed point property holds for the set P consisting
% 0.80/0.83 % of the combinators B and L2, where ((Bx)y)z = x(yz), (L2x)y
% 0.80/0.83 % = y(xx).
% 0.80/0.83
% 0.80/0.83 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
% 0.80/0.83 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
% 0.80/0.83 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% 0.80/0.83 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb
% 0.80/0.83 % Source : [MW88]
% 0.80/0.83 % Names : - [MW88]
% 0.80/0.83
% 0.80/0.83 % Status : Unsatisfiable
% 0.80/0.83 % Rating : 0.29 v8.1.0, 0.30 v7.5.0, 0.29 v7.4.0, 0.35 v7.3.0, 0.32 v7.1.0, 0.22 v7.0.0, 0.21 v6.4.0, 0.26 v6.3.0, 0.24 v6.2.0, 0.21 v6.1.0, 0.12 v6.0.0, 0.33 v5.5.0, 0.21 v5.4.0, 0.27 v5.3.0, 0.17 v5.2.0, 0.14 v5.1.0, 0.20 v5.0.0, 0.21 v4.1.0, 0.18 v4.0.1, 0.21 v4.0.0, 0.23 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 v2.2.1, 0.33 v2.2.0, 0.14 v2.1.0, 0.38 v2.0.0
% 0.80/0.83 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR)
% 0.80/0.83 % Number of literals : 3 ( 3 equ; 1 neg)
% 0.80/0.83 % Maximal clause size : 1 ( 1 avg)
% 0.80/0.83 % Maximal term depth : 4 ( 2 avg)
% 0.80/0.83 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.80/0.83 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 0.80/0.83 % Number of variables : 6 ( 0 sgn)
% 0.80/0.83 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.80/0.83
% 0.80/0.83 % Comments :
% 0.80/0.83 %--------------------------------------------------------------------------
% 0.80/0.83 cnf(b_definition,axiom,
% 0.80/0.83 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
% 0.80/0.83
% 0.80/0.83 cnf(l2_definition,axiom,
% 0.80/0.83 apply(apply(l2,X),Y) = apply(Y,apply(X,X)) ).
% 0.80/0.83
% 0.80/0.83 cnf(prove_fixed_point,negated_conjecture,
% 0.80/0.83 Y != apply(combinator,Y) ).
% 0.80/0.83
% 0.80/0.83 %--------------------------------------------------------------------------
% 0.80/0.83 %-------------------------------------------
% 0.80/0.83 % Proof found
% 0.80/0.83 % SZS status Theorem for theBenchmark
% 0.80/0.83 % SZS output start Proof
% 0.80/0.83 %ClaNum:8(EqnAxiom:5)
% 0.80/0.83 %VarNum:13(SingletonVarNum:6)
% 0.80/0.83 %MaxLitNum:1
% 0.80/0.83 %MaxfuncDepth:3
% 0.80/0.83 %SharedTerms:3
% 0.80/0.83 %goalClause: 8
% 0.80/0.83 %singleGoalClaCount:1
% 0.80/0.83 [8]~E(f2(a4,x81),x81)
% 0.80/0.83 [6]E(f2(f2(a1,x61),x62),f2(x62,f2(x61,x61)))
% 0.80/0.83 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(x71,f2(x72,x73)))
% 0.80/0.83 %EqnAxiom
% 0.80/0.83 [1]E(x11,x11)
% 0.80/0.83 [2]E(x22,x21)+~E(x21,x22)
% 0.80/0.83 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.80/0.83 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.80/0.83 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.80/0.83
% 0.80/0.83 %-------------------------------------------
% 0.80/0.83 cnf(9,plain,
% 0.80/0.83 (E(f2(x91,f2(x92,x92)),f2(f2(a1,x92),x91))),
% 0.80/0.83 inference(scs_inference,[],[6,2])).
% 0.80/0.83 cnf(13,plain,
% 0.80/0.83 (~E(f2(f2(a1,x131),a4),f2(x131,x131))),
% 0.80/0.83 inference(scs_inference,[],[8,9,2,3])).
% 0.80/0.83 cnf(17,plain,
% 0.80/0.83 (E(f2(x171,f2(x172,x173)),f2(f2(f2(a3,x171),x172),x173))),
% 0.80/0.83 inference(scs_inference,[],[7,2])).
% 0.80/0.83 cnf(18,plain,
% 0.80/0.83 (~E(f2(x181,x181),f2(f2(a1,x181),a4))),
% 0.80/0.83 inference(scs_inference,[],[13,2])).
% 0.80/0.83 cnf(19,plain,
% 0.80/0.83 (E(f2(f2(f2(a3,x191),x192),x192),f2(f2(a1,x192),x191))),
% 0.80/0.83 inference(scs_inference,[],[7,9,3])).
% 0.80/0.83 cnf(39,plain,
% 0.80/0.83 (~E(f2(x391,x391),f2(f2(f2(a3,a4),x391),x391))),
% 0.80/0.83 inference(scs_inference,[],[19,18,3])).
% 0.80/0.83 cnf(41,plain,
% 0.80/0.83 (~E(x411,f2(f2(a3,a4),x411))),
% 0.80/0.83 inference(scs_inference,[],[39,4])).
% 0.80/0.83 cnf(45,plain,
% 0.80/0.83 (~E(f2(f2(a3,a4),x451),x451)),
% 0.80/0.83 inference(scs_inference,[],[41,2])).
% 0.80/0.83 cnf(70,plain,
% 0.80/0.83 (~E(f2(f2(a3,a4),f2(f2(a1,x701),x702)),f2(x702,f2(x701,x701)))),
% 0.80/0.83 inference(scs_inference,[],[45,9,3])).
% 0.80/0.83 cnf(72,plain,
% 0.80/0.83 (~E(f2(f2(a1,x721),f2(a3,a4)),f2(x721,x721))),
% 0.80/0.83 inference(scs_inference,[],[45,9,3,5])).
% 0.80/0.83 cnf(77,plain,
% 0.80/0.83 (E(f2(x771,f2(x772,x773)),f2(f2(f2(a3,x771),x772),x773))),
% 0.80/0.83 inference(rename_variables,[],[17])).
% 0.80/0.83 cnf(78,plain,
% 0.80/0.83 ($false),
% 0.80/0.83 inference(scs_inference,[],[70,72,17,77,4,3,5]),
% 0.80/0.83 ['proof']).
% 0.80/0.83 % SZS output end Proof
% 0.80/0.83 % Total time :0.160000s
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