TSTP Solution File: COL030-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COL030-1 : 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 : n003.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 18:21:23 EDT 2023
% Result : Unsatisfiable 243.72s 243.82s
% Output : CNFRefutation 243.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : COL030-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 04:34:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 243.66/243.75 %-------------------------------------------
% 243.66/243.75 % File :CSE---1.6
% 243.66/243.75 % Problem :theBenchmark
% 243.66/243.75 % Transform :cnf
% 243.66/243.75 % Format :tptp:raw
% 243.66/243.75 % Command :java -jar mcs_scs.jar %d %s
% 243.66/243.75
% 243.66/243.75 % Result :Theorem 243.030000s
% 243.66/243.75 % Output :CNFRefutation 243.030000s
% 243.66/243.75 %-------------------------------------------
% 243.72/243.82 %--------------------------------------------------------------------------
% 243.72/243.82 % File : COL030-1 : TPTP v8.1.2. Released v1.0.0.
% 243.72/243.82 % Domain : Combinatory Logic
% 243.72/243.82 % Problem : Strong fixed point for S and L
% 243.72/243.82 % Version : [WM88] (equality) axioms.
% 243.72/243.82 % English : The strong fixed point property holds for the set
% 243.72/243.82 % P consisting of the combinators S and L, where ((Sx)y)z
% 243.72/243.82 % = (xz)(yz), (Lx)y = x(yy).
% 243.72/243.82
% 243.72/243.82 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
% 243.72/243.82 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
% 243.72/243.82 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% 243.72/243.82 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb
% 243.72/243.82 % Source : [MW88]
% 243.72/243.82 % Names : - [MW88]
% 243.72/243.82
% 243.72/243.82 % Status : Unsatisfiable
% 243.72/243.82 % Rating : 0.17 v8.1.0, 0.30 v7.5.0, 0.25 v7.4.0, 0.30 v7.3.0, 0.16 v7.1.0, 0.11 v6.4.0, 0.16 v6.3.0, 0.06 v6.2.0, 0.07 v6.1.0, 0.12 v6.0.0, 0.24 v5.5.0, 0.21 v5.4.0, 0.20 v5.3.0, 0.17 v5.2.0, 0.14 v5.1.0, 0.20 v5.0.0, 0.14 v4.1.0, 0.18 v4.0.1, 0.14 v4.0.0, 0.15 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.1.0, 0.11 v2.7.0, 0.09 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.13 v2.0.0
% 243.72/243.82 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR)
% 243.72/243.82 % Number of literals : 3 ( 3 equ; 1 neg)
% 243.72/243.82 % Maximal clause size : 1 ( 1 avg)
% 243.72/243.82 % Maximal term depth : 4 ( 2 avg)
% 243.72/243.82 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 243.72/243.82 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 243.72/243.82 % Number of variables : 6 ( 0 sgn)
% 243.72/243.82 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 243.72/243.82
% 243.72/243.82 % Comments :
% 243.72/243.82 %--------------------------------------------------------------------------
% 243.72/243.82 cnf(s_definition,axiom,
% 243.72/243.82 apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ).
% 243.72/243.82
% 243.72/243.82 cnf(l_definition,axiom,
% 243.72/243.82 apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ).
% 243.72/243.82
% 243.72/243.82 cnf(prove_fixed_point,negated_conjecture,
% 243.72/243.82 apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).
% 243.72/243.82
% 243.72/243.82 %--------------------------------------------------------------------------
% 243.72/243.82 %-------------------------------------------
% 243.72/243.82 % Proof found
% 243.72/243.82 % SZS status Theorem for theBenchmark
% 243.72/243.82 % SZS output start Proof
% 243.72/243.88 %ClaNum:9(EqnAxiom:6)
% 243.72/243.88 %VarNum:17(SingletonVarNum:6)
% 243.72/243.88 %MaxLitNum:1
% 243.72/243.88 %MaxfuncDepth:3
% 243.72/243.88 %SharedTerms:2
% 243.72/243.88 %goalClause: 9
% 243.72/243.88 %singleGoalClaCount:1
% 243.72/243.88 [9]~E(f2(f3(x91),f2(x91,f3(x91))),f2(x91,f3(x91)))
% 243.72/243.88 [7]E(f2(f2(a1,x71),x72),f2(x71,f2(x72,x72)))
% 243.72/243.88 [8]E(f2(f2(f2(a4,x81),x82),x83),f2(f2(x81,x83),f2(x82,x83)))
% 243.72/243.88 %EqnAxiom
% 243.72/243.88 [1]E(x11,x11)
% 243.72/243.88 [2]E(x22,x21)+~E(x21,x22)
% 243.72/243.88 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 243.72/243.88 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 243.72/243.88 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 243.72/243.88 [6]~E(x61,x62)+E(f3(x61),f3(x62))
% 243.72/243.88
% 243.72/243.88 %-------------------------------------------
% 243.72/243.95 cnf(16,plain,
% 243.72/243.96 (E(f2(x161,f2(f2(x162,x161),f2(x162,x161))),f2(f2(f2(a4,a1),x162),x161))),
% 243.72/243.96 inference(scs_inference,[],[7,8,3,2])).
% 243.72/243.96 cnf(157,plain,
% 243.72/243.96 ($false),
% 243.72/243.96 inference(scs_inference,[],[9,16,8,3,5]),
% 243.72/243.96 ['proof']).
% 243.72/243.96 % SZS output end Proof
% 243.72/243.96 % Total time :243.030000s
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