TSTP Solution File: COL020-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COL020-1 : 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 : n020.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 18:21:21 EDT 2023
% Result : Unsatisfiable 0.23s 0.70s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.19 % Problem : COL020-1 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.20 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.17/0.41 % Computer : n020.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8042.1875MB
% 0.17/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Sun Aug 27 04:01:15 EDT 2023
% 0.17/0.41 % CPUTime :
% 0.23/0.64 start to proof:theBenchmark
% 0.23/0.70 %-------------------------------------------
% 0.23/0.70 % File :CSE---1.6
% 0.23/0.70 % Problem :theBenchmark
% 0.23/0.70 % Transform :cnf
% 0.23/0.70 % Format :tptp:raw
% 0.23/0.70 % Command :java -jar mcs_scs.jar %d %s
% 0.23/0.70
% 0.23/0.70 % Result :Theorem 0.010000s
% 0.23/0.70 % Output :CNFRefutation 0.010000s
% 0.23/0.70 %-------------------------------------------
% 0.23/0.70 %--------------------------------------------------------------------------
% 0.23/0.70 % File : COL020-1 : TPTP v8.1.2. Released v1.0.0.
% 0.23/0.70 % Domain : Combinatory Logic
% 0.23/0.70 % Problem : Weak fixed point for B, S, and C
% 0.23/0.70 % Version : [WM88] (equality) axioms.
% 0.23/0.70 % English : The weak fixed point property holds for the set P consisting
% 0.23/0.70 % of the combinators B, S, and C, where ((Sx)y)z = (xz)(yz),
% 0.23/0.70 % ((Bx)y)z = x(yz), ((Cx)y)z = (xz)y.
% 0.23/0.70
% 0.23/0.70 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
% 0.23/0.70 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
% 0.23/0.70 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% 0.23/0.70 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb
% 0.23/0.70 % Source : [MW88]
% 0.23/0.70 % Names : - [MW88]
% 0.23/0.70
% 0.23/0.70 % Status : Unsatisfiable
% 0.23/0.70 % Rating : 0.21 v8.1.0, 0.25 v7.5.0, 0.29 v7.4.0, 0.35 v7.3.0, 0.37 v7.1.0, 0.28 v7.0.0, 0.26 v6.4.0, 0.37 v6.3.0, 0.41 v6.2.0, 0.43 v6.1.0, 0.12 v6.0.0, 0.19 v5.5.0, 0.16 v5.4.0, 0.13 v5.3.0, 0.17 v5.2.0, 0.14 v5.1.0, 0.13 v5.0.0, 0.14 v4.1.0, 0.09 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 v2.6.0, 0.17 v2.5.0, 0.00 v2.4.0, 0.33 v2.3.0, 0.00 v2.0.0
% 0.23/0.70 % Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 1 RR)
% 0.23/0.70 % Number of literals : 4 ( 4 equ; 1 neg)
% 0.23/0.70 % Maximal clause size : 1 ( 1 avg)
% 0.23/0.70 % Maximal term depth : 4 ( 2 avg)
% 0.23/0.70 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.23/0.70 % Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% 0.23/0.70 % Number of variables : 10 ( 0 sgn)
% 0.23/0.70 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.23/0.70
% 0.23/0.70 % Comments :
% 0.23/0.70 %--------------------------------------------------------------------------
% 0.23/0.70 cnf(s_definition,axiom,
% 0.23/0.70 apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ).
% 0.23/0.70
% 0.23/0.70 cnf(b_definition,axiom,
% 0.23/0.70 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
% 0.23/0.70
% 0.23/0.70 cnf(c_definition,axiom,
% 0.23/0.70 apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y) ).
% 0.23/0.70
% 0.23/0.70 cnf(prove_fixed_point,negated_conjecture,
% 0.23/0.70 Y != apply(combinator,Y) ).
% 0.23/0.70
% 0.23/0.70 %--------------------------------------------------------------------------
% 0.23/0.70 %-------------------------------------------
% 0.23/0.70 % Proof found
% 0.23/0.70 % SZS status Theorem for theBenchmark
% 0.23/0.70 % SZS output start Proof
% 0.23/0.71 %ClaNum:9(EqnAxiom:5)
% 0.23/0.71 %VarNum:21(SingletonVarNum:10)
% 0.23/0.71 %MaxLitNum:1
% 0.23/0.71 %MaxfuncDepth:3
% 0.23/0.71 %SharedTerms:4
% 0.23/0.71 %goalClause: 9
% 0.23/0.71 %singleGoalClaCount:1
% 0.23/0.71 [9]~E(f2(a5,x91),x91)
% 0.23/0.71 [6]E(f2(f2(f2(a1,x61),x62),x63),f2(x61,f2(x62,x63)))
% 0.23/0.71 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(f2(x71,x73),x72))
% 0.23/0.71 [8]E(f2(f2(f2(a4,x81),x82),x83),f2(f2(x81,x83),f2(x82,x83)))
% 0.23/0.71 %EqnAxiom
% 0.23/0.71 [1]E(x11,x11)
% 0.23/0.71 [2]E(x22,x21)+~E(x21,x22)
% 0.23/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.23/0.71 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.23/0.71 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.23/0.71
% 0.23/0.71 %-------------------------------------------
% 0.23/0.71 cnf(11,plain,
% 0.23/0.71 (~E(f2(f2(f2(a1,a5),x111),x112),f2(x111,x112))),
% 0.23/0.71 inference(scs_inference,[],[9,6,2,3])).
% 0.23/0.71 cnf(16,plain,
% 0.23/0.71 (~E(f2(x161,x162),f2(f2(f2(a1,a5),x161),x162))),
% 0.23/0.71 inference(scs_inference,[],[11,2])).
% 0.23/0.71 cnf(17,plain,
% 0.23/0.71 ($false),
% 0.23/0.71 inference(scs_inference,[],[7,8,16,3]),
% 0.23/0.71 ['proof']).
% 0.23/0.71 % SZS output end Proof
% 0.23/0.71 % Total time :0.010000s
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