TSTP Solution File: COL026-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COL026-1 : 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 : n001.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 18:21:22 EDT 2023
% Result : Unsatisfiable 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COL026-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.16/0.35 % Computer : n001.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sun Aug 27 05:36:02 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % File :CSE---1.6
% 0.20/0.63 % Problem :theBenchmark
% 0.20/0.63 % Transform :cnf
% 0.20/0.63 % Format :tptp:raw
% 0.20/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.63
% 0.20/0.63 % Result :Theorem 0.000000s
% 0.20/0.63 % Output :CNFRefutation 0.000000s
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 %--------------------------------------------------------------------------
% 0.20/0.63 % File : COL026-1 : TPTP v8.1.2. Released v1.0.0.
% 0.20/0.63 % Domain : Combinatory Logic
% 0.20/0.63 % Problem : Weak fixed point for B and W1
% 0.20/0.63 % Version : [WM88] (equality) axioms.
% 0.20/0.63 % English : The weak fixed point property holds for the set P consisting
% 0.20/0.63 % of the combinators B and W1, where ((Bx)y)z = x(yz), (W1x)y
% 0.20/0.63 % = (yx)x.
% 0.20/0.63
% 0.20/0.63 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
% 0.20/0.63 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
% 0.20/0.63 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% 0.20/0.63 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb
% 0.20/0.63 % Source : [MW88]
% 0.20/0.63 % Names : - [MW88]
% 0.20/0.63
% 0.20/0.63 % Status : Unsatisfiable
% 0.20/0.63 % Rating : 0.25 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, 0.29 v6.1.0, 0.12 v6.0.0, 0.24 v5.5.0, 0.16 v5.4.0, 0.20 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, 0.29 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
% 0.20/0.63 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR)
% 0.20/0.63 % Number of literals : 3 ( 3 equ; 1 neg)
% 0.20/0.63 % Maximal clause size : 1 ( 1 avg)
% 0.20/0.63 % Maximal term depth : 4 ( 2 avg)
% 0.20/0.63 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.20/0.63 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 0.20/0.63 % Number of variables : 6 ( 0 sgn)
% 0.20/0.63 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.20/0.63
% 0.20/0.63 % Comments :
% 0.20/0.63 %--------------------------------------------------------------------------
% 0.20/0.63 cnf(b_definition,axiom,
% 0.20/0.63 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
% 0.20/0.63
% 0.20/0.63 cnf(w1_definition,axiom,
% 0.20/0.63 apply(apply(w1,X),Y) = apply(apply(Y,X),X) ).
% 0.20/0.63
% 0.20/0.63 cnf(prove_fixed_point,negated_conjecture,
% 0.20/0.63 Y != apply(combinator,Y) ).
% 0.20/0.63
% 0.20/0.63 %--------------------------------------------------------------------------
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark
% 0.20/0.63 % SZS output start Proof
% 0.20/0.63 %ClaNum:8(EqnAxiom:5)
% 0.20/0.63 %VarNum:13(SingletonVarNum:6)
% 0.20/0.63 %MaxLitNum:1
% 0.20/0.63 %MaxfuncDepth:3
% 0.20/0.63 %SharedTerms:3
% 0.20/0.63 %goalClause: 8
% 0.20/0.63 %singleGoalClaCount:1
% 0.20/0.63 [8]~E(f2(a4,x81),x81)
% 0.20/0.63 [6]E(f2(f2(a1,x61),x62),f2(f2(x62,x61),x61))
% 0.20/0.63 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(x71,f2(x72,x73)))
% 0.20/0.63 %EqnAxiom
% 0.20/0.63 [1]E(x11,x11)
% 0.20/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.64 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.20/0.64 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.20/0.64
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 cnf(10,plain,
% 0.20/0.64 (~E(f2(a4,f2(f2(x101,x102),x102)),f2(f2(a1,x102),x101))),
% 0.20/0.64 inference(scs_inference,[],[8,6,2,3])).
% 0.20/0.64 cnf(13,plain,
% 0.20/0.64 (~E(f2(f2(x131,x132),x132),f2(a4,f2(f2(a1,x132),x131)))),
% 0.20/0.64 inference(scs_inference,[],[8,6,2,3])).
% 0.20/0.64 cnf(30,plain,
% 0.20/0.64 (E(f2(f2(f2(a3,x301),x302),x303),f2(x301,f2(x302,x303)))),
% 0.20/0.64 inference(rename_variables,[],[7])).
% 0.20/0.64 cnf(31,plain,
% 0.20/0.64 ($false),
% 0.20/0.64 inference(scs_inference,[],[7,30,10,13,2,3,4]),
% 0.20/0.64 ['proof']).
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time :0.000000s
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