TSTP Solution File: COL009-1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : COL009-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 : Mon Jun 24 04:44:46 EDT 2024
% Result : Unsatisfiable 58.71s 58.77s
% Output : CNFRefutation 58.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL009-1 : TPTP v8.2.0. Released v1.0.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Jun 18 16:27:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.51/0.56 start to proof:theBenchmark
% 58.69/58.75 %-------------------------------------------
% 58.69/58.75 % File :CSE---1.7
% 58.69/58.75 % Problem :theBenchmark
% 58.69/58.75 % Transform :cnf
% 58.69/58.75 % Format :tptp:raw
% 58.69/58.75 % Command :java -jar mcs_scs.jar %d %s
% 58.69/58.75
% 58.69/58.75 % Result :Theorem 58.150000s
% 58.69/58.75 % Output :CNFRefutation 58.150000s
% 58.69/58.75 %-------------------------------------------
% 58.71/58.77 %--------------------------------------------------------------------------
% 58.71/58.77 % File : COL009-1 : TPTP v8.2.0. Released v1.0.0.
% 58.71/58.77 % Domain : Combinatory Logic
% 58.71/58.77 % Problem : Weak fixed point for B and L2
% 58.71/58.77 % Version : [WM88] (equality) axioms.
% 58.71/58.77 % English : The weak fixed point property holds for the set P consisting
% 58.71/58.77 % of the combinators B and L2, where ((Bx)y)z = x(yz), (L2x)y
% 58.71/58.77 % = y(xx).
% 58.71/58.77
% 58.71/58.77 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
% 58.71/58.77 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
% 58.71/58.77 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% 58.71/58.77 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb
% 58.71/58.77 % Source : [MW88]
% 58.71/58.77 % Names : - [MW88]
% 58.71/58.77
% 58.71/58.77 % Status : Unsatisfiable
% 58.71/58.77 % Rating : 0.27 v8.2.0, 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
% 58.71/58.77 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR)
% 58.71/58.77 % Number of literals : 3 ( 3 equ; 1 neg)
% 58.71/58.77 % Maximal clause size : 1 ( 1 avg)
% 58.71/58.77 % Maximal term depth : 4 ( 2 avg)
% 58.71/58.77 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 58.71/58.77 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 58.71/58.77 % Number of variables : 6 ( 0 sgn)
% 58.71/58.77 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 58.71/58.77
% 58.71/58.77 % Comments :
% 58.71/58.77 %--------------------------------------------------------------------------
% 58.71/58.77 cnf(b_definition,axiom,
% 58.71/58.77 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
% 58.71/58.77
% 58.71/58.77 cnf(l2_definition,axiom,
% 58.71/58.77 apply(apply(l2,X),Y) = apply(Y,apply(X,X)) ).
% 58.71/58.77
% 58.71/58.77 cnf(prove_fixed_point,negated_conjecture,
% 58.71/58.77 Y != apply(combinator,Y) ).
% 58.71/58.77
% 58.71/58.77 %--------------------------------------------------------------------------
% 58.71/58.77 %-------------------------------------------
% 58.71/58.77 % Proof found
% 58.71/58.77 % SZS status Theorem for theBenchmark
% 58.71/58.77 % SZS output start Proof
% 58.71/58.78 %ClaNum:8(EqnAxiom:5)
% 58.71/58.78 %VarNum:13(SingletonVarNum:6)
% 58.71/58.78 %MaxLitNum:1
% 58.71/58.78 %MaxfuncDepth:3
% 58.71/58.78 %SharedTerms:3
% 58.71/58.78 %goalClause: 8
% 58.71/58.78 %singleGoalClaCount:1
% 58.71/58.78 [8]~E(f2(a4,x81),x81)
% 58.71/58.78 [6]E(f2(f2(a1,x61),x62),f2(x62,f2(x61,x61)))
% 58.71/58.78 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(x71,f2(x72,x73)))
% 58.71/58.78 %EqnAxiom
% 58.71/58.78 [1]E(x11,x11)
% 58.71/58.78 [2]E(x22,x21)+~E(x21,x22)
% 58.71/58.78 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 58.71/58.78 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 58.71/58.78 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 58.71/58.78
% 58.71/58.78 %-------------------------------------------
% 58.71/58.79 cnf(9,plain,
% 58.71/58.79 (E(f2(x91,f2(x92,x92)),f2(f2(a1,x92),x91))),
% 58.71/58.79 inference(scs_inference,[],[6,2])).
% 58.71/58.79 cnf(12,plain,
% 58.71/58.79 (E(f2(x121,f2(x122,x123)),f2(f2(f2(a3,x121),x122),x123))),
% 58.71/58.79 inference(scs_inference,[],[7,2])).
% 58.71/58.79 cnf(13,plain,
% 58.71/58.79 (~E(f2(a4,f2(f2(a1,x131),x132)),f2(x132,f2(x131,x131)))),
% 58.71/58.79 inference(scs_inference,[],[8,9,7,2,3])).
% 58.71/58.79 cnf(144,plain,
% 58.71/58.79 (E(f2(x1441,f2(x1442,x1443)),f2(f2(f2(a3,x1441),x1442),x1443))),
% 58.71/58.79 inference(rename_variables,[],[12])).
% 58.71/58.80 cnf(146,plain,
% 58.71/58.80 ($false),
% 58.71/58.80 inference(scs_inference,[],[13,12,144,3,2,4]),
% 58.71/58.80 ['proof']).
% 58.71/58.80 % SZS output end Proof
% 58.71/58.80 % Total time :58.150000s
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