TSTP Solution File: COL035-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COL035-1 : 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 : n031.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 18:21:24 EDT 2023
% Result : Unsatisfiable 0.20s 0.66s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COL035-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 04:59:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % File :CSE---1.6
% 0.20/0.65 % Problem :theBenchmark
% 0.20/0.65 % Transform :cnf
% 0.20/0.65 % Format :tptp:raw
% 0.20/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.65
% 0.20/0.65 % Result :Theorem 0.040000s
% 0.20/0.65 % Output :CNFRefutation 0.040000s
% 0.20/0.65 %-------------------------------------------
% 0.20/0.66 %--------------------------------------------------------------------------
% 0.20/0.66 % File : COL035-1 : TPTP v8.1.2. Released v1.0.0.
% 0.20/0.66 % Domain : Combinatory Logic
% 0.20/0.66 % Problem : Strong fixed point for W, Q, and L
% 0.20/0.66 % Version : [WM88] (equality) axioms.
% 0.20/0.66 % English : The strong fixed point property holds for the set
% 0.20/0.66 % P consisting of the combinators W, Q, and L, where (Lx)y
% 0.20/0.66 % = x(yy), (Wx)y = (xy)y, ((Qx)y)z = y(xz).
% 0.20/0.66
% 0.20/0.66 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
% 0.20/0.66 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
% 0.20/0.66 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% 0.20/0.66 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb
% 0.20/0.66 % Source : [MW88]
% 0.20/0.66 % Names : - [MW88]
% 0.20/0.66
% 0.20/0.66 % Status : Unsatisfiable
% 0.20/0.66 % Rating : 0.29 v8.1.0, 0.30 v7.5.0, 0.33 v7.4.0, 0.39 v7.3.0, 0.37 v7.1.0, 0.28 v7.0.0, 0.26 v6.4.0, 0.32 v6.3.0, 0.29 v6.1.0, 0.31 v6.0.0, 0.33 v5.5.0, 0.37 v5.4.0, 0.33 v5.3.0, 0.42 v5.2.0, 0.36 v5.1.0, 0.40 v5.0.0, 0.36 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, 0.21 v3.2.0, 0.14 v3.1.0, 0.22 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, 0.25 v2.0.0
% 0.20/0.66 % Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 1 RR)
% 0.20/0.66 % Number of literals : 4 ( 4 equ; 1 neg)
% 0.20/0.66 % Maximal clause size : 1 ( 1 avg)
% 0.20/0.66 % Maximal term depth : 4 ( 2 avg)
% 0.20/0.66 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.20/0.66 % Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% 0.20/0.66 % Number of variables : 8 ( 0 sgn)
% 0.20/0.66 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.20/0.66
% 0.20/0.66 % Comments :
% 0.20/0.66 %--------------------------------------------------------------------------
% 0.20/0.66 cnf(l_definition,axiom,
% 0.20/0.66 apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ).
% 0.20/0.66
% 0.20/0.66 cnf(w_definition,axiom,
% 0.20/0.66 apply(apply(w,X),Y) = apply(apply(X,Y),Y) ).
% 0.20/0.66
% 0.20/0.66 cnf(q_definition,axiom,
% 0.20/0.66 apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ).
% 0.20/0.66
% 0.20/0.66 cnf(prove_fixed_point,negated_conjecture,
% 0.20/0.66 apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).
% 0.20/0.66
% 0.20/0.66 %--------------------------------------------------------------------------
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 % Proof found
% 0.20/0.66 % SZS status Theorem for theBenchmark
% 0.20/0.66 % SZS output start Proof
% 0.20/0.66 %ClaNum:10(EqnAxiom:6)
% 0.20/0.66 %VarNum:21(SingletonVarNum:8)
% 0.20/0.66 %MaxLitNum:1
% 0.20/0.66 %MaxfuncDepth:3
% 0.20/0.66 %SharedTerms:3
% 0.20/0.66 %goalClause: 10
% 0.20/0.66 %singleGoalClaCount:1
% 0.20/0.66 [10]~E(f2(f3(x101),f2(x101,f3(x101))),f2(x101,f3(x101)))
% 0.20/0.66 [7]E(f2(f2(a1,x71),x72),f2(x71,f2(x72,x72)))
% 0.20/0.66 [8]E(f2(f2(a4,x81),x82),f2(f2(x81,x82),x82))
% 0.20/0.66 [9]E(f2(f2(f2(a5,x91),x92),x93),f2(x92,f2(x91,x93)))
% 0.20/0.66 %EqnAxiom
% 0.20/0.66 [1]E(x11,x11)
% 0.20/0.66 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.66 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.20/0.66 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.20/0.66 [6]~E(x61,x62)+E(f3(x61),f3(x62))
% 0.20/0.66
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 cnf(11,plain,
% 0.20/0.66 (E(f2(x111,f2(x112,x112)),f2(f2(a1,x111),x112))),
% 0.20/0.66 inference(scs_inference,[],[7,2])).
% 0.20/0.66 cnf(16,plain,
% 0.20/0.66 (E(f2(x161,f2(x162,x163)),f2(f2(f2(a5,x162),x161),x163))),
% 0.20/0.66 inference(scs_inference,[],[9,2])).
% 0.20/0.66 cnf(17,plain,
% 0.20/0.66 (~E(f2(f2(f2(a5,x171),f3(x171)),f3(x171)),f2(x171,f3(x171)))),
% 0.20/0.66 inference(scs_inference,[],[9,10,2,3])).
% 0.20/0.66 cnf(19,plain,
% 0.20/0.66 (~E(f2(x191,f3(x191)),f2(f2(f2(a5,x191),f3(x191)),f3(x191)))),
% 0.20/0.66 inference(scs_inference,[],[17,2])).
% 0.20/0.66 cnf(25,plain,
% 0.20/0.66 (~E(f2(x251,f3(x251)),f2(f2(a4,f2(a5,x251)),f3(x251)))),
% 0.20/0.66 inference(scs_inference,[],[8,19,3])).
% 0.20/0.66 cnf(30,plain,
% 0.20/0.66 (~E(x301,f2(a4,f2(a5,x301)))),
% 0.20/0.66 inference(scs_inference,[],[25,2,4])).
% 0.20/0.66 cnf(31,plain,
% 0.20/0.66 (~E(x311,f2(a5,f2(a4,x311)))),
% 0.20/0.66 inference(scs_inference,[],[30,5])).
% 0.20/0.66 cnf(34,plain,
% 0.20/0.66 (~E(f2(a5,f2(a4,x341)),x341)),
% 0.20/0.66 inference(scs_inference,[],[31,2])).
% 0.20/0.66 cnf(43,plain,
% 0.20/0.66 ($false),
% 0.20/0.66 inference(scs_inference,[],[34,16,11,3]),
% 0.20/0.66 ['proof']).
% 0.20/0.66 % SZS output end Proof
% 0.20/0.66 % Total time :0.040000s
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