TSTP Solution File: COL019-1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : COL019-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 04:44:48 EDT 2024
% Result : Unsatisfiable 0.55s 0.70s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL019-1 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Jun 18 16:23:39 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.47/0.58 start to proof:theBenchmark
% 0.55/0.69 %-------------------------------------------
% 0.55/0.69 % File :CSE---1.7
% 0.55/0.69 % Problem :theBenchmark
% 0.55/0.69 % Transform :cnf
% 0.55/0.69 % Format :tptp:raw
% 0.55/0.69 % Command :java -jar mcs_scs.jar %d %s
% 0.55/0.69
% 0.55/0.69 % Result :Theorem 0.070000s
% 0.55/0.69 % Output :CNFRefutation 0.070000s
% 0.55/0.69 %-------------------------------------------
% 0.55/0.69 %--------------------------------------------------------------------------
% 0.55/0.69 % File : COL019-1 : TPTP v8.2.0. Released v1.0.0.
% 0.55/0.69 % Domain : Combinatory Logic
% 0.55/0.69 % Problem : Weak fixed point for B, S, and T
% 0.55/0.69 % Version : [WM88] (equality) axioms.
% 0.55/0.69 % English : The weak fixed point property holds for the set P consisting
% 0.55/0.69 % of the combinators B, S, and T, where ((Sx)y)z = (xz)(yz),
% 0.55/0.69 % ((Bx)y)z = x(yz), (Tx)y = yx.
% 0.55/0.69
% 0.55/0.69 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
% 0.55/0.69 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
% 0.55/0.69 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% 0.55/0.69 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb
% 0.55/0.69 % Source : [MW88]
% 0.55/0.69 % Names : - [MW88]
% 0.55/0.69
% 0.55/0.69 % Status : Unsatisfiable
% 0.55/0.69 % Rating : 0.14 v8.2.0, 0.21 v8.1.0, 0.25 v7.5.0, 0.21 v7.4.0, 0.30 v7.3.0, 0.21 v7.1.0, 0.11 v6.4.0, 0.16 v6.3.0, 0.18 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.00 v5.1.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.15 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v2.1.0, 0.13 v2.0.0
% 0.55/0.69 % Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 1 RR)
% 0.55/0.70 % Number of literals : 4 ( 4 equ; 1 neg)
% 0.55/0.70 % Maximal clause size : 1 ( 1 avg)
% 0.55/0.70 % Maximal term depth : 4 ( 2 avg)
% 0.55/0.70 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.55/0.70 % Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% 0.55/0.70 % Number of variables : 9 ( 0 sgn)
% 0.55/0.70 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.55/0.70
% 0.55/0.70 % Comments :
% 0.55/0.70 %--------------------------------------------------------------------------
% 0.55/0.70 cnf(s_definition,axiom,
% 0.55/0.70 apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ).
% 0.55/0.70
% 0.55/0.70 cnf(b_definition,axiom,
% 0.55/0.70 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
% 0.55/0.70
% 0.55/0.70 cnf(t_definition,axiom,
% 0.55/0.70 apply(apply(t,X),Y) = apply(Y,X) ).
% 0.55/0.70
% 0.55/0.70 cnf(prove_fixed_point,negated_conjecture,
% 0.55/0.70 Y != apply(combinator,Y) ).
% 0.55/0.70
% 0.55/0.70 %--------------------------------------------------------------------------
% 0.55/0.70 %-------------------------------------------
% 0.55/0.70 % Proof found
% 0.55/0.70 % SZS status Theorem for theBenchmark
% 0.55/0.70 % SZS output start Proof
% 0.55/0.70 %ClaNum:9(EqnAxiom:5)
% 0.55/0.70 %VarNum:19(SingletonVarNum:9)
% 0.55/0.70 %MaxLitNum:1
% 0.55/0.70 %MaxfuncDepth:3
% 0.55/0.70 %SharedTerms:4
% 0.55/0.70 %goalClause: 9
% 0.55/0.70 %singleGoalClaCount:1
% 0.55/0.70 [9]~E(f2(a5,x91),x91)
% 0.55/0.70 [6]E(f2(f2(a1,x61),x62),f2(x62,x61))
% 0.55/0.70 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(x71,f2(x72,x73)))
% 0.55/0.70 [8]E(f2(f2(f2(a4,x81),x82),x83),f2(f2(x81,x83),f2(x82,x83)))
% 0.55/0.70 %EqnAxiom
% 0.55/0.70 [1]E(x11,x11)
% 0.55/0.70 [2]E(x22,x21)+~E(x21,x22)
% 0.55/0.70 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.55/0.70 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.55/0.70 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.55/0.70
% 0.55/0.70 %-------------------------------------------
% 0.55/0.70 cnf(10,plain,
% 0.55/0.70 (E(f2(x101,x102),f2(f2(a1,x102),x101))),
% 0.55/0.70 inference(scs_inference,[],[6,2])).
% 0.55/0.70 cnf(13,plain,
% 0.55/0.70 (E(f2(f2(x131,x132),f2(x133,x132)),f2(f2(f2(a4,x131),x133),x132))),
% 0.55/0.70 inference(scs_inference,[],[8,2])).
% 0.55/0.70 cnf(14,plain,
% 0.55/0.70 (~E(f2(a5,f2(f2(a1,x141),x142)),f2(x142,x141))),
% 0.55/0.70 inference(scs_inference,[],[9,10,8,2,3])).
% 0.55/0.70 cnf(18,plain,
% 0.55/0.70 (E(f2(x181,f2(x182,x183)),f2(f2(f2(a3,x181),x182),x183))),
% 0.55/0.70 inference(scs_inference,[],[7,2])).
% 0.55/0.70 cnf(22,plain,
% 0.55/0.70 (~E(f2(a5,f2(f2(a1,x221),f2(a1,x222))),f2(x221,x222))),
% 0.55/0.70 inference(scs_inference,[],[14,10,3])).
% 0.55/0.70 cnf(41,plain,
% 0.55/0.70 ($false),
% 0.55/0.70 inference(scs_inference,[],[22,13,18,3]),
% 0.55/0.70 ['proof']).
% 0.55/0.70 % SZS output end Proof
% 0.55/0.70 % Total time :0.070000s
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