TSTP Solution File: COL011-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COL011-1 : 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 : n008.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 18:21:18 EDT 2023
% Result : Unsatisfiable 124.07s 124.21s
% Output : CNFRefutation 124.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL011-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n008.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 04:28:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 124.01/124.20 %-------------------------------------------
% 124.01/124.20 % File :CSE---1.6
% 124.01/124.20 % Problem :theBenchmark
% 124.01/124.20 % Transform :cnf
% 124.01/124.20 % Format :tptp:raw
% 124.01/124.20 % Command :java -jar mcs_scs.jar %d %s
% 124.01/124.20
% 124.01/124.20 % Result :Theorem 123.440000s
% 124.01/124.20 % Output :CNFRefutation 123.440000s
% 124.01/124.20 %-------------------------------------------
% 124.01/124.21 %--------------------------------------------------------------------------
% 124.01/124.21 % File : COL011-1 : TPTP v8.1.2. Released v1.0.0.
% 124.01/124.21 % Domain : Combinatory Logic
% 124.07/124.21 % Problem : Weak fixed point for O and Q1
% 124.07/124.21 % Version : [WM88] (equality) axioms.
% 124.07/124.21 % English : The weak fixed point property holds for the set P consisting
% 124.07/124.21 % of the combinators O and Q1, where (Ox)y = y(xy), ((Q1x)y)z
% 124.07/124.21 % = x(zy).
% 124.07/124.21
% 124.07/124.21 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
% 124.07/124.21 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem
% 124.07/124.21 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq
% 124.07/124.21 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb
% 124.07/124.21 % Source : [MW88]
% 124.07/124.21 % Names : - [MW88]
% 124.07/124.21
% 124.07/124.21 % Status : Unsatisfiable
% 124.07/124.21 % Rating : 0.50 v8.1.0, 0.65 v7.5.0, 0.67 v7.4.0, 0.61 v7.3.0, 0.58 v7.1.0, 0.50 v7.0.0, 0.47 v6.4.0, 0.53 v6.2.0, 0.50 v6.1.0, 0.56 v6.0.0, 0.57 v5.5.0, 0.53 v5.4.0, 0.67 v5.3.0, 0.58 v5.2.0, 0.57 v5.1.0, 0.60 v5.0.0, 0.57 v4.1.0, 0.45 v4.0.1, 0.57 v4.0.0, 0.62 v3.7.0, 0.22 v3.4.0, 0.25 v3.3.0, 0.36 v3.1.0, 0.67 v2.7.0, 0.36 v2.6.0, 0.33 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.14 v2.1.0, 0.62 v2.0.0
% 124.07/124.21 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR)
% 124.07/124.21 % Number of literals : 3 ( 3 equ; 1 neg)
% 124.07/124.21 % Maximal clause size : 1 ( 1 avg)
% 124.07/124.21 % Maximal term depth : 4 ( 2 avg)
% 124.07/124.21 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 124.07/124.21 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% 124.07/124.21 % Number of variables : 6 ( 0 sgn)
% 124.07/124.21 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 124.07/124.21
% 124.07/124.21 % Comments :
% 124.07/124.21 %--------------------------------------------------------------------------
% 124.07/124.21 cnf(o_definition,axiom,
% 124.07/124.21 apply(apply(o,X),Y) = apply(Y,apply(X,Y)) ).
% 124.07/124.21
% 124.07/124.21 cnf(q1_definition,axiom,
% 124.07/124.21 apply(apply(apply(q1,X),Y),Z) = apply(X,apply(Z,Y)) ).
% 124.07/124.21
% 124.07/124.21 cnf(prove_fixed_point,negated_conjecture,
% 124.07/124.21 Y != apply(combinator,Y) ).
% 124.07/124.21
% 124.07/124.21 %--------------------------------------------------------------------------
% 124.07/124.21 %-------------------------------------------
% 124.07/124.21 % Proof found
% 124.07/124.21 % SZS status Theorem for theBenchmark
% 124.07/124.21 % SZS output start Proof
% 124.07/124.21 %ClaNum:8(EqnAxiom:5)
% 124.07/124.21 %VarNum:13(SingletonVarNum:6)
% 124.07/124.21 %MaxLitNum:1
% 124.07/124.21 %MaxfuncDepth:3
% 124.07/124.21 %SharedTerms:3
% 124.07/124.21 %goalClause: 8
% 124.07/124.21 %singleGoalClaCount:1
% 124.07/124.21 [8]~E(f2(a3,x81),x81)
% 124.07/124.21 [6]E(f2(f2(a1,x61),x62),f2(x62,f2(x61,x62)))
% 124.07/124.21 [7]E(f2(f2(f2(a4,x71),x72),x73),f2(x71,f2(x73,x72)))
% 124.07/124.21 %EqnAxiom
% 124.07/124.21 [1]E(x11,x11)
% 124.07/124.21 [2]E(x22,x21)+~E(x21,x22)
% 124.07/124.21 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 124.07/124.21 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 124.07/124.21 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 124.07/124.21
% 124.07/124.21 %-------------------------------------------
% 124.07/124.22 cnf(9,plain,
% 124.07/124.22 (E(f2(x91,f2(x92,x91)),f2(f2(a1,x92),x91))),
% 124.07/124.22 inference(scs_inference,[],[6,2])).
% 124.07/124.22 cnf(10,plain,
% 124.07/124.22 (~E(f2(a3,f2(x101,f2(x102,x101))),f2(f2(a1,x102),x101))),
% 124.07/124.22 inference(scs_inference,[],[8,6,2,3])).
% 124.07/124.22 cnf(12,plain,
% 124.07/124.22 (~E(x121,f2(a3,x121))),
% 124.07/124.22 inference(scs_inference,[],[8,2])).
% 124.07/124.22 cnf(16,plain,
% 124.07/124.22 (~E(f2(a1,x161),x161)),
% 124.07/124.22 inference(scs_inference,[],[8,9,2,3,4])).
% 124.07/124.22 cnf(17,plain,
% 124.07/124.22 (E(f2(x171,f2(x172,x173)),f2(f2(f2(a4,x171),x173),x172))),
% 124.07/124.22 inference(scs_inference,[],[7,2])).
% 124.07/124.22 cnf(19,plain,
% 124.07/124.22 (E(f2(f2(f2(a4,x191),x191),x192),f2(f2(a1,x192),x191))),
% 124.07/124.22 inference(scs_inference,[],[7,9,3])).
% 124.07/124.22 cnf(23,plain,
% 124.07/124.22 (~E(f2(x231,x232),f2(f2(f2(a4,a3),x232),x231))),
% 124.07/124.22 inference(scs_inference,[],[7,10,12,2,3])).
% 124.07/124.22 cnf(27,plain,
% 124.07/124.22 (~E(f2(x271,x272),f2(f2(f2(a4,a3),x272),x271))),
% 124.07/124.22 inference(rename_variables,[],[23])).
% 124.07/124.22 cnf(28,plain,
% 124.07/124.22 (~E(f2(f2(f2(a4,a3),x281),x282),f2(x282,x281))),
% 124.07/124.22 inference(scs_inference,[],[23,27,5,2])).
% 124.07/124.22 cnf(34,plain,
% 124.07/124.22 (~E(f2(f2(f2(a4,a1),x341),x342),f2(x342,x341))),
% 124.07/124.22 inference(scs_inference,[],[17,16,3])).
% 124.07/124.22 cnf(38,plain,
% 124.07/124.22 (~E(f2(x381,x382),f2(f2(f2(a4,a1),x382),x381))),
% 124.07/124.22 inference(scs_inference,[],[34,2])).
% 124.07/124.22 cnf(41,plain,
% 124.07/124.22 (~E(f2(f2(f2(a4,a3),x411),f2(a1,x412)),f2(f2(f2(a4,x411),x411),x412))),
% 124.07/124.22 inference(scs_inference,[],[19,38,28,4,3])).
% 124.07/124.22 cnf(46,plain,
% 124.07/124.22 (~E(f2(f2(f2(a4,x461),x461),x462),f2(f2(f2(a4,a3),x461),f2(a1,x462)))),
% 124.07/124.22 inference(scs_inference,[],[41,2])).
% 124.07/124.22 cnf(61,plain,
% 124.07/124.22 (~E(f2(f2(f2(a4,a1),x611),f2(f2(a4,x612),x613)),f2(x612,f2(x611,x613)))),
% 124.07/124.22 inference(scs_inference,[],[34,17,3])).
% 124.07/124.22 cnf(68,plain,
% 124.07/124.22 (~E(f2(f2(a4,a1),f2(a4,x681)),x681)),
% 124.07/124.22 inference(scs_inference,[],[34,61,19,3,4])).
% 124.07/124.22 cnf(70,plain,
% 124.07/124.22 (~E(f2(a4,f2(f2(a4,a1),x701)),x701)),
% 124.07/124.22 inference(scs_inference,[],[68,5])).
% 124.07/124.22 cnf(76,plain,
% 124.07/124.22 (~E(f2(f2(f2(a4,a4),x761),f2(a4,a1)),x761)),
% 124.07/124.22 inference(scs_inference,[],[70,17,3])).
% 124.07/124.22 cnf(175,plain,
% 124.07/124.22 (~E(f2(x1751,f2(x1752,x1751)),f2(f2(f2(a4,a3),x1751),f2(a1,x1752)))),
% 124.07/124.22 inference(scs_inference,[],[46,7,3])).
% 124.07/124.22 cnf(185,plain,
% 124.07/124.22 (~E(f2(x1851,f2(x1852,x1851)),f2(a3,f2(f2(a1,x1852),x1851)))),
% 124.07/124.22 inference(scs_inference,[],[175,17,3])).
% 124.07/124.22 cnf(188,plain,
% 124.07/124.22 (~E(f2(f2(a1,f2(a4,a1)),a4),a4)),
% 124.07/124.22 inference(scs_inference,[],[185,76,19,2,3])).
% 124.07/124.22 cnf(192,plain,
% 124.07/124.23 (~E(f2(x1921,f2(x1922,x1923)),f2(f2(f2(a4,a3),x1922),f2(f2(a4,x1921),x1923)))),
% 124.07/124.23 inference(scs_inference,[],[188,23,7,2,3])).
% 124.07/124.23 cnf(376,plain,
% 124.07/124.23 (~E(f2(x3761,f2(x3762,x3763)),f2(f2(a4,a3),f2(a4,f2(f2(f2(a4,x3761),x3763),x3762))))),
% 124.07/124.23 inference(scs_inference,[],[192,7,4,3])).
% 124.07/124.23 cnf(393,plain,
% 124.07/124.23 (E(f2(x3931,f2(f2(a1,x3932),x3933)),f2(x3931,f2(x3933,f2(x3932,x3933))))),
% 124.07/124.23 inference(scs_inference,[],[9,5,2])).
% 124.07/124.23 cnf(1082,plain,
% 124.07/124.23 (E(f2(f2(f2(a4,x10821),x10822),f2(a1,x10823)),f2(x10821,f2(x10822,f2(x10823,x10822))))),
% 124.07/124.23 inference(scs_inference,[],[393,7,3])).
% 124.07/124.23 cnf(1600,plain,
% 124.07/124.23 ($false),
% 124.07/124.23 inference(scs_inference,[],[1082,376,5]),
% 124.07/124.23 ['proof']).
% 124.07/124.23 % SZS output end Proof
% 124.07/124.23 % Total time :123.440000s
%------------------------------------------------------------------------------