TSTP Solution File: COL052-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : COL052-2 : 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 : n026.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 18:21:29 EDT 2023
% Result : Unsatisfiable 0.19s 0.62s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL052-2 : 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
% 0.13/0.34 % Computer : n026.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 05:36:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 % File :CSE---1.6
% 0.19/0.61 % Problem :theBenchmark
% 0.19/0.61 % Transform :cnf
% 0.19/0.61 % Format :tptp:raw
% 0.19/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.61
% 0.19/0.61 % Result :Theorem 0.010000s
% 0.19/0.61 % Output :CNFRefutation 0.010000s
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 %--------------------------------------------------------------------------
% 0.19/0.61 % File : COL052-2 : TPTP v8.1.2. Released v1.0.0.
% 0.19/0.61 % Domain : Combinatory Logic
% 0.19/0.61 % Problem : A Question on Agreeable Birds
% 0.19/0.61 % Version : Especial.
% 0.19/0.61 % Theorem formulation : Explicit definition of agreeable.
% 0.19/0.61 % English : For all birds x and y, there exists a bird z that composes
% 0.19/0.61 % x with y for all birds w. Prove that if C is agreeable then
% 0.19/0.61 % A is agreeable.
% 0.19/0.61
% 0.19/0.61 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi
% 0.19/0.61 % Source : [ANL]
% 0.19/0.61 % Names : bird4.ver2.in [ANL]
% 0.19/0.61
% 0.19/0.61 % Status : Unsatisfiable
% 0.19/0.61 % Rating : 0.08 v8.1.0, 0.11 v7.5.0, 0.10 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.29 v6.3.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.12 v5.4.0, 0.13 v5.3.0, 0.33 v5.2.0, 0.12 v5.1.0, 0.14 v5.0.0, 0.00 v4.1.0, 0.11 v4.0.1, 0.00 v3.3.0, 0.14 v3.2.0, 0.00 v2.4.0, 0.00 v2.0.0
% 0.19/0.61 % Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 4 RR)
% 0.19/0.61 % Number of literals : 8 ( 4 equ; 3 neg)
% 0.19/0.61 % Maximal clause size : 2 ( 1 avg)
% 0.19/0.61 % Maximal term depth : 3 ( 2 avg)
% 0.19/0.61 % Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% 0.19/0.61 % Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% 0.19/0.61 % Number of variables : 7 ( 0 sgn)
% 0.19/0.61 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.19/0.61
% 0.19/0.61 % Comments :
% 0.19/0.61 %--------------------------------------------------------------------------
% 0.19/0.61 %----For all birds x and y, there exists a bird z that composes x with
% 0.19/0.61 %----y for all birds w.
% 0.19/0.61 %---- FAx FAy TEz FAw [response(z,w) = response(x,response(y,w))].
% 0.19/0.61 %---- response(comp(x,y),w) = response(x,response(y,w)).
% 0.19/0.61 cnf(composer_exists,axiom,
% 0.19/0.61 response(compose(X,Y),W) = response(X,response(Y,W)) ).
% 0.19/0.61
% 0.19/0.61 %----Definition of agreeable: A bird x is agreeable if and only if for all
% 0.19/0.61 %----birds y there exists a bird z such that xz = yz.
% 0.19/0.61 %---- 1) If agreeable(x) then FAy TEz [response(x,z) =
% 0.19/0.61 %---- response(y,z)] and
% 0.19/0.61 %---- 2) if TEx FAy TEz [response(x,z) = response(y,z)] then
% 0.19/0.61 %---- agreeable(x).
% 0.19/0.61 %---- 1) -agreeable(x) | response(x,common_bird(y)) =
% 0.19/0.61 %---- response(y,common_bird(y)).
% 0.19/0.61 %---- 2) FAx TEy FAz -[response(x,z) = response(y,z)] |
% 0.19/0.61 %---- agreeable(x).
% 0.19/0.61 %---- -[response(x,z) = response(compatible(x),z)] |
% 0.19/0.61 %---- agreeable(x).
% 0.19/0.61 cnf(agreeable1,axiom,
% 0.19/0.61 ( ~ agreeable(X)
% 0.19/0.61 | response(X,common_bird(Y)) = response(Y,common_bird(Y)) ) ).
% 0.19/0.61
% 0.19/0.62 cnf(agreeable2,axiom,
% 0.19/0.62 ( response(X,Z) != response(compatible(X),Z)
% 0.19/0.62 | agreeable(X) ) ).
% 0.19/0.62
% 0.19/0.62 %----Hypothesis: If C is agreeable then A is agreeable.
% 0.19/0.62 %---- - [ If agreeable(C) then agreeable(A) ].
% 0.19/0.62 %---- - [ -agreeable(C) | agreeable(A) ].
% 0.19/0.62 %---- agreeable(C) and -agreeable(A).
% 0.19/0.62 cnf(c_is_agreeable,hypothesis,
% 0.19/0.62 agreeable(c) ).
% 0.19/0.62
% 0.19/0.62 cnf(prove_a_is_agreeable,negated_conjecture,
% 0.19/0.62 ~ agreeable(a) ).
% 0.19/0.62
% 0.19/0.62 %----C composes A with B. WHY IS THIS HERE??
% 0.19/0.62 cnf(c_composes_a_with_b,hypothesis,
% 0.19/0.62 c = compose(a,b) ).
% 0.19/0.62
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % Proof found
% 0.19/0.62 % SZS status Theorem for theBenchmark
% 0.19/0.62 % SZS output start Proof
% 0.19/0.62 %ClaNum:16(EqnAxiom:10)
% 0.19/0.62 %VarNum:16(SingletonVarNum:7)
% 0.19/0.62 %MaxLitNum:2
% 0.19/0.62 %MaxfuncDepth:2
% 0.19/0.62 %SharedTerms:7
% 0.19/0.62 %goalClause: 14
% 0.19/0.62 %singleGoalClaCount:1
% 0.19/0.62 [11]P1(a1)
% 0.19/0.62 [14]~P1(a2)
% 0.19/0.62 [12]E(f4(a2,a3),a1)
% 0.19/0.62 [13]E(f7(f4(x131,x132),x133),f7(x131,f7(x132,x133)))
% 0.19/0.62 [15]~P1(x151)+E(f7(x151,f5(x152)),f7(x152,f5(x152)))
% 0.19/0.62 [16]P1(x161)+~E(f7(f6(x161),x162),f7(x161,x162))
% 0.19/0.62 %EqnAxiom
% 0.19/0.62 [1]E(x11,x11)
% 0.19/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.62 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43))
% 0.19/0.62 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52))
% 0.19/0.62 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63))
% 0.19/0.62 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72))
% 0.19/0.62 [8]~E(x81,x82)+E(f6(x81),f6(x82))
% 0.19/0.62 [9]~E(x91,x92)+E(f5(x91),f5(x92))
% 0.19/0.62 [10]~P1(x101)+P1(x102)+~E(x101,x102)
% 0.19/0.62
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 cnf(17,plain,
% 0.19/0.62 (E(a1,f4(a2,a3))),
% 0.19/0.62 inference(scs_inference,[],[12,2])).
% 0.19/0.62 cnf(18,plain,
% 0.19/0.62 (P1(f4(a2,a3))),
% 0.19/0.62 inference(scs_inference,[],[11,12,2,10])).
% 0.19/0.62 cnf(19,plain,
% 0.19/0.62 (E(f7(a1,f5(x191)),f7(x191,f5(x191)))),
% 0.19/0.62 inference(scs_inference,[],[11,12,2,10,15])).
% 0.19/0.62 cnf(23,plain,
% 0.19/0.62 (E(f7(x231,f4(a2,a3)),f7(x231,a1))),
% 0.19/0.62 inference(scs_inference,[],[11,12,2,10,15,9,8,7])).
% 0.19/0.62 cnf(27,plain,
% 0.19/0.62 (~E(f7(f6(a2),x271),f7(a2,x271))),
% 0.19/0.62 inference(scs_inference,[],[14,11,12,2,10,15,9,8,7,6,5,4,16])).
% 0.19/0.62 cnf(29,plain,
% 0.19/0.62 (~E(f7(f6(a2),a1),f7(a2,f4(a2,a3)))),
% 0.19/0.62 inference(scs_inference,[],[14,11,12,2,10,15,9,8,7,6,5,4,16,3])).
% 0.19/0.62 cnf(30,plain,
% 0.19/0.62 (~E(f7(a2,x301),f7(f6(a2),x301))),
% 0.19/0.62 inference(scs_inference,[],[27,2])).
% 0.19/0.62 cnf(31,plain,
% 0.19/0.62 (~P1(f6(a2))),
% 0.19/0.62 inference(scs_inference,[],[27,2,15])).
% 0.19/0.62 cnf(32,plain,
% 0.19/0.62 (~E(f7(f6(a2),x321),f7(a2,x321))),
% 0.19/0.62 inference(rename_variables,[],[27])).
% 0.19/0.62 cnf(36,plain,
% 0.19/0.62 (E(f7(f4(x361,x362),f4(a2,a3)),f7(x361,f7(x362,a1)))),
% 0.19/0.62 inference(scs_inference,[],[14,13,11,23,27,32,2,15,6,10,3])).
% 0.19/0.62 cnf(39,plain,
% 0.19/0.62 (E(f7(f4(a2,a3),f5(x391)),f7(x391,f5(x391)))),
% 0.19/0.62 inference(scs_inference,[],[18,15])).
% 0.19/0.62 cnf(41,plain,
% 0.19/0.62 (E(f7(x411,f7(x412,x413)),f7(f4(x411,x412),x413))),
% 0.19/0.62 inference(scs_inference,[],[13,18,15,2])).
% 0.19/0.62 cnf(44,plain,
% 0.19/0.62 (~E(f7(a2,f7(x441,a1)),f7(f4(f6(a2),x441),f4(a2,a3)))),
% 0.19/0.62 inference(scs_inference,[],[11,17,13,36,30,18,31,15,2,6,10,3])).
% 0.19/0.62 cnf(52,plain,
% 0.19/0.62 (~E(f4(a2,a3),f6(a2))),
% 0.19/0.62 inference(scs_inference,[],[41,29,44,30,18,31,2,6,3,10])).
% 0.19/0.62 cnf(53,plain,
% 0.19/0.62 (E(f7(x531,f5(x531)),f7(f4(a2,a3),f5(x531)))),
% 0.19/0.62 inference(scs_inference,[],[39,2])).
% 0.19/0.62 cnf(64,plain,
% 0.19/0.62 (~E(f7(f6(a2),f7(x641,x642)),f7(f4(a2,x641),x642))),
% 0.19/0.62 inference(scs_inference,[],[13,52,27,2,3])).
% 0.19/0.62 cnf(69,plain,
% 0.19/0.62 ($false),
% 0.19/0.62 inference(scs_inference,[],[19,53,64,41,2,3]),
% 0.19/0.62 ['proof']).
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time :0.010000s
%------------------------------------------------------------------------------