TSTP Solution File: LCL686+1.001 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL686+1.001 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n025.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 : Thu Aug 31 06:50:30 EDT 2023
% Result : Theorem 0.16s 0.63s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL686+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.10/0.31 % Computer : n025.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Aug 25 07:35:21 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.55 start to proof:theBenchmark
% 0.16/0.63 %-------------------------------------------
% 0.16/0.63 % File :CSE---1.6
% 0.16/0.63 % Problem :theBenchmark
% 0.16/0.63 % Transform :cnf
% 0.16/0.63 % Format :tptp:raw
% 0.16/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.16/0.63
% 0.16/0.63 % Result :Theorem 0.020000s
% 0.16/0.63 % Output :CNFRefutation 0.020000s
% 0.16/0.63 %-------------------------------------------
% 0.16/0.63 %------------------------------------------------------------------------------
% 0.16/0.63 % File : LCL686+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.16/0.63 % Domain : Logic Calculi (Modal Logic)
% 0.16/0.63 % Problem : In S4, formula provable in S5 embedding, size 1
% 0.16/0.63 % Version : Especial.
% 0.16/0.63 % English :
% 0.16/0.63
% 0.16/0.63 % Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
% 0.16/0.63 % : [Kam08] Kaminski (2008), Email to G. Sutcliffe
% 0.16/0.63 % Source : [Kam08]
% 0.16/0.63 % Names : s4_s5_p [BHS00]
% 0.16/0.63
% 0.16/0.63 % Status : Theorem
% 0.16/0.63 % Rating : 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.17 v5.4.0, 0.13 v5.3.0, 0.17 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.11 v4.0.0
% 0.16/0.63 % Syntax : Number of formulae : 3 ( 1 unt; 0 def)
% 0.16/0.63 % Number of atoms : 24 ( 0 equ)
% 0.16/0.63 % Maximal formula atoms : 20 ( 8 avg)
% 0.16/0.63 % Number of connectives : 41 ( 20 ~; 15 |; 5 &)
% 0.16/0.63 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.16/0.63 % Maximal formula depth : 20 ( 9 avg)
% 0.16/0.63 % Maximal term depth : 1 ( 1 avg)
% 0.16/0.63 % Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% 0.16/0.63 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.16/0.63 % Number of variables : 13 ( 12 !; 1 ?)
% 0.16/0.63 % SPC : FOF_THM_RFO_NEQ
% 0.16/0.63
% 0.16/0.63 % Comments : A naive relational encoding of the modal logic problem into
% 0.16/0.63 % first-order logic.
% 0.16/0.63 %------------------------------------------------------------------------------
% 0.16/0.63 fof(reflexivity,axiom,
% 0.16/0.63 ! [X] : r1(X,X) ).
% 0.16/0.63
% 0.16/0.63 fof(transitivity,axiom,
% 0.16/0.63 ! [X,Y,Z] :
% 0.16/0.63 ( ( r1(X,Y)
% 0.16/0.63 & r1(Y,Z) )
% 0.16/0.63 => r1(X,Z) ) ).
% 0.16/0.63
% 0.16/0.63 fof(main,conjecture,
% 0.16/0.63 ~ ? [X] :
% 0.16/0.63 ~ ( ! [Y] :
% 0.16/0.63 ( ~ r1(X,Y)
% 0.16/0.63 | ~ p3(Y)
% 0.16/0.63 | ! [X] :
% 0.16/0.63 ( ~ r1(Y,X)
% 0.16/0.63 | ~ p1(X) ) )
% 0.16/0.63 | ! [Y] :
% 0.16/0.63 ( ~ r1(X,Y)
% 0.16/0.63 | ~ ! [X] :
% 0.16/0.63 ( ~ r1(Y,X)
% 0.16/0.63 | ~ ( ! [Y] :
% 0.16/0.63 ( ~ r1(X,Y)
% 0.16/0.63 | $false )
% 0.16/0.63 | ~ ! [Y] :
% 0.16/0.63 ( ~ r1(X,Y)
% 0.16/0.63 | ~ ( ( p2(Y)
% 0.16/0.63 & ~ p1(Y) )
% 0.16/0.63 | ( ~ p2(Y)
% 0.16/0.63 & p1(Y) ) ) )
% 0.16/0.63 | ! [Y] :
% 0.16/0.63 ( ~ r1(X,Y)
% 0.16/0.63 | p3(Y) )
% 0.16/0.63 | ! [Y] :
% 0.16/0.63 ( ~ r1(X,Y)
% 0.16/0.63 | ( ~ p1(Y)
% 0.16/0.63 & ~ p2(Y) )
% 0.16/0.63 | ( p2(Y)
% 0.16/0.63 & p1(Y) ) ) ) ) ) ) ).
% 0.16/0.63
% 0.16/0.63 %------------------------------------------------------------------------------
% 0.16/0.63 %-------------------------------------------
% 0.16/0.63 % Proof found
% 0.16/0.63 % SZS status Theorem for theBenchmark
% 0.16/0.63 % SZS output start Proof
% 0.16/0.64 %ClaNum:15(EqnAxiom:0)
% 0.16/0.64 %VarNum:35(SingletonVarNum:14)
% 0.16/0.64 %MaxLitNum:4
% 0.16/0.64 %MaxfuncDepth:1
% 0.16/0.64 %SharedTerms:9
% 0.16/0.64 %goalClause: 1 2 3 4 5 7 8 9 10 11 12 13 14
% 0.16/0.64 %singleGoalClaCount:5
% 0.16/0.64 [1]P1(a1)
% 0.16/0.64 [2]P2(a3)
% 0.16/0.64 [3]P4(a2,a1)
% 0.16/0.64 [4]P4(a2,a4)
% 0.16/0.64 [5]P4(a1,a3)
% 0.16/0.64 [6]P4(x61,x61)
% 0.16/0.64 [7]~P4(a4,x71)+~P1(f5(x71))
% 0.16/0.64 [8]~P4(a4,x81)+P4(x81,f6(x81))
% 0.16/0.64 [9]~P4(a4,x91)+P4(x91,f5(x91))
% 0.16/0.64 [10]~P4(a4,x101)+P4(x101,f7(x101))
% 0.16/0.64 [11]~P4(a4,x111)+P2(f7(x111))+P3(f7(x111))
% 0.16/0.64 [12]~P4(a4,x121)+~P2(f7(x121))+~P3(f7(x121))
% 0.16/0.64 [15]~P4(x151,x153)+P4(x151,x152)+~P4(x153,x152)
% 0.16/0.64 [13]~P3(x131)+P2(x131)+~P4(x132,x131)+~P4(a4,x132)
% 0.16/0.64 [14]~P2(x141)+P3(x141)+~P4(x142,x141)+~P4(a4,x142)
% 0.16/0.64 %EqnAxiom
% 0.16/0.64
% 0.16/0.64 %-------------------------------------------
% 0.16/0.64 cnf(16,plain,
% 0.16/0.64 (P4(a4,f7(a4))),
% 0.16/0.64 inference(scs_inference,[],[6,10])).
% 0.16/0.64 cnf(17,plain,
% 0.16/0.64 (P4(x171,x171)),
% 0.16/0.64 inference(rename_variables,[],[6])).
% 0.16/0.64 cnf(19,plain,
% 0.16/0.64 (P4(x191,x191)),
% 0.16/0.64 inference(rename_variables,[],[6])).
% 0.16/0.64 cnf(22,plain,
% 0.16/0.64 (P4(x221,x221)),
% 0.16/0.64 inference(rename_variables,[],[6])).
% 0.16/0.64 cnf(24,plain,
% 0.16/0.64 (~P3(f7(a4))+~P2(f7(a4))),
% 0.16/0.64 inference(scs_inference,[],[6,17,19,22,10,9,8,12])).
% 0.16/0.64 cnf(42,plain,
% 0.16/0.64 (P2(f7(a4))+~P3(f7(a4))),
% 0.16/0.64 inference(scs_inference,[],[16,4,6,15,13])).
% 0.16/0.64 cnf(79,plain,
% 0.16/0.64 (P4(f7(a4),f5(f7(a4)))),
% 0.16/0.64 inference(scs_inference,[],[16,8,10,9])).
% 0.16/0.64 cnf(95,plain,
% 0.16/0.64 (P3(f7(a4))+~P2(f7(a4))),
% 0.16/0.64 inference(scs_inference,[],[16,79,6,15,14])).
% 0.16/0.64 cnf(104,plain,
% 0.16/0.64 (~P2(f7(a4))),
% 0.16/0.64 inference(scs_inference,[],[24,95])).
% 0.16/0.64 cnf(105,plain,
% 0.16/0.64 (~P3(f7(a4))),
% 0.16/0.64 inference(scs_inference,[],[104,42])).
% 0.16/0.64 cnf(106,plain,
% 0.16/0.64 (P3(f7(a4))),
% 0.16/0.64 inference(scs_inference,[],[104,6,11])).
% 0.16/0.64 cnf(113,plain,
% 0.16/0.64 ($false),
% 0.16/0.64 inference(scs_inference,[],[105,106]),
% 0.16/0.64 ['proof']).
% 0.16/0.64 % SZS output end Proof
% 0.16/0.64 % Total time :0.020000s
%------------------------------------------------------------------------------