TSTP Solution File: LCL654+1.001 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL654+1.001 : TPTP v8.1.2. Released v4.0.0.
% 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 : Thu Aug 31 06:50:07 EDT 2023
% Result : Theorem 2.96s 3.05s
% Output : CNFRefutation 2.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL654+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 24 20:09:32 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.57 start to proof:theBenchmark
% 2.96/3.04 %-------------------------------------------
% 2.96/3.04 % File :CSE---1.6
% 2.96/3.04 % Problem :theBenchmark
% 2.96/3.04 % Transform :cnf
% 2.96/3.04 % Format :tptp:raw
% 2.96/3.04 % Command :java -jar mcs_scs.jar %d %s
% 2.96/3.04
% 2.96/3.04 % Result :Theorem 2.410000s
% 2.96/3.04 % Output :CNFRefutation 2.410000s
% 2.96/3.04 %-------------------------------------------
% 2.96/3.05 %------------------------------------------------------------------------------
% 2.96/3.05 % File : LCL654+1.001 : TPTP v8.1.2. Released v4.0.0.
% 2.96/3.05 % Domain : Logic Calculi (Modal Logic)
% 2.96/3.05 % Problem : In KT, A5{box p0/p0} & box A5{~p0/p0} -> A4, size 1
% 2.96/3.05 % Version : Especial.
% 2.96/3.05 % English :
% 2.96/3.05
% 2.96/3.05 % Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
% 2.96/3.05 % : [Kam08] Kaminski (2008), Email to G. Sutcliffe
% 2.96/3.05 % Source : [Kam08]
% 2.96/3.05 % Names : kt_45_p [BHS00]
% 2.96/3.05
% 2.96/3.05 % Status : Theorem
% 2.96/3.05 % Rating : 0.00 v7.5.0, 0.05 v7.4.0, 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.1.0, 0.08 v6.0.0, 0.25 v5.5.0, 0.17 v5.3.0, 0.26 v5.2.0, 0.07 v5.0.0, 0.10 v4.1.0, 0.11 v4.0.1, 0.16 v4.0.0
% 2.96/3.05 % Syntax : Number of formulae : 2 ( 1 unt; 0 def)
% 2.96/3.05 % Number of atoms : 30 ( 0 equ)
% 2.96/3.05 % Maximal formula atoms : 29 ( 15 avg)
% 2.96/3.05 % Number of connectives : 70 ( 42 ~; 25 |; 3 &)
% 2.96/3.05 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 2.96/3.05 % Maximal formula depth : 22 ( 12 avg)
% 2.96/3.05 % Maximal term depth : 1 ( 1 avg)
% 2.96/3.05 % Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% 2.96/3.05 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 2.96/3.05 % Number of variables : 22 ( 21 !; 1 ?)
% 2.96/3.05 % SPC : FOF_THM_RFO_NEQ
% 2.96/3.05
% 2.96/3.05 % Comments : A naive relational encoding of the modal logic problem into
% 2.96/3.05 % first-order logic.
% 2.96/3.05 %------------------------------------------------------------------------------
% 2.96/3.05 fof(reflexivity,axiom,
% 2.96/3.05 ! [X] : r1(X,X) ).
% 2.96/3.05
% 2.96/3.05 fof(main,conjecture,
% 2.96/3.05 ~ ? [X] :
% 2.96/3.05 ~ ( ~ ! [Y] :
% 2.96/3.05 ( ~ r1(X,Y)
% 2.96/3.05 | ~ ( ~ ! [X] :
% 2.96/3.05 ( ~ r1(Y,X)
% 2.96/3.05 | ~ ! [Y] :
% 2.96/3.05 ( ~ r1(X,Y)
% 2.96/3.05 | ~ p1(Y) ) )
% 2.96/3.05 & p1(Y) ) )
% 2.96/3.05 | ~ ! [Y] :
% 2.96/3.05 ( ~ r1(X,Y)
% 2.96/3.05 | ! [X] :
% 2.96/3.05 ( ~ r1(Y,X)
% 2.96/3.05 | ~ ( ~ ! [Y] :
% 2.96/3.05 ( ~ r1(X,Y)
% 2.96/3.05 | ~ ! [X] :
% 2.96/3.05 ( ~ r1(Y,X)
% 2.96/3.05 | p1(X) ) )
% 2.96/3.05 & ~ ! [Y] :
% 2.96/3.05 ( ~ r1(X,Y)
% 2.96/3.05 | p1(Y) ) ) ) )
% 2.96/3.05 | ~ ! [Y] :
% 2.96/3.05 ( ~ r1(X,Y)
% 2.96/3.05 | ~ ( ~ ! [X] :
% 2.96/3.05 ( ~ r1(Y,X)
% 2.96/3.05 | ~ ! [Y] :
% 2.96/3.05 ( ~ r1(X,Y)
% 2.96/3.05 | ~ ! [X] :
% 2.96/3.05 ( ~ r1(Y,X)
% 2.96/3.05 | p1(X) ) ) )
% 2.96/3.05 & ~ ! [X] :
% 2.96/3.05 ( ~ r1(Y,X)
% 2.96/3.05 | ~ ! [Y] :
% 2.96/3.05 ( ~ r1(X,Y)
% 2.96/3.05 | p1(Y) ) ) ) )
% 2.96/3.05 | ~ ! [Y] :
% 2.96/3.05 ( ~ r1(X,Y)
% 2.96/3.05 | ~ ! [X] :
% 2.96/3.05 ( ~ r1(Y,X)
% 2.96/3.05 | $false ) )
% 2.96/3.05 | ! [Y] :
% 2.96/3.05 ( ~ r1(X,Y)
% 2.96/3.05 | ! [X] :
% 2.96/3.05 ( ~ r1(Y,X)
% 2.96/3.05 | ! [Y] :
% 2.96/3.05 ( ~ r1(X,Y)
% 2.96/3.05 | p1(Y) ) )
% 2.96/3.05 | ~ ! [X] :
% 2.96/3.05 ( ~ r1(Y,X)
% 2.96/3.05 | p1(X) ) ) ) ).
% 2.96/3.05
% 2.96/3.05 %------------------------------------------------------------------------------
% 2.96/3.05 %-------------------------------------------
% 2.96/3.05 % Proof found
% 2.96/3.05 % SZS status Theorem for theBenchmark
% 2.96/3.05 % SZS output start Proof
% 2.96/3.05 %ClaNum:15(EqnAxiom:0)
% 2.96/3.05 %VarNum:87(SingletonVarNum:29)
% 2.96/3.05 %MaxLitNum:6
% 2.96/3.05 %MaxfuncDepth:1
% 2.96/3.05 %SharedTerms:8
% 2.96/3.05 %goalClause: 1 2 3 5 6 7 8 9 10 11 12 13 14 15
% 2.96/3.05 %singleGoalClaCount:4
% 2.96/3.05 [1]P1(a1,a2)
% 2.96/3.05 [2]P1(a2,a8)
% 2.96/3.05 [3]P1(a8,a9)
% 2.96/3.05 [5]~P2(a9)
% 2.96/3.05 [4]P1(x41,x41)
% 2.96/3.05 [6]P2(x61)+~P1(a2,x61)
% 2.96/3.05 [7]~P1(a1,x71)+P1(x71,f3(x71))
% 2.96/3.05 [8]~P2(x81)+~P1(x81,x82)+~P1(a1,x81)+P2(f4(x81,x82))
% 2.96/3.05 [9]~P2(x92)+~P1(x92,x91)+~P1(a1,x92)+P1(x91,f4(x92,x91))
% 2.96/3.05 [10]~P1(x102,x101)+~P1(x102,x103)+~P1(a1,x102)+P1(x101,f5(x102,x101))+P1(x103,f7(x102,x103))
% 2.96/3.05 [11]~P1(x112,x111)+~P1(x112,x113)+~P1(a1,x112)+P1(x111,f5(x112,x111))+~P2(f7(x112,x113))
% 2.96/3.05 [12]~P1(x123,x122)+P2(x121)+~P1(x123,x124)+~P1(a1,x123)+~P1(f5(x123,x124),x121)+P1(x122,f7(x123,x122))
% 2.96/3.05 [13]P2(x131)+~P1(x132,x133)+~P1(x132,x134)+~P1(a1,x132)+~P1(f5(x132,x133),x131)+~P2(f7(x132,x134))
% 2.96/3.05 [14]~P1(x144,x141)+~P1(x144,x142)+~P1(x143,x144)+P2(x141)+~P1(a1,x143)+P1(x142,f6(x143,x144,x142))
% 2.96/3.05 [15]P2(x151)+~P1(x152,x151)+~P1(x152,x153)+~P1(x154,x152)+~P1(a1,x154)+~P2(f6(x154,x152,x153))
% 2.96/3.05 %EqnAxiom
% 2.96/3.05
% 2.96/3.05 %-------------------------------------------
% 2.96/3.06 cnf(16,plain,
% 2.96/3.06 (P2(a2)),
% 2.96/3.06 inference(scs_inference,[],[4,6])).
% 2.96/3.06 cnf(17,plain,
% 2.96/3.06 (P1(x171,x171)),
% 2.96/3.06 inference(rename_variables,[],[4])).
% 2.96/3.06 cnf(18,plain,
% 2.96/3.06 (P1(a2,f4(a2,a2))),
% 2.96/3.06 inference(scs_inference,[],[1,4,17,6,9])).
% 2.96/3.06 cnf(21,plain,
% 2.96/3.06 (P1(a2,f3(a2))),
% 2.96/3.06 inference(scs_inference,[],[1,4,17,6,9,7])).
% 2.96/3.06 cnf(55,plain,
% 2.96/3.06 (P1(a8,f4(a2,a8))),
% 2.96/3.06 inference(scs_inference,[],[1,2,3,4,5,16,8,6,15,14,10,9])).
% 2.96/3.06 cnf(67,plain,
% 2.96/3.06 (P1(a8,f6(a2,a8,a8))),
% 2.96/3.06 inference(scs_inference,[],[2,4,3,16,5,21,1,8,14])).
% 2.96/3.06 cnf(70,plain,
% 2.96/3.06 (P2(a8)),
% 2.96/3.06 inference(scs_inference,[],[2,4,3,16,5,21,1,8,14,6])).
% 2.96/3.06 cnf(102,plain,
% 2.96/3.06 (P1(a1,f3(a1))),
% 2.96/3.06 inference(scs_inference,[],[4,21,6,7])).
% 2.96/3.06 cnf(247,plain,
% 2.96/3.06 (~P2(f6(a2,a8,f4(a2,a8)))),
% 2.96/3.06 inference(scs_inference,[],[55,3,2,5,1,15])).
% 2.96/3.06 cnf(2777,plain,
% 2.96/3.06 (~P2(f6(a2,a8,a8))),
% 2.96/3.06 inference(scs_inference,[],[1,2,5,3,4,70,8,15])).
% 2.96/3.06 cnf(4102,plain,
% 2.96/3.06 (P2(f7(a2,a2))+P1(a8,f5(a2,a8))),
% 2.96/3.06 inference(scs_inference,[],[2,4,1,10,6])).
% 2.96/3.06 cnf(4572,plain,
% 2.96/3.06 (P1(a8,f5(a2,a8))),
% 2.96/3.06 inference(scs_inference,[],[2,4,1,11,4102])).
% 2.96/3.06 cnf(4575,plain,
% 2.96/3.06 (P1(f5(a2,a8),f6(a2,a8,f5(a2,a8)))),
% 2.96/3.06 inference(scs_inference,[],[2,5,3,4572,1,13,14])).
% 2.96/3.06 cnf(4816,plain,
% 2.96/3.06 (P2(f6(a2,a8,f5(a2,a8)))+P1(f4(a2,a2),f7(a2,f4(a2,a2)))),
% 2.96/3.06 inference(scs_inference,[],[67,4575,18,2,247,2777,102,1,14,6,12])).
% 2.96/3.06 cnf(4874,plain,
% 2.96/3.06 (P2(f6(a2,a8,f5(a2,a8)))+P1(a2,f7(a2,a2))),
% 2.96/3.06 inference(scs_inference,[],[102,4575,4,2,2777,67,1,14,12])).
% 2.96/3.06 cnf(4875,plain,
% 2.96/3.06 (P1(x48751,x48751)),
% 2.96/3.06 inference(rename_variables,[],[4])).
% 2.96/3.06 cnf(4877,plain,
% 2.96/3.06 (P2(f6(a2,a8,f5(a2,a8)))+~P2(f7(a2,a2))),
% 2.96/3.06 inference(scs_inference,[],[102,4575,4,4875,2,2777,67,1,14,12,13])).
% 2.96/3.06 cnf(5113,plain,
% 2.96/3.06 (~P2(f6(a2,a8,f5(a2,a8)))),
% 2.96/3.06 inference(scs_inference,[],[2777,4572,2,1,67,15])).
% 2.96/3.06 cnf(5123,plain,
% 2.96/3.06 (P2(f7(a2,a2))),
% 2.96/3.06 inference(scs_inference,[],[2777,4575,4572,2,1,70,67,15,8,12,13,4874,4816,6])).
% 2.96/3.06 cnf(5132,plain,
% 2.96/3.06 ($false),
% 2.96/3.06 inference(scs_inference,[],[5113,5123,4877]),
% 2.96/3.06 ['proof']).
% 2.96/3.06 % SZS output end Proof
% 2.96/3.06 % Total time :2.410000s
%------------------------------------------------------------------------------