%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:19:24 AM UTC 2026
% Result : Theorem 115.97s 116.18s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.08/0.34 % Computer : n010.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 4 19:37:53 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.23/0.51 start to proof:theBenchmark
% 115.97/116.17 %-------------------------------------------
% 115.97/116.17 % File :CSE---1.7
% 115.97/116.17 % Problem :theBenchmark
% 115.97/116.17 % Transform :cnf
% 115.97/116.17 % Format :tptp:raw
% 115.97/116.17 % Command :java -jar mcs_scs.jar %d %s
% 115.97/116.17
% 115.97/116.17 % Result :Theorem 115.602584s
% 115.97/116.17 % Output :CNFRefutation 115.602584s
% 115.97/116.17 %-------------------------------------------
% 115.97/116.17 %------------------------------------------------------------------------------
% 115.97/116.17 % File : LCL638+1.001 : TPTP v9.3.1. Released v4.0.0.
% 115.97/116.17 % Domain : Logic Calculi (Modal Logic)
% 115.97/116.17 % Problem : In K, D & A4 & B{~p0/p0} -> T, size 1
% 115.97/116.17 % Version : Especial.
% 115.97/116.17 % English :
% 115.97/116.17
% 115.97/116.17 % Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
% 115.97/116.17 % : [Kam08] Kaminski (2008), Email to G. Sutcliffe
% 115.97/116.17 % Source : [Kam08]
% 115.97/116.17 % Names : k_d4_p [BHS00]
% 115.97/116.17
% 115.97/116.17 % Status : Theorem
% 115.97/116.17 % Rating : 0.00 v9.1.0, 0.07 v9.0.0, 0.00 v6.1.0, 0.04 v6.0.0, 0.25 v5.5.0, 0.08 v5.4.0, 0.13 v5.3.0, 0.22 v5.2.0, 0.07 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.11 v4.0.0
% 115.97/116.17 % Syntax : Number of formulae : 1 ( 0 unt; 0 def)
% 115.97/116.17 % Number of atoms : 31 ( 0 equ)
% 115.97/116.17 % Maximal formula atoms : 31 ( 31 avg)
% 115.97/116.17 % Number of connectives : 75 ( 45 ~; 26 |; 4 &)
% 115.97/116.17 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 115.97/116.17 % Maximal formula depth : 21 ( 21 avg)
% 115.97/116.17 % Maximal term depth : 1 ( 1 avg)
% 115.97/116.17 % Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% 115.97/116.17 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 115.97/116.17 % Number of variables : 21 ( 20 !; 1 ?)
% 115.97/116.17 % SPC : FOF_THM_RFO_NEQ
% 115.97/116.17
% 115.97/116.17 % Comments : A naive relational encoding of the modal logic problem into
% 115.97/116.18 % first-order logic.
% 115.97/116.18 %------------------------------------------------------------------------------
% 115.97/116.18 fof(main,conjecture,
% 115.97/116.18 ~ ? [X] :
% 115.97/116.18 ~ ( ~ ! [Y] :
% 115.97/116.18 ( ~ r1(X,Y)
% 115.97/116.18 | ~ ( ~ ! [X] :
% 115.97/116.18 ( ~ r1(Y,X)
% 115.97/116.18 | ~ ! [Y] :
% 115.97/116.18 ( ~ r1(X,Y)
% 115.97/116.18 | p1(Y) ) )
% 115.97/116.18 & ~ p1(Y) ) )
% 115.97/116.18 | ~ ! [Y] :
% 115.97/116.18 ( ~ r1(X,Y)
% 115.97/116.18 | ~ ( ~ ! [X] :
% 115.97/116.18 ( ~ r1(Y,X)
% 115.97/116.18 | ~ ! [Y] :
% 115.97/116.18 ( ~ r1(X,Y)
% 115.97/116.18 | ~ p1(Y) ) )
% 115.97/116.18 & p1(Y) ) )
% 115.97/116.18 | ~ ! [Y] :
% 115.97/116.18 ( ~ r1(X,Y)
% 115.97/116.18 | ~ ( ~ ! [X] :
% 115.97/116.18 ( ~ r1(Y,X)
% 115.97/116.18 | ! [Y] :
% 115.97/116.18 ( ~ r1(X,Y)
% 115.97/116.18 | ~ ! [X] :
% 115.97/116.18 ( ~ r1(Y,X)
% 115.97/116.18 | ~ p1(X) ) ) )
% 115.97/116.18 & ! [X] :
% 115.97/116.18 ( ~ r1(Y,X)
% 115.97/116.18 | ~ ! [Y] :
% 115.97/116.18 ( ~ r1(X,Y)
% 115.97/116.18 | ~ p1(Y) ) ) ) )
% 115.97/116.18 | ~ ! [Y] :
% 115.97/116.18 ( ~ r1(X,Y)
% 115.97/116.18 | ~ ( ~ ! [X] :
% 115.97/116.18 ( ~ r1(Y,X)
% 115.97/116.18 | ! [Y] :
% 115.97/116.18 ( ~ r1(X,Y)
% 115.97/116.18 | p1(Y) ) )
% 115.97/116.18 & ! [X] :
% 115.97/116.18 ( ~ r1(Y,X)
% 115.97/116.18 | p1(X) ) ) )
% 115.97/116.18 | ~ ! [Y] :
% 115.97/116.18 ( ~ r1(X,Y)
% 115.97/116.18 | ~ ! [X] :
% 115.97/116.18 ( ~ r1(Y,X)
% 115.97/116.18 | $false ) )
% 115.97/116.18 | ! [Y] :
% 115.97/116.18 ( ~ r1(X,Y)
% 115.97/116.18 | p1(Y)
% 115.97/116.18 | ~ ! [X] :
% 115.97/116.18 ( ~ r1(Y,X)
% 115.97/116.18 | p1(X) ) ) ) ).
% 115.97/116.18
% 115.97/116.18 %------------------------------------------------------------------------------
% 115.97/116.18 %-------------------------------------------
% 115.97/116.18 % Proof found
% 115.97/116.18 % SZS status Theorem for theBenchmark
% 115.97/116.18 % SZS output start Proof
% 115.97/116.18 %ClaNum:14(EqnAxiom:0)
% 115.97/116.18 %VarNum:90(SingletonVarNum:30)
% 115.97/116.18 %MaxLitNum:6
% 115.97/116.18 %MaxfuncDepth:1
% 115.97/116.18 %SharedTerms:4
% 115.97/116.18 %goalClause: 1 2 3 4 5 6 7 8 9 10 11 12 13 14
% 115.97/116.18 %singleGoalClaCount:2
% 115.97/116.18 [1]P1(a1,a2)
% 115.97/116.18 [2]~P2(a2)
% 115.97/116.18 [3]P2(x31)+~P1(a2,x31)
% 115.97/116.18 [4]~P1(a1,x41)+P1(x41,f3(x41))
% 115.97/116.18 [5]~P2(x51)+~P1(x51,x52)+~P1(a1,x51)+P2(f4(x51,x52))
% 115.97/116.18 [7]~P1(x71,x72)+P2(x71)+~P1(a1,x71)+P1(x72,f5(x71,x72))
% 115.97/116.18 [8]~P2(x82)+~P1(x82,x81)+~P1(a1,x82)+P1(x81,f4(x82,x81))
% 115.97/116.18 [10]P2(x101)+~P1(x101,x102)+~P1(a1,x101)+~P2(f5(x101,x102))
% 115.97/116.18 [6]P2(x61)+~P1(x62,x61)+~P1(x63,x62)+~P1(a1,x63)+~P2(f6(x63))
% 115.97/116.18 [9]~P1(x92,x93)+P2(x91)+~P1(x93,x91)+~P1(a1,x92)+P1(x92,f6(x92))
% 115.97/116.18 [11]~P1(x112,x113)+~P1(x111,x112)+~P1(a1,x111)+P1(x111,f7(x111))+P2(f8(x111,x112,x113))
% 115.97/116.18 [12]~P1(x123,x122)+~P1(x121,x123)+~P1(a1,x121)+P1(x121,f7(x121))+P1(x122,f8(x121,x123,x122))
% 115.97/116.18 [13]~P1(x132,x133)+~P1(x131,x132)+~P2(x134)+~P1(a1,x131)+~P1(f7(x131),x134)+P2(f8(x131,x132,x133))
% 115.97/116.18 [14]~P1(x143,x141)+~P1(x142,x143)+~P2(x144)+~P1(a1,x142)+~P1(f7(x142),x144)+P1(x141,f8(x142,x143,x141))
% 115.97/116.18 %EqnAxiom
% 115.97/116.18
% 115.97/116.18 %-------------------------------------------
% 116.45/116.64 cnf(270732,plain,
% 116.45/116.64 (P1(a2,f3(a2))),
% 116.45/116.64 inference(scs_inference,[],[1,4])).
% 116.45/116.64 cnf(508816,plain,
% 116.45/116.64 (~P2(f5(a2,f3(a2)))),
% 116.45/116.64 inference(scs_inference,[],[2,270732,1,3,10])).
% 116.45/116.64 cnf(508818,plain,
% 116.45/116.64 (P1(f3(a2),f5(a2,f3(a2)))),
% 116.45/116.64 inference(scs_inference,[],[2,270732,1,3,10,7])).
% 116.45/116.64 cnf(508820,plain,
% 116.45/116.64 (~P2(f6(a2))),
% 116.45/116.64 inference(scs_inference,[],[2,270732,1,3,10,7,6])).
% 116.45/116.64 cnf(508822,plain,
% 116.45/116.64 (~P1(a2,f6(a2))),
% 116.45/116.64 inference(scs_inference,[],[508820,3])).
% 116.45/116.64 cnf(508829,plain,
% 116.45/116.64 ($false),
% 116.45/116.64 inference(scs_inference,[],[508822,508818,508816,270732,1,3,9]),
% 116.45/116.64 ['proof']).
% 116.56/116.78 % SZS output end Proof
% 116.56/116.78 % Total time :115.602584s
%------------------------------------------------------------------------------