TSTP Solution File: LCL678+1.001 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LCL678+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 : 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 06:50:24 EDT 2023
% Result : Theorem 0.23s 0.65s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL678+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 20:23:17 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.23/0.59 start to proof:theBenchmark
% 0.23/0.64 %-------------------------------------------
% 0.23/0.64 % File :CSE---1.6
% 0.23/0.64 % Problem :theBenchmark
% 0.23/0.64 % Transform :cnf
% 0.23/0.64 % Format :tptp:raw
% 0.23/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.23/0.64
% 0.23/0.64 % Result :Theorem 0.000000s
% 0.23/0.64 % Output :CNFRefutation 0.000000s
% 0.23/0.64 %-------------------------------------------
% 0.23/0.65 %------------------------------------------------------------------------------
% 0.23/0.65 % File : LCL678+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.23/0.65 % Domain : Logic Calculi (Modal Logic)
% 0.23/0.65 % Problem : In S4, formula provable in intuitionistic logic, size 1
% 0.23/0.65 % Version : Especial.
% 0.23/0.65 % English :
% 0.23/0.65
% 0.23/0.65 % Refs : [BHS00] Balsiger et al. (2000), A Benchmark Method for the Pro
% 0.23/0.65 % : [Kam08] Kaminski (2008), Email to G. Sutcliffe
% 0.23/0.65 % Source : [Kam08]
% 0.23/0.65 % Names : s4_ipc_p [BHS00]
% 0.23/0.65
% 0.23/0.65 % Status : Theorem
% 0.23/0.65 % Rating : 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
% 0.23/0.65 % Syntax : Number of formulae : 3 ( 1 unt; 0 def)
% 0.23/0.65 % Number of atoms : 12 ( 0 equ)
% 0.23/0.65 % Maximal formula atoms : 8 ( 4 avg)
% 0.23/0.65 % Number of connectives : 18 ( 9 ~; 7 |; 1 &)
% 0.23/0.65 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.23/0.65 % Maximal formula depth : 17 ( 8 avg)
% 0.23/0.65 % Maximal term depth : 1 ( 1 avg)
% 0.23/0.65 % Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% 0.23/0.65 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.23/0.65 % Number of variables : 9 ( 8 !; 1 ?)
% 0.23/0.65 % SPC : FOF_THM_RFO_NEQ
% 0.23/0.65
% 0.23/0.65 % Comments : A naive relational encoding of the modal logic problem into
% 0.23/0.65 % first-order logic.
% 0.23/0.65 %------------------------------------------------------------------------------
% 0.23/0.65 fof(reflexivity,axiom,
% 0.23/0.65 ! [X] : r1(X,X) ).
% 0.23/0.65
% 0.23/0.65 fof(transitivity,axiom,
% 0.23/0.65 ! [X,Y,Z] :
% 0.23/0.65 ( ( r1(X,Y)
% 0.23/0.65 & r1(Y,Z) )
% 0.23/0.65 => r1(X,Z) ) ).
% 0.23/0.65
% 0.23/0.65 fof(main,conjecture,
% 0.23/0.65 ~ ? [X] :
% 0.23/0.65 ~ ( $false
% 0.23/0.65 | ~ ! [Y] :
% 0.23/0.65 ( ~ r1(X,Y)
% 0.23/0.65 | $false
% 0.23/0.65 | ~ ! [X] :
% 0.23/0.65 ( ~ r1(Y,X)
% 0.23/0.65 | ! [Y] :
% 0.23/0.65 ( ~ r1(X,Y)
% 0.23/0.65 | p1(Y) )
% 0.23/0.65 | ~ ! [Y] :
% 0.23/0.65 ( ~ r1(X,Y)
% 0.23/0.65 | p1(Y) ) ) ) ) ).
% 0.23/0.65
% 0.23/0.65 %------------------------------------------------------------------------------
% 0.23/0.65 %-------------------------------------------
% 0.23/0.65 % Proof found
% 0.23/0.65 % SZS status Theorem for theBenchmark
% 0.23/0.65 % SZS output start Proof
% 0.23/0.65 %ClaNum:6(EqnAxiom:0)
% 0.23/0.65 %VarNum:20(SingletonVarNum:9)
% 0.23/0.65 %MaxLitNum:3
% 0.23/0.65 %MaxfuncDepth:1
% 0.23/0.65 %SharedTerms:1
% 0.23/0.65 %goalClause: 2 3 4 5
% 0.23/0.65 [1]P1(x11,x11)
% 0.23/0.65 [2]~P1(a2,x21)+~P2(f1(x21))
% 0.23/0.65 [3]~P1(a2,x31)+P1(x31,f3(x31))
% 0.23/0.65 [4]~P1(a2,x41)+P1(f3(x41),f1(x41))
% 0.23/0.65 [5]P2(x51)+~P1(f3(x52),x51)+~P1(a2,x52)
% 0.23/0.65 [6]~P1(x61,x63)+P1(x61,x62)+~P1(x63,x62)
% 0.23/0.65 %EqnAxiom
% 0.23/0.65
% 0.23/0.65 %-------------------------------------------
% 0.23/0.65 cnf(8,plain,
% 0.23/0.65 (P1(x81,x81)),
% 0.23/0.65 inference(rename_variables,[],[1])).
% 0.23/0.65 cnf(9,plain,
% 0.23/0.65 (~P2(f1(a2))),
% 0.23/0.65 inference(scs_inference,[],[1,8,3,2])).
% 0.23/0.65 cnf(10,plain,
% 0.23/0.65 (P1(x101,x101)),
% 0.23/0.65 inference(rename_variables,[],[1])).
% 0.23/0.65 cnf(12,plain,
% 0.23/0.65 (P1(f3(a2),f1(a2))),
% 0.23/0.65 inference(scs_inference,[],[1,8,10,3,2,4])).
% 0.23/0.65 cnf(18,plain,
% 0.23/0.65 ($false),
% 0.23/0.65 inference(scs_inference,[],[1,12,9,5]),
% 0.23/0.65 ['proof']).
% 0.23/0.65 % SZS output end Proof
% 0.23/0.65 % Total time :0.000000s
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