TSTP Solution File: SEU167+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU167+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n005.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 16:18:04 EDT 2023
% Result : Theorem 0.14s 0.59s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU167+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.10/0.33 % Computer : n005.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Wed Aug 23 15:10:09 EDT 2023
% 0.10/0.34 % CPUTime :
% 0.14/0.54 start to proof:theBenchmark
% 0.14/0.58 %-------------------------------------------
% 0.14/0.58 % File :CSE---1.6
% 0.14/0.58 % Problem :theBenchmark
% 0.14/0.58 % Transform :cnf
% 0.14/0.58 % Format :tptp:raw
% 0.14/0.58 % Command :java -jar mcs_scs.jar %d %s
% 0.14/0.58
% 0.14/0.58 % Result :Theorem 0.000000s
% 0.14/0.58 % Output :CNFRefutation 0.000000s
% 0.14/0.58 %-------------------------------------------
% 0.14/0.59 %------------------------------------------------------------------------------
% 0.14/0.59 % File : SEU167+3 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.59 % Domain : Set theory
% 0.14/0.59 % Problem : Basic properties of sets, theorem 119
% 0.14/0.59 % Version : [Urb06] axioms : Especial.
% 0.14/0.59 % English :
% 0.14/0.59
% 0.14/0.59 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.14/0.59 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.14/0.59 % Source : [Urb06]
% 0.14/0.59 % Names : zfmisc_1__t119_zfmisc_1 [Urb06]
% 0.14/0.59
% 0.14/0.59 % Status : Theorem
% 0.14/0.59 % Rating : 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v6.0.0, 0.25 v5.5.0, 0.12 v5.4.0, 0.04 v5.3.0, 0.13 v5.2.0, 0.00 v3.2.0
% 0.14/0.59 % Syntax : Number of formulae : 6 ( 3 unt; 0 def)
% 0.14/0.59 % Number of atoms : 12 ( 0 equ)
% 0.14/0.59 % Maximal formula atoms : 3 ( 2 avg)
% 0.14/0.59 % Number of connectives : 7 ( 1 ~; 0 |; 3 &)
% 0.14/0.59 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.14/0.59 % Maximal formula depth : 7 ( 5 avg)
% 0.14/0.59 % Maximal term depth : 2 ( 1 avg)
% 0.14/0.59 % Number of predicates : 2 ( 2 usr; 0 prp; 1-2 aty)
% 0.14/0.59 % Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% 0.14/0.59 % Number of variables : 14 ( 12 !; 2 ?)
% 0.14/0.59 % SPC : FOF_THM_RFO_NEQ
% 0.14/0.59
% 0.14/0.59 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.14/0.59 % library, www.mizar.org
% 0.14/0.59 %------------------------------------------------------------------------------
% 0.14/0.59 fof(rc1_xboole_0,axiom,
% 0.14/0.59 ? [A] : empty(A) ).
% 0.14/0.59
% 0.14/0.59 fof(rc2_xboole_0,axiom,
% 0.14/0.59 ? [A] : ~ empty(A) ).
% 0.14/0.59
% 0.14/0.59 fof(reflexivity_r1_tarski,axiom,
% 0.14/0.59 ! [A,B] : subset(A,A) ).
% 0.14/0.59
% 0.14/0.59 fof(t118_zfmisc_1,axiom,
% 0.14/0.59 ! [A,B,C] :
% 0.14/0.59 ( subset(A,B)
% 0.14/0.59 => ( subset(cartesian_product2(A,C),cartesian_product2(B,C))
% 0.14/0.59 & subset(cartesian_product2(C,A),cartesian_product2(C,B)) ) ) ).
% 0.14/0.59
% 0.14/0.59 fof(t119_zfmisc_1,conjecture,
% 0.14/0.59 ! [A,B,C,D] :
% 0.14/0.59 ( ( subset(A,B)
% 0.14/0.59 & subset(C,D) )
% 0.14/0.59 => subset(cartesian_product2(A,C),cartesian_product2(B,D)) ) ).
% 0.14/0.59
% 0.14/0.59 fof(t1_xboole_1,axiom,
% 0.14/0.59 ! [A,B,C] :
% 0.14/0.59 ( ( subset(A,B)
% 0.14/0.59 & subset(B,C) )
% 0.14/0.59 => subset(A,C) ) ).
% 0.14/0.59
% 0.14/0.59 %------------------------------------------------------------------------------
% 0.14/0.59 %-------------------------------------------
% 0.14/0.59 % Proof found
% 0.14/0.59 % SZS status Theorem for theBenchmark
% 0.14/0.59 % SZS output start Proof
% 0.14/0.59 %ClaNum:9(EqnAxiom:0)
% 0.14/0.59 %VarNum:20(SingletonVarNum:10)
% 0.14/0.59 %MaxLitNum:3
% 0.14/0.59 %MaxfuncDepth:1
% 0.14/0.59 %SharedTerms:13
% 0.14/0.59 %goalClause: 2 3 6
% 0.14/0.59 %singleGoalClaCount:3
% 0.14/0.59 [1]P1(a1)
% 0.14/0.59 [2]P2(a3,a5)
% 0.14/0.59 [3]P2(a6,a7)
% 0.14/0.59 [5]~P1(a4)
% 0.14/0.59 [6]~P2(f2(a3,a6),f2(a5,a7))
% 0.14/0.59 [4]P2(x41,x41)
% 0.14/0.59 [8]~P2(x81,x83)+P2(f2(x81,x82),f2(x83,x82))
% 0.14/0.59 [9]~P2(x92,x93)+P2(f2(x91,x92),f2(x91,x93))
% 0.14/0.59 [7]~P2(x71,x73)+P2(x71,x72)+~P2(x73,x72)
% 0.14/0.59 %EqnAxiom
% 0.14/0.59
% 0.14/0.59 %-------------------------------------------
% 0.14/0.59 cnf(12,plain,
% 0.14/0.59 (~P2(f2(a5,a6),f2(a5,a7))),
% 0.14/0.59 inference(scs_inference,[],[2,6,9,8,7])).
% 0.14/0.59 cnf(14,plain,
% 0.14/0.59 ($false),
% 0.14/0.59 inference(scs_inference,[],[3,12,9]),
% 0.14/0.59 ['proof']).
% 0.14/0.59 % SZS output end Proof
% 0.14/0.59 % Total time :0.000000s
%------------------------------------------------------------------------------