TSTP Solution File: SET047+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% 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 14:28:12 EDT 2023
% Result : Theorem 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 13:23:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.19/0.60 %-------------------------------------------
% 0.19/0.60 % File :CSE---1.6
% 0.19/0.60 % Problem :theBenchmark
% 0.19/0.60 % Transform :cnf
% 0.19/0.60 % Format :tptp:raw
% 0.19/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.60
% 0.19/0.60 % Result :Theorem 0.000000s
% 0.19/0.60 % Output :CNFRefutation 0.000000s
% 0.19/0.60 %-------------------------------------------
% 0.19/0.60 %--------------------------------------------------------------------------
% 0.19/0.60 % File : SET047+1 : TPTP v8.1.2. Released v2.0.0.
% 0.19/0.60 % Domain : Set Theory
% 0.19/0.60 % Problem : Set equality is symmetric
% 0.19/0.60 % Version : Especial.
% 0.19/0.60 % English : Define set equality as having exactly the same members. Prove
% 0.19/0.60 % set equality is symmetric.
% 0.19/0.60
% 0.19/0.60 % Refs : [DeC79] DeChampeaux (1979), Sub-problem Finder and Instance Ch
% 0.19/0.60 % : [KM64] Kalish & Montegue (1964), Logic: Techniques of Formal
% 0.19/0.60 % : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.19/0.60 % : [Hah94] Haehnle (1994), Email to G. Sutcliffe
% 0.19/0.60 % Source : [Pel86]
% 0.19/0.60 % Names : Pelletier 43 [Pel86]
% 0.19/0.60
% 0.19/0.60 % Status : Theorem
% 0.19/0.60 % Rating : 0.00 v6.1.0, 0.04 v6.0.0, 0.50 v5.5.0, 0.04 v5.3.0, 0.17 v5.2.0, 0.00 v4.0.0, 0.05 v3.7.0, 0.00 v3.3.0, 0.11 v3.2.0, 0.22 v3.1.0, 0.17 v2.7.0, 0.00 v2.1.0
% 0.19/0.60 % Syntax : Number of formulae : 2 ( 0 unt; 0 def)
% 0.19/0.60 % Number of atoms : 5 ( 0 equ)
% 0.19/0.60 % Maximal formula atoms : 3 ( 2 avg)
% 0.19/0.60 % Number of connectives : 3 ( 0 ~; 0 |; 0 &)
% 0.19/0.60 % ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.60 % Maximal formula depth : 6 ( 5 avg)
% 0.19/0.60 % Maximal term depth : 1 ( 1 avg)
% 0.19/0.60 % Number of predicates : 2 ( 2 usr; 0 prp; 2-2 aty)
% 0.19/0.60 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.60 % Number of variables : 5 ( 5 !; 0 ?)
% 0.19/0.60 % SPC : FOF_THM_RFO_NEQ
% 0.19/0.60
% 0.19/0.60 % Comments : The version in [Hah94] is a bit expanded.
% 0.19/0.60 %--------------------------------------------------------------------------
% 0.19/0.60 fof(pel43_1,axiom,
% 0.19/0.60 ! [X,Y] :
% 0.19/0.60 ( set_equal(X,Y)
% 0.19/0.60 <=> ! [Z] :
% 0.19/0.60 ( element(Z,X)
% 0.19/0.60 <=> element(Z,Y) ) ) ).
% 0.19/0.60
% 0.19/0.60 fof(pel43,conjecture,
% 0.19/0.60 ! [X,Y] :
% 0.19/0.60 ( set_equal(X,Y)
% 0.19/0.60 <=> set_equal(Y,X) ) ).
% 0.19/0.60
% 0.19/0.60 %--------------------------------------------------------------------------
% 0.19/0.60 %-------------------------------------------
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark
% 0.19/0.60 % SZS output start Proof
% 0.19/0.60 %ClaNum:6(EqnAxiom:0)
% 0.19/0.60 %VarNum:28(SingletonVarNum:10)
% 0.19/0.60 %MaxLitNum:3
% 0.19/0.60 %MaxfuncDepth:1
% 0.19/0.60 %SharedTerms:6
% 0.19/0.60 %goalClause: 1 2
% 0.19/0.60 [1]P1(a1,a3)+P1(a3,a1)
% 0.19/0.60 [2]~P1(a1,a3)+~P1(a3,a1)
% 0.19/0.60 [5]P1(x51,x52)+P2(f2(x51,x52),x52)+P2(f2(x51,x52),x51)
% 0.19/0.60 [6]P1(x61,x62)+~P2(f2(x61,x62),x62)+~P2(f2(x61,x62),x61)
% 0.19/0.60 [3]~P2(x31,x33)+P2(x31,x32)+~P1(x32,x33)
% 0.19/0.60 [4]~P2(x41,x43)+P2(x41,x42)+~P1(x43,x42)
% 0.19/0.60 %EqnAxiom
% 0.19/0.60
% 0.19/0.60 %-------------------------------------------
% 0.19/0.61 cnf(8,plain,
% 0.19/0.61 (~P2(x81,a3)+P2(x81,a1)+P1(a3,a1)),
% 0.19/0.61 inference(scs_inference,[],[3,1])).
% 0.19/0.61 cnf(9,plain,
% 0.19/0.61 (~P2(x91,a1)+P2(x91,a3)+P1(a3,a1)),
% 0.19/0.61 inference(scs_inference,[],[4,1])).
% 0.19/0.61 cnf(10,plain,
% 0.19/0.61 (P1(x101,a1)+~P2(f2(x101,a1),x101)+~P2(f2(x101,a1),a3)+P1(a3,a1)),
% 0.19/0.61 inference(scs_inference,[],[8,6])).
% 0.19/0.61 cnf(11,plain,
% 0.19/0.61 (~P2(f2(a3,a1),a1)+P1(a3,a1)),
% 0.19/0.61 inference(scs_inference,[],[9,10])).
% 0.19/0.61 cnf(12,plain,
% 0.19/0.61 (P1(a3,a1)+P2(f2(a3,a1),a3)),
% 0.19/0.61 inference(scs_inference,[],[11,5])).
% 0.19/0.61 cnf(13,plain,
% 0.19/0.61 (P2(f2(a3,a1),a3)+~P1(a1,a3)),
% 0.19/0.61 inference(scs_inference,[],[12,2])).
% 0.19/0.61 cnf(14,plain,
% 0.19/0.61 (P1(a3,a1)+~P1(a1,a3)),
% 0.19/0.61 inference(scs_inference,[],[13,10])).
% 0.19/0.61 cnf(15,plain,
% 0.19/0.61 (~P1(a1,a3)),
% 0.19/0.61 inference(scs_inference,[],[14,2])).
% 0.19/0.61 cnf(16,plain,
% 0.19/0.61 (P1(a3,a1)),
% 0.19/0.61 inference(scs_inference,[],[15,1])).
% 0.19/0.61 cnf(20,plain,
% 0.19/0.61 (~P1(a3,a1)+~P2(f2(a1,a3),a3)),
% 0.19/0.61 inference(scs_inference,[],[15,6,5,4])).
% 0.19/0.61 cnf(29,plain,
% 0.19/0.61 ($false),
% 0.19/0.61 inference(scs_inference,[],[15,16,20,3,5]),
% 0.19/0.61 ['proof']).
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time :0.000000s
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