TSTP Solution File: SET788+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET788+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n016.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 14:31:03 EDT 2023
% Result : Theorem 0.21s 0.68s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET788+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sat Aug 26 16:20:12 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.21/0.62 start to proof:theBenchmark
% 0.21/0.67 %-------------------------------------------
% 0.21/0.67 % File :CSE---1.6
% 0.21/0.67 % Problem :theBenchmark
% 0.21/0.67 % Transform :cnf
% 0.21/0.67 % Format :tptp:raw
% 0.21/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.67
% 0.21/0.67 % Result :Theorem 0.000000s
% 0.21/0.67 % Output :CNFRefutation 0.000000s
% 0.21/0.67 %-------------------------------------------
% 0.21/0.67 %--------------------------------------------------------------------------
% 0.21/0.67 % File : SET788+1 : TPTP v8.1.2. Released v3.1.0.
% 0.21/0.67 % Domain : Set theory
% 0.21/0.67 % Problem : Symmetry of equality from set membership
% 0.21/0.68 % Version : Especial.
% 0.21/0.68 % English :
% 0.21/0.68
% 0.21/0.68 % Refs : [Shu04] Shults (2004), Email to G. Sutcliffe
% 0.21/0.68 % Source : [Shu04]
% 0.21/0.68 % Names :
% 0.21/0.68
% 0.21/0.68 % Status : Theorem
% 0.21/0.68 % Rating : 0.00 v6.3.0, 0.08 v6.2.0, 0.00 v5.3.0, 0.09 v5.2.0, 0.00 v4.0.0, 0.05 v3.7.0, 0.00 v3.3.0, 0.11 v3.2.0, 0.33 v3.1.0, 0.00 v2.5.0
% 0.21/0.68 % Syntax : Number of formulae : 1 ( 0 unt; 0 def)
% 0.21/0.68 % Number of atoms : 5 ( 0 equ)
% 0.21/0.68 % Maximal formula atoms : 5 ( 5 avg)
% 0.21/0.68 % Number of connectives : 4 ( 0 ~; 0 |; 0 &)
% 0.21/0.68 % ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% 0.21/0.68 % Maximal formula depth : 7 ( 7 avg)
% 0.21/0.68 % Maximal term depth : 1 ( 1 avg)
% 0.21/0.68 % Number of predicates : 2 ( 2 usr; 0 prp; 2-2 aty)
% 0.21/0.68 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.21/0.68 % Number of variables : 5 ( 5 !; 0 ?)
% 0.21/0.68 % SPC : FOF_THM_RFO_NEQ
% 0.21/0.68
% 0.21/0.68 % Comments :
% 0.21/0.68 %--------------------------------------------------------------------------
% 0.21/0.68 fof(prove_this,conjecture,
% 0.21/0.68 ( ! [X,Y] :
% 0.21/0.68 ( equalish(X,Y)
% 0.21/0.68 <=> ! [Z] :
% 0.21/0.68 ( a_member_of(Z,X)
% 0.21/0.68 <=> a_member_of(Z,Y) ) )
% 0.21/0.68 => ! [X,Y] :
% 0.21/0.68 ( equalish(X,Y)
% 0.21/0.68 <=> equalish(Y,X) ) ) ).
% 0.21/0.68
% 0.21/0.68 %--------------------------------------------------------------------------
% 0.21/0.68 %-------------------------------------------
% 0.21/0.68 % Proof found
% 0.21/0.68 % SZS status Theorem for theBenchmark
% 0.21/0.68 % SZS output start Proof
% 0.21/0.68 %ClaNum:6(EqnAxiom:0)
% 0.21/0.68 %VarNum:28(SingletonVarNum:10)
% 0.21/0.68 %MaxLitNum:3
% 0.21/0.68 %MaxfuncDepth:1
% 0.21/0.68 %SharedTerms:6
% 0.21/0.68 %goalClause: 1 2 3 4 5 6
% 0.21/0.68 [1]P1(a1,a3)+P1(a3,a1)
% 0.21/0.68 [2]~P1(a1,a3)+~P1(a3,a1)
% 0.21/0.68 [5]P1(x51,x52)+P2(f2(x51,x52),x52)+P2(f2(x51,x52),x51)
% 0.21/0.68 [6]P1(x61,x62)+~P2(f2(x61,x62),x62)+~P2(f2(x61,x62),x61)
% 0.21/0.68 [3]~P2(x31,x33)+P2(x31,x32)+~P1(x32,x33)
% 0.21/0.68 [4]~P2(x41,x43)+P2(x41,x42)+~P1(x43,x42)
% 0.21/0.68 %EqnAxiom
% 0.21/0.68
% 0.21/0.68 %-------------------------------------------
% 0.21/0.68 cnf(8,plain,
% 0.21/0.68 (~P2(x81,a3)+P2(x81,a1)+P1(a3,a1)),
% 0.21/0.68 inference(scs_inference,[],[3,1])).
% 0.21/0.68 cnf(9,plain,
% 0.21/0.68 (~P2(x91,a1)+P2(x91,a3)+P1(a3,a1)),
% 0.21/0.68 inference(scs_inference,[],[4,1])).
% 0.21/0.68 cnf(10,plain,
% 0.21/0.68 (P1(x101,a1)+~P2(f2(x101,a1),x101)+~P2(f2(x101,a1),a3)+P1(a3,a1)),
% 0.21/0.68 inference(scs_inference,[],[8,6])).
% 0.21/0.68 cnf(11,plain,
% 0.21/0.68 (~P2(f2(a3,a1),a1)+P1(a3,a1)),
% 0.21/0.68 inference(scs_inference,[],[9,10])).
% 0.21/0.68 cnf(12,plain,
% 0.21/0.68 (P1(a3,a1)+P2(f2(a3,a1),a3)),
% 0.21/0.68 inference(scs_inference,[],[11,5])).
% 0.21/0.68 cnf(13,plain,
% 0.21/0.68 (P2(f2(a3,a1),a3)+~P1(a1,a3)),
% 0.21/0.68 inference(scs_inference,[],[12,2])).
% 0.21/0.68 cnf(14,plain,
% 0.21/0.68 (P1(a3,a1)+~P1(a1,a3)),
% 0.21/0.68 inference(scs_inference,[],[13,10])).
% 0.21/0.68 cnf(15,plain,
% 0.21/0.68 (~P1(a1,a3)),
% 0.21/0.68 inference(scs_inference,[],[14,2])).
% 0.21/0.68 cnf(16,plain,
% 0.21/0.68 (P1(a3,a1)),
% 0.21/0.68 inference(scs_inference,[],[15,1])).
% 0.21/0.68 cnf(20,plain,
% 0.21/0.68 (~P1(a3,a1)+~P2(f2(a1,a3),a3)),
% 0.21/0.68 inference(scs_inference,[],[15,6,5,4])).
% 0.21/0.68 cnf(29,plain,
% 0.21/0.68 ($false),
% 0.21/0.68 inference(scs_inference,[],[15,16,20,3,5]),
% 0.21/0.68 ['proof']).
% 0.21/0.68 % SZS output end Proof
% 0.21/0.68 % Total time :0.000000s
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