TSTP Solution File: SET886+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET886+1 : 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 : n028.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 14:31:34 EDT 2023
% Result : Theorem 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n028.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 16:28:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % File :CSE---1.6
% 0.19/0.63 % Problem :theBenchmark
% 0.19/0.63 % Transform :cnf
% 0.19/0.63 % Format :tptp:raw
% 0.19/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.63
% 0.19/0.63 % Result :Theorem 0.010000s
% 0.19/0.63 % Output :CNFRefutation 0.010000s
% 0.19/0.63 %-------------------------------------------
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 % File : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.64 % Domain : Set theory
% 0.19/0.64 % Problem : subset(uno_pair(A,B),singleton(C)) => uno_pair(A,B) = singleton(C)
% 0.19/0.64 % Version : [Urb06] axioms : Especial.
% 0.19/0.64 % English :
% 0.19/0.64
% 0.19/0.64 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.19/0.64 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.19/0.64 % Source : [Urb06]
% 0.19/0.64 % Names : zfmisc_1__t27_zfmisc_1 [Urb06]
% 0.19/0.64
% 0.19/0.64 % Status : Theorem
% 0.19/0.64 % Rating : 0.06 v7.4.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.04 v5.3.0, 0.15 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.0, 0.08 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.07 v3.2.0
% 0.19/0.64 % Syntax : Number of formulae : 7 ( 5 unt; 0 def)
% 0.19/0.64 % Number of atoms : 9 ( 4 equ)
% 0.19/0.64 % Maximal formula atoms : 2 ( 1 avg)
% 0.19/0.64 % Number of connectives : 3 ( 1 ~; 0 |; 0 &)
% 0.19/0.64 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.64 % Maximal formula depth : 5 ( 3 avg)
% 0.19/0.64 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.64 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.19/0.64 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.19/0.64 % Number of variables : 13 ( 11 !; 2 ?)
% 0.19/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.64
% 0.19/0.64 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.64 % library, www.mizar.org
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 fof(commutativity_k2_tarski,axiom,
% 0.19/0.64 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 0.19/0.64
% 0.19/0.64 fof(rc1_xboole_0,axiom,
% 0.19/0.64 ? [A] : empty(A) ).
% 0.19/0.64
% 0.19/0.64 fof(rc2_xboole_0,axiom,
% 0.19/0.64 ? [A] : ~ empty(A) ).
% 0.19/0.64
% 0.19/0.64 fof(reflexivity_r1_tarski,axiom,
% 0.19/0.64 ! [A,B] : subset(A,A) ).
% 0.19/0.64
% 0.19/0.64 fof(t26_zfmisc_1,axiom,
% 0.19/0.64 ! [A,B,C] :
% 0.19/0.64 ( subset(unordered_pair(A,B),singleton(C))
% 0.19/0.64 => A = C ) ).
% 0.19/0.64
% 0.19/0.64 fof(t27_zfmisc_1,conjecture,
% 0.19/0.64 ! [A,B,C] :
% 0.19/0.64 ( subset(unordered_pair(A,B),singleton(C))
% 0.19/0.64 => unordered_pair(A,B) = singleton(C) ) ).
% 0.19/0.64
% 0.19/0.64 fof(t69_enumset1,axiom,
% 0.19/0.64 ! [A] : unordered_pair(A,A) = singleton(A) ).
% 0.19/0.64
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 % Proof found
% 0.19/0.64 % SZS status Theorem for theBenchmark
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 %ClaNum:15(EqnAxiom:8)
% 0.19/0.64 %VarNum:12(SingletonVarNum:6)
% 0.19/0.64 %MaxLitNum:2
% 0.19/0.64 %MaxfuncDepth:1
% 0.19/0.64 %SharedTerms:11
% 0.19/0.64 %goalClause: 12 14
% 0.19/0.64 %singleGoalClaCount:2
% 0.19/0.64 [9]P1(a1)
% 0.19/0.64 [13]~P1(a4)
% 0.19/0.64 [12]P2(f2(a3,a5),f2(a6,a6))
% 0.19/0.64 [14]~E(f2(a6,a6),f2(a3,a5))
% 0.19/0.64 [10]P2(x101,x101)
% 0.19/0.64 [11]E(f2(x111,x112),f2(x112,x111))
% 0.19/0.64 [15]E(x151,x152)+~P2(f2(x151,x153),f2(x152,x152))
% 0.19/0.64 %EqnAxiom
% 0.19/0.64 [1]E(x11,x11)
% 0.19/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.64 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.19/0.64 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.19/0.64 [6]~P1(x61)+P1(x62)+~E(x61,x62)
% 0.19/0.64 [7]P2(x72,x73)+~E(x71,x72)+~P2(x71,x73)
% 0.19/0.64 [8]P2(x83,x82)+~E(x81,x82)+~P2(x83,x81)
% 0.19/0.64
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 cnf(16,plain,
% 0.19/0.65 (E(a3,a6)),
% 0.19/0.65 inference(scs_inference,[],[12,15])).
% 0.19/0.65 cnf(19,plain,
% 0.19/0.65 (P2(f2(a5,a3),f2(a6,a6))),
% 0.19/0.65 inference(scs_inference,[],[12,10,11,15,8,7])).
% 0.19/0.65 cnf(20,plain,
% 0.19/0.65 (E(f2(x201,x202),f2(x202,x201))),
% 0.19/0.65 inference(rename_variables,[],[11])).
% 0.19/0.65 cnf(21,plain,
% 0.19/0.65 (~E(f2(a6,a6),f2(a5,a3))),
% 0.19/0.65 inference(scs_inference,[],[12,10,14,11,20,15,8,7,3])).
% 0.19/0.65 cnf(23,plain,
% 0.19/0.65 (~E(f2(a3,a5),f2(a6,a6))),
% 0.19/0.65 inference(scs_inference,[],[12,10,14,11,20,15,8,7,3,2])).
% 0.19/0.65 cnf(24,plain,
% 0.19/0.65 (E(f2(x241,a3),f2(x241,a6))),
% 0.19/0.65 inference(scs_inference,[],[12,10,14,11,20,15,8,7,3,2,5])).
% 0.19/0.65 cnf(25,plain,
% 0.19/0.65 (E(f2(a3,x251),f2(a6,x251))),
% 0.19/0.65 inference(scs_inference,[],[12,10,14,11,20,15,8,7,3,2,5,4])).
% 0.19/0.65 cnf(26,plain,
% 0.19/0.65 (~E(a1,a4)),
% 0.19/0.65 inference(scs_inference,[],[12,10,9,13,14,11,20,15,8,7,3,2,5,4,6])).
% 0.19/0.65 cnf(27,plain,
% 0.19/0.65 (~P2(f2(a1,x271),f2(a4,a4))),
% 0.19/0.65 inference(scs_inference,[],[26,15])).
% 0.19/0.65 cnf(29,plain,
% 0.19/0.65 (~P2(f2(x291,a1),f2(a4,a4))),
% 0.19/0.65 inference(scs_inference,[],[11,26,15,7])).
% 0.19/0.65 cnf(30,plain,
% 0.19/0.65 (E(f2(x301,x302),f2(x302,x301))),
% 0.19/0.65 inference(rename_variables,[],[11])).
% 0.19/0.65 cnf(33,plain,
% 0.19/0.65 (E(f2(x331,a6),f2(x331,a3))),
% 0.19/0.65 inference(scs_inference,[],[11,30,23,24,26,15,7,3,2])).
% 0.19/0.65 cnf(37,plain,
% 0.19/0.65 (E(a5,a6)),
% 0.19/0.65 inference(scs_inference,[],[19,15])).
% 0.19/0.65 cnf(40,plain,
% 0.19/0.65 (P2(x401,x401)),
% 0.19/0.65 inference(rename_variables,[],[10])).
% 0.19/0.65 cnf(44,plain,
% 0.19/0.65 (~E(f2(x441,a1),f2(a4,a4))),
% 0.19/0.65 inference(scs_inference,[],[16,10,40,11,25,29,19,15,7,3,8])).
% 0.19/0.65 cnf(46,plain,
% 0.19/0.65 (~E(a4,a1)),
% 0.19/0.65 inference(scs_inference,[],[16,10,40,11,25,29,19,26,15,7,3,8,2])).
% 0.19/0.65 cnf(47,plain,
% 0.19/0.65 (~P2(f2(a4,x471),f2(a1,a1))),
% 0.19/0.65 inference(scs_inference,[],[46,15])).
% 0.19/0.65 cnf(50,plain,
% 0.19/0.65 (P2(x501,x501)),
% 0.19/0.65 inference(rename_variables,[],[10])).
% 0.19/0.65 cnf(55,plain,
% 0.19/0.65 (E(a6,a3)),
% 0.19/0.65 inference(scs_inference,[],[16,10,50,21,33,27,46,15,7,3,8,2])).
% 0.19/0.65 cnf(56,plain,
% 0.19/0.65 (~E(a6,a5)),
% 0.19/0.65 inference(scs_inference,[],[16,10,50,21,33,27,46,15,7,3,8,2,4])).
% 0.19/0.65 cnf(57,plain,
% 0.19/0.65 (E(f2(a5,x571),f2(a6,x571))),
% 0.19/0.65 inference(scs_inference,[],[37,4])).
% 0.19/0.65 cnf(60,plain,
% 0.19/0.65 (E(f2(x601,x602),f2(x602,x601))),
% 0.19/0.65 inference(rename_variables,[],[11])).
% 0.19/0.65 cnf(62,plain,
% 0.19/0.65 (~E(f2(x621,a1),f2(a4,a4))),
% 0.19/0.65 inference(rename_variables,[],[44])).
% 0.19/0.65 cnf(68,plain,
% 0.19/0.65 (~P2(f2(a6,x681),f2(a5,a5))),
% 0.19/0.65 inference(scs_inference,[],[10,11,60,44,62,47,56,37,4,7,3,8,2,5,15])).
% 0.19/0.65 cnf(82,plain,
% 0.19/0.65 ($false),
% 0.19/0.65 inference(scs_inference,[],[10,68,55,57,4,7]),
% 0.19/0.65 ['proof']).
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65 % Total time :0.010000s
%------------------------------------------------------------------------------