TSTP Solution File: SET979+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET979+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 : n023.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 14:31:52 EDT 2023
% Result : Theorem 0.53s 0.59s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET979+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 09:32:11 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.53/0.59 %-------------------------------------------
% 0.53/0.59 % File :CSE---1.6
% 0.53/0.59 % Problem :theBenchmark
% 0.53/0.59 % Transform :cnf
% 0.53/0.59 % Format :tptp:raw
% 0.53/0.59 % Command :java -jar mcs_scs.jar %d %s
% 0.53/0.59
% 0.53/0.59 % Result :Theorem 0.000000s
% 0.53/0.59 % Output :CNFRefutation 0.000000s
% 0.53/0.59 %-------------------------------------------
% 0.53/0.59 %------------------------------------------------------------------------------
% 0.53/0.59 % File : SET979+1 : TPTP v8.1.2. Released v3.2.0.
% 0.53/0.59 % Domain : Set theory
% 0.53/0.59 % Problem : Basic properties of sets, theorem 132
% 0.53/0.59 % Version : [Urb06] axioms : Especial.
% 0.53/0.59 % English :
% 0.53/0.59
% 0.53/0.59 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.53/0.59 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.53/0.59 % Source : [Urb06]
% 0.53/0.59 % Names : zfmisc_1__t132_zfmisc_1 [Urb06]
% 0.53/0.59
% 0.53/0.59 % Status : Theorem
% 0.53/0.59 % Rating : 0.14 v8.1.0, 0.19 v7.5.0, 0.22 v7.4.0, 0.13 v7.3.0, 0.10 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.12 v6.2.0, 0.20 v6.0.0, 0.13 v5.5.0, 0.19 v5.4.0, 0.21 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.12 v4.1.0, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.07 v3.2.0
% 0.53/0.59 % Syntax : Number of formulae : 10 ( 6 unt; 0 def)
% 0.53/0.59 % Number of atoms : 14 ( 8 equ)
% 0.53/0.59 % Maximal formula atoms : 2 ( 1 avg)
% 0.53/0.59 % Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% 0.53/0.59 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.53/0.59 % Maximal formula depth : 5 ( 4 avg)
% 0.53/0.59 % Maximal term depth : 4 ( 2 avg)
% 0.53/0.59 % Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% 0.53/0.59 % Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% 0.53/0.59 % Number of variables : 20 ( 18 !; 2 ?)
% 0.53/0.59 % SPC : FOF_THM_RFO_SEQ
% 0.53/0.59
% 0.53/0.59 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.53/0.59 % library, www.mizar.org
% 0.53/0.59 %------------------------------------------------------------------------------
% 0.53/0.59 fof(commutativity_k2_tarski,axiom,
% 0.53/0.59 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 0.53/0.59
% 0.53/0.59 fof(commutativity_k2_xboole_0,axiom,
% 0.53/0.59 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.53/0.59
% 0.53/0.59 fof(fc2_xboole_0,axiom,
% 0.53/0.59 ! [A,B] :
% 0.53/0.59 ( ~ empty(A)
% 0.53/0.59 => ~ empty(set_union2(A,B)) ) ).
% 0.53/0.59
% 0.53/0.59 fof(fc3_xboole_0,axiom,
% 0.53/0.59 ! [A,B] :
% 0.53/0.59 ( ~ empty(A)
% 0.53/0.59 => ~ empty(set_union2(B,A)) ) ).
% 0.53/0.59
% 0.53/0.59 fof(idempotence_k2_xboole_0,axiom,
% 0.53/0.59 ! [A,B] : set_union2(A,A) = A ).
% 0.53/0.59
% 0.53/0.59 fof(rc1_xboole_0,axiom,
% 0.53/0.59 ? [A] : empty(A) ).
% 0.53/0.59
% 0.53/0.59 fof(rc2_xboole_0,axiom,
% 0.53/0.59 ? [A] : ~ empty(A) ).
% 0.53/0.59
% 0.53/0.59 fof(t120_zfmisc_1,axiom,
% 0.53/0.59 ! [A,B,C] :
% 0.53/0.59 ( cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C))
% 0.53/0.59 & cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) ) ).
% 0.53/0.59
% 0.53/0.59 fof(t132_zfmisc_1,conjecture,
% 0.53/0.59 ! [A,B,C] :
% 0.53/0.59 ( cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C))
% 0.53/0.59 & cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))) ) ).
% 0.53/0.59
% 0.53/0.59 fof(t41_enumset1,axiom,
% 0.53/0.59 ! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)) ).
% 0.53/0.59
% 0.53/0.59 %------------------------------------------------------------------------------
% 0.53/0.59 %-------------------------------------------
% 0.53/0.59 % Proof found
% 0.53/0.59 % SZS status Theorem for theBenchmark
% 0.53/0.59 % SZS output start Proof
% 0.53/0.59 %ClaNum:19(EqnAxiom:9)
% 0.53/0.59 %VarNum:27(SingletonVarNum:13)
% 0.53/0.59 %MaxLitNum:2
% 0.53/0.59 %MaxfuncDepth:3
% 0.53/0.59 %SharedTerms:20
% 0.53/0.59 %goalClause: 19
% 0.53/0.59 [10]P1(a1)
% 0.53/0.59 [16]~P1(a4)
% 0.53/0.59 [11]E(f3(x111,x111),x111)
% 0.53/0.59 [12]E(f3(x121,x122),f3(x122,x121))
% 0.53/0.59 [14]E(f3(f2(x141,x142),f2(x141,x143)),f2(x141,f3(x142,x143)))
% 0.53/0.59 [15]E(f3(f2(x151,x152),f2(x153,x152)),f2(f3(x151,x153),x152))
% 0.53/0.59 [19]~E(f3(f2(f8(a6),a5),f2(f8(a7),a5)),f2(f3(f8(a6),f8(a7)),a5))+~E(f3(f2(a5,f8(a6)),f2(a5,f8(a7))),f2(a5,f3(f8(a6),f8(a7))))
% 0.53/0.59 [17]P1(x171)+~P1(f3(x172,x171))
% 0.53/0.59 [18]P1(x181)+~P1(f3(x181,x182))
% 0.53/0.59 %EqnAxiom
% 0.53/0.59 [1]E(x11,x11)
% 0.53/0.59 [2]E(x22,x21)+~E(x21,x22)
% 0.53/0.59 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.53/0.60 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.53/0.60 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.53/0.60 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63))
% 0.53/0.60 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72))
% 0.53/0.60 [8]~E(x81,x82)+E(f8(x81),f8(x82))
% 0.53/0.60 [9]~P1(x91)+P1(x92)+~E(x91,x92)
% 0.53/0.60
% 0.53/0.60 %-------------------------------------------
% 0.53/0.60 cnf(20,plain,
% 0.53/0.60 ($false),
% 0.53/0.60 inference(scs_inference,[],[15,14,19]),
% 0.53/0.60 ['proof']).
% 0.53/0.60 % SZS output end Proof
% 0.53/0.60 % Total time :0.000000s
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