TSTP Solution File: SET891+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET891+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 14:31:35 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET891+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/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 12:58:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.20/0.60 %-------------------------------------------
% 0.20/0.60 % File :CSE---1.6
% 0.20/0.60 % Problem :theBenchmark
% 0.20/0.60 % Transform :cnf
% 0.20/0.60 % Format :tptp:raw
% 0.20/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.60
% 0.20/0.60 % Result :Theorem 0.000000s
% 0.20/0.60 % Output :CNFRefutation 0.000000s
% 0.20/0.60 %-------------------------------------------
% 0.20/0.61 %------------------------------------------------------------------------------
% 0.20/0.61 % File : SET891+1 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.61 % Domain : Set theory
% 0.20/0.61 % Problem : union(uno_pair(singleton(A),singleton(B))) = uno_pair(A,B)
% 0.20/0.61 % Version : [Urb06] axioms : Especial.
% 0.20/0.61 % English :
% 0.20/0.61
% 0.20/0.61 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.20/0.61 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.20/0.61 % Source : [Urb06]
% 0.20/0.61 % Names : zfmisc_1__t32_zfmisc_1 [Urb06]
% 0.20/0.61
% 0.20/0.61 % Status : Theorem
% 0.20/0.61 % Rating : 0.06 v8.1.0, 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, 0.20 v6.0.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.12 v4.1.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.21 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.07 v3.2.0
% 0.20/0.61 % Syntax : Number of formulae : 10 ( 8 unt; 0 def)
% 0.20/0.61 % Number of atoms : 12 ( 6 equ)
% 0.20/0.61 % Maximal formula atoms : 2 ( 1 avg)
% 0.20/0.61 % Number of connectives : 7 ( 5 ~; 0 |; 0 &)
% 0.20/0.61 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.61 % Maximal formula depth : 5 ( 3 avg)
% 0.20/0.61 % Maximal term depth : 4 ( 1 avg)
% 0.20/0.61 % Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% 0.20/0.61 % Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% 0.20/0.61 % Number of variables : 18 ( 16 !; 2 ?)
% 0.20/0.61 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.61
% 0.20/0.61 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.20/0.61 % library, www.mizar.org
% 0.20/0.61 %------------------------------------------------------------------------------
% 0.20/0.61 fof(commutativity_k2_tarski,axiom,
% 0.20/0.61 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 0.20/0.61
% 0.20/0.61 fof(commutativity_k2_xboole_0,axiom,
% 0.20/0.61 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.20/0.61
% 0.20/0.61 fof(fc2_xboole_0,axiom,
% 0.20/0.61 ! [A,B] :
% 0.20/0.61 ( ~ empty(A)
% 0.20/0.61 => ~ empty(set_union2(A,B)) ) ).
% 0.20/0.61
% 0.20/0.61 fof(fc3_xboole_0,axiom,
% 0.20/0.61 ! [A,B] :
% 0.20/0.61 ( ~ empty(A)
% 0.20/0.61 => ~ empty(set_union2(B,A)) ) ).
% 0.20/0.61
% 0.20/0.61 fof(idempotence_k2_xboole_0,axiom,
% 0.20/0.61 ! [A,B] : set_union2(A,A) = A ).
% 0.20/0.61
% 0.20/0.61 fof(l52_zfmisc_1,axiom,
% 0.20/0.61 ! [A,B] : union(unordered_pair(A,B)) = set_union2(A,B) ).
% 0.20/0.61
% 0.20/0.61 fof(rc1_xboole_0,axiom,
% 0.20/0.61 ? [A] : empty(A) ).
% 0.20/0.61
% 0.20/0.61 fof(rc2_xboole_0,axiom,
% 0.20/0.61 ? [A] : ~ empty(A) ).
% 0.20/0.61
% 0.20/0.61 fof(t32_zfmisc_1,conjecture,
% 0.20/0.61 ! [A,B] : union(unordered_pair(singleton(A),singleton(B))) = unordered_pair(A,B) ).
% 0.20/0.61
% 0.20/0.61 fof(t41_enumset1,axiom,
% 0.20/0.61 ! [A,B] : unordered_pair(A,B) = set_union2(singleton(A),singleton(B)) ).
% 0.20/0.61
% 0.20/0.61 %------------------------------------------------------------------------------
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark
% 0.20/0.61 % SZS output start Proof
% 0.20/0.61 %ClaNum:17(EqnAxiom:8)
% 0.20/0.61 %VarNum:21(SingletonVarNum:11)
% 0.20/0.61 %MaxLitNum:2
% 0.20/0.61 %MaxfuncDepth:3
% 0.20/0.61 %SharedTerms:12
% 0.20/0.61 %goalClause: 15
% 0.20/0.61 %singleGoalClaCount:1
% 0.20/0.61 [9]P1(a1)
% 0.20/0.61 [14]~P1(a5)
% 0.20/0.61 [15]~E(f3(f2(f4(a6),f4(a7))),f2(a6,a7))
% 0.20/0.61 [11]E(f3(f2(x111,x111)),x111)
% 0.20/0.61 [10]E(f2(x101,x102),f2(x102,x101))
% 0.20/0.61 [12]E(f3(f2(x121,x122)),f3(f2(x122,x121)))
% 0.20/0.61 [13]E(f3(f2(f4(x131),f4(x132))),f2(x131,x132))
% 0.20/0.61 [16]P1(x161)+~P1(f3(f2(x162,x161)))
% 0.20/0.61 [17]P1(x171)+~P1(f3(f2(x171,x172)))
% 0.20/0.61 %EqnAxiom
% 0.20/0.61 [1]E(x11,x11)
% 0.20/0.61 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.61 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.20/0.61 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.20/0.61 [6]~E(x61,x62)+E(f3(x61),f3(x62))
% 0.20/0.61 [7]~E(x71,x72)+E(f4(x71),f4(x72))
% 0.20/0.61 [8]~P1(x81)+P1(x82)+~E(x81,x82)
% 0.20/0.61
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 cnf(18,plain,
% 0.20/0.61 ($false),
% 0.20/0.61 inference(scs_inference,[],[15,13]),
% 0.20/0.61 ['proof']).
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time :0.000000s
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