TSTP Solution File: SET954+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET954+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 : n022.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 14:31:48 EDT 2023
% Result : Theorem 0.21s 0.62s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET954+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 : n022.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 08:31:55 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.21/0.57 start to proof:theBenchmark
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 % File :CSE---1.6
% 0.21/0.62 % Problem :theBenchmark
% 0.21/0.62 % Transform :cnf
% 0.21/0.62 % Format :tptp:raw
% 0.21/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.62
% 0.21/0.62 % Result :Theorem 0.000000s
% 0.21/0.62 % Output :CNFRefutation 0.000000s
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 %------------------------------------------------------------------------------
% 0.21/0.62 % File : SET954+1 : TPTP v8.1.2. Released v3.2.0.
% 0.21/0.62 % Domain : Set theory
% 0.21/0.62 % Problem : in(o_pair(A,B),cart_prod(C,D)) => in(o_pair(B,A),cart_prod(D,C))
% 0.21/0.62 % Version : [Urb06] axioms : Especial.
% 0.21/0.62 % English :
% 0.21/0.62
% 0.21/0.62 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.21/0.62 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.21/0.62 % Source : [Urb06]
% 0.21/0.62 % Names : zfmisc_1__t107_zfmisc_1 [Urb06]
% 0.21/0.62
% 0.21/0.62 % Status : Theorem
% 0.21/0.62 % Rating : 0.06 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.12 v6.3.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 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, 0.10 v3.5.0, 0.11 v3.3.0, 0.07 v3.2.0
% 0.21/0.62 % Syntax : Number of formulae : 8 ( 5 unt; 0 def)
% 0.21/0.62 % Number of atoms : 12 ( 2 equ)
% 0.21/0.62 % Maximal formula atoms : 3 ( 1 avg)
% 0.21/0.62 % Number of connectives : 7 ( 3 ~; 0 |; 1 &)
% 0.21/0.62 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.21/0.62 % Maximal formula depth : 7 ( 4 avg)
% 0.21/0.62 % Maximal term depth : 3 ( 1 avg)
% 0.21/0.62 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.21/0.62 % Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% 0.21/0.62 % Number of variables : 18 ( 16 !; 2 ?)
% 0.21/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.62
% 0.21/0.62 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.21/0.62 % library, www.mizar.org
% 0.21/0.62 %------------------------------------------------------------------------------
% 0.21/0.62 fof(antisymmetry_r2_hidden,axiom,
% 0.21/0.62 ! [A,B] :
% 0.21/0.62 ( in(A,B)
% 0.21/0.62 => ~ in(B,A) ) ).
% 0.21/0.62
% 0.21/0.62 fof(commutativity_k2_tarski,axiom,
% 0.21/0.62 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 0.21/0.62
% 0.21/0.62 fof(d5_tarski,axiom,
% 0.21/0.62 ! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ).
% 0.21/0.62
% 0.21/0.62 fof(fc1_zfmisc_1,axiom,
% 0.21/0.62 ! [A,B] : ~ empty(ordered_pair(A,B)) ).
% 0.21/0.62
% 0.21/0.62 fof(l55_zfmisc_1,axiom,
% 0.21/0.62 ! [A,B,C,D] :
% 0.21/0.62 ( in(ordered_pair(A,B),cartesian_product2(C,D))
% 0.21/0.62 <=> ( in(A,C)
% 0.21/0.62 & in(B,D) ) ) ).
% 0.21/0.62
% 0.21/0.62 fof(rc1_xboole_0,axiom,
% 0.21/0.62 ? [A] : empty(A) ).
% 0.21/0.62
% 0.21/0.62 fof(rc2_xboole_0,axiom,
% 0.21/0.62 ? [A] : ~ empty(A) ).
% 0.21/0.62
% 0.21/0.62 fof(t107_zfmisc_1,conjecture,
% 0.21/0.62 ! [A,B,C,D] :
% 0.21/0.62 ( in(ordered_pair(A,B),cartesian_product2(C,D))
% 0.21/0.62 => in(ordered_pair(B,A),cartesian_product2(D,C)) ) ).
% 0.21/0.62
% 0.21/0.62 %------------------------------------------------------------------------------
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 % Proof found
% 0.21/0.62 % SZS status Theorem for theBenchmark
% 0.21/0.62 % SZS output start Proof
% 0.21/0.62 %ClaNum:21(EqnAxiom:11)
% 0.21/0.62 %VarNum:34(SingletonVarNum:18)
% 0.21/0.62 %MaxLitNum:3
% 0.21/0.62 %MaxfuncDepth:2
% 0.21/0.62 %SharedTerms:18
% 0.21/0.62 %goalClause: 14 17
% 0.21/0.62 %singleGoalClaCount:2
% 0.21/0.62 [12]P1(a1)
% 0.21/0.62 [15]~P1(a5)
% 0.21/0.62 [14]P2(f3(f3(a4,a6),f7(a4)),f2(a8,a9))
% 0.21/0.62 [17]~P2(f3(f3(a6,a4),f7(a6)),f2(a9,a8))
% 0.21/0.62 [13]E(f3(x131,x132),f3(x132,x131))
% 0.21/0.62 [16]~P1(f3(f3(x161,x162),f7(x161)))
% 0.21/0.62 [18]~P2(x182,x181)+~P2(x181,x182)
% 0.21/0.62 [20]P2(x201,x202)+~P2(f3(f3(x203,x201),f7(x203)),f2(x204,x202))
% 0.21/0.62 [21]P2(x211,x212)+~P2(f3(f3(x211,x213),f7(x211)),f2(x212,x214))
% 0.21/0.62 [19]~P2(x192,x194)+~P2(x191,x193)+P2(f3(f3(x191,x192),f7(x191)),f2(x193,x194))
% 0.21/0.62 %EqnAxiom
% 0.21/0.62 [1]E(x11,x11)
% 0.21/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.62 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.21/0.62 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.21/0.62 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63))
% 0.21/0.62 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72))
% 0.21/0.62 [8]~E(x81,x82)+E(f7(x81),f7(x82))
% 0.21/0.62 [9]~P1(x91)+P1(x92)+~E(x91,x92)
% 0.21/0.62 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103)
% 0.21/0.62 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111)
% 0.21/0.62
% 0.21/0.63 %-------------------------------------------
% 0.21/0.63 cnf(27,plain,
% 0.21/0.63 (E(f3(x271,x272),f3(x272,x271))),
% 0.21/0.63 inference(rename_variables,[],[13])).
% 0.21/0.63 cnf(30,plain,
% 0.21/0.63 ($false),
% 0.21/0.63 inference(scs_inference,[],[14,17,13,27,16,18,20,21,10,9,19]),
% 0.21/0.63 ['proof']).
% 0.21/0.63 % SZS output end Proof
% 0.21/0.63 % Total time :0.000000s
%------------------------------------------------------------------------------