TSTP Solution File: SEU165+3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU165+3 : 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 : n031.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 16:18:03 EDT 2023
% Result : Theorem 116.11s 116.15s
% Output : CNFRefutation 116.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU165+3 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 22:36:05 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof:theBenchmark
% 116.11/116.14 %-------------------------------------------
% 116.11/116.14 % File :CSE---1.6
% 116.11/116.14 % Problem :theBenchmark
% 116.11/116.14 % Transform :cnf
% 116.11/116.14 % Format :tptp:raw
% 116.11/116.14 % Command :java -jar mcs_scs.jar %d %s
% 116.11/116.14
% 116.11/116.14 % Result :Theorem 115.520000s
% 116.11/116.14 % Output :CNFRefutation 115.520000s
% 116.11/116.14 %-------------------------------------------
% 116.11/116.15 %------------------------------------------------------------------------------
% 116.11/116.15 % File : SEU165+3 : TPTP v8.1.2. Released v3.2.0.
% 116.11/116.15 % Domain : Set theory
% 116.11/116.15 % Problem : Basic properties of sets, theorem 106
% 116.11/116.15 % Version : [Urb06] axioms : Especial.
% 116.11/116.15 % English :
% 116.11/116.15
% 116.11/116.15 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 116.11/116.15 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 116.11/116.15 % Source : [Urb06]
% 116.11/116.15 % Names : zfmisc_1__t106_zfmisc_1 [Urb06]
% 116.11/116.15
% 116.11/116.15 % Status : Theorem
% 116.11/116.15 % Rating : 0.06 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.07 v6.0.0, 0.04 v5.5.0, 0.00 v5.4.0, 0.04 v5.3.0, 0.11 v5.2.0, 0.00 v4.1.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.00 v3.4.0, 0.05 v3.3.0, 0.07 v3.2.0
% 116.11/116.15 % Syntax : Number of formulae : 8 ( 5 unt; 0 def)
% 116.11/116.15 % Number of atoms : 13 ( 2 equ)
% 116.11/116.15 % Maximal formula atoms : 3 ( 1 avg)
% 116.11/116.15 % Number of connectives : 8 ( 3 ~; 0 |; 2 &)
% 116.11/116.15 % ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% 116.11/116.15 % Maximal formula depth : 7 ( 4 avg)
% 116.11/116.15 % Maximal term depth : 3 ( 1 avg)
% 116.11/116.15 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 116.11/116.15 % Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% 116.11/116.15 % Number of variables : 18 ( 16 !; 2 ?)
% 116.11/116.15 % SPC : FOF_THM_RFO_SEQ
% 116.11/116.15
% 116.11/116.15 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 116.11/116.15 % library, www.mizar.org
% 116.11/116.15 %------------------------------------------------------------------------------
% 116.11/116.15 fof(commutativity_k2_tarski,axiom,
% 116.11/116.15 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 116.11/116.15
% 116.11/116.15 fof(antisymmetry_r2_hidden,axiom,
% 116.11/116.15 ! [A,B] :
% 116.11/116.15 ( in(A,B)
% 116.11/116.15 => ~ in(B,A) ) ).
% 116.11/116.15
% 116.11/116.15 fof(fc1_zfmisc_1,axiom,
% 116.11/116.15 ! [A,B] : ~ empty(ordered_pair(A,B)) ).
% 116.11/116.15
% 116.11/116.15 fof(rc1_xboole_0,axiom,
% 116.11/116.15 ? [A] : empty(A) ).
% 116.11/116.15
% 116.11/116.15 fof(rc2_xboole_0,axiom,
% 116.11/116.15 ? [A] : ~ empty(A) ).
% 116.11/116.15
% 116.11/116.15 fof(d5_tarski,axiom,
% 116.11/116.15 ! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ).
% 116.11/116.15
% 116.11/116.15 fof(t106_zfmisc_1,conjecture,
% 116.11/116.15 ! [A,B,C,D] :
% 116.11/116.15 ( in(ordered_pair(A,B),cartesian_product2(C,D))
% 116.11/116.15 <=> ( in(A,C)
% 116.11/116.15 & in(B,D) ) ) ).
% 116.11/116.15
% 116.11/116.15 fof(l55_zfmisc_1,axiom,
% 116.11/116.15 ! [A,B,C,D] :
% 116.11/116.15 ( in(ordered_pair(A,B),cartesian_product2(C,D))
% 116.11/116.15 <=> ( in(A,C)
% 116.11/116.15 & in(B,D) ) ) ).
% 116.11/116.15
% 116.11/116.15 %------------------------------------------------------------------------------
% 116.11/116.15 %-------------------------------------------
% 116.11/116.15 % Proof found
% 116.11/116.15 % SZS status Theorem for theBenchmark
% 116.11/116.15 % SZS output start Proof
% 116.11/116.16 %ClaNum:22(EqnAxiom:11)
% 116.11/116.16 %VarNum:34(SingletonVarNum:18)
% 116.11/116.16 %MaxLitNum:3
% 116.11/116.16 %MaxfuncDepth:2
% 116.11/116.16 %SharedTerms:18
% 116.11/116.16 %goalClause: 17 18 20
% 116.11/116.16 [12]P1(a1)
% 116.11/116.16 [14]~P1(a4)
% 116.11/116.16 [13]E(f3(x131,x132),f3(x132,x131))
% 116.11/116.16 [15]~P1(f3(f3(x151,x152),f5(x151)))
% 116.11/116.16 [17]P2(a6,a7)+P2(f3(f3(a6,a8),f5(a6)),f2(a7,a9))
% 116.11/116.16 [18]P2(a8,a9)+P2(f3(f3(a6,a8),f5(a6)),f2(a7,a9))
% 116.11/116.16 [16]~P2(x162,x161)+~P2(x161,x162)
% 116.11/116.16 [21]P2(x211,x212)+~P2(f3(f3(x213,x211),f5(x213)),f2(x214,x212))
% 116.11/116.16 [22]P2(x221,x222)+~P2(f3(f3(x221,x223),f5(x221)),f2(x222,x224))
% 116.11/116.16 [20]~P2(a6,a7)+~P2(a8,a9)+~P2(f3(f3(a6,a8),f5(a6)),f2(a7,a9))
% 116.11/116.16 [19]~P2(x192,x194)+~P2(x191,x193)+P2(f3(f3(x191,x192),f5(x191)),f2(x193,x194))
% 116.11/116.16 %EqnAxiom
% 116.11/116.16 [1]E(x11,x11)
% 116.11/116.16 [2]E(x22,x21)+~E(x21,x22)
% 116.11/116.16 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 116.11/116.16 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 116.11/116.16 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 116.11/116.16 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63))
% 116.11/116.16 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72))
% 116.11/116.16 [8]~E(x81,x82)+E(f5(x81),f5(x82))
% 116.11/116.16 [9]~P1(x91)+P1(x92)+~E(x91,x92)
% 116.11/116.16 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103)
% 116.11/116.16 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111)
% 116.11/116.16
% 116.11/116.16 %-------------------------------------------
% 116.11/116.16 cnf(114,plain,
% 116.11/116.16 (~P2(f3(x1141,x1142),x1143)+P2(f3(x1142,x1141),x1143)),
% 116.11/116.16 inference(scs_inference,[],[13,10])).
% 116.11/116.16 cnf(188,plain,
% 116.11/116.16 (~P2(f2(x1881,x1882),f3(f3(x1883,x1884),f5(x1883)))+~P2(x1884,x1882)+~P2(x1883,x1881)),
% 116.11/116.16 inference(scs_inference,[],[16,19])).
% 116.11/116.16 cnf(463,plain,
% 116.11/116.16 (P2(f3(f5(x4631),f3(x4631,x4632)),f2(x4633,x4634))+~P2(x4632,x4634)+~P2(x4631,x4633)),
% 116.11/116.16 inference(scs_inference,[],[114,19])).
% 116.11/116.16 cnf(1006,plain,
% 116.11/116.16 (~P2(f3(f5(x10061),f3(x10061,x10062)),f2(x10063,x10064))+P2(x10062,x10064)),
% 116.11/116.16 inference(scs_inference,[],[114,21])).
% 116.11/116.16 cnf(1007,plain,
% 116.11/116.16 (~P2(x10071,x10072)+~P2(f3(f5(x10073),f3(x10073,x10072)),f2(x10074,x10071))),
% 116.11/116.16 inference(scs_inference,[],[1006,16])).
% 116.11/116.16 cnf(1137,plain,
% 116.11/116.16 (~P2(f3(f5(x11371),f3(x11371,x11372)),f2(x11373,x11374))+P2(x11371,x11373)),
% 116.11/116.16 inference(scs_inference,[],[114,22])).
% 116.11/116.16 cnf(1138,plain,
% 116.11/116.17 (~P2(x11381,x11382)+~P2(f3(f5(x11382),f3(x11382,x11383)),f2(x11381,x11384))),
% 116.11/116.17 inference(scs_inference,[],[1137,16])).
% 116.11/116.17 cnf(1986,plain,
% 116.11/116.17 (P2(a6,a7)),
% 116.11/116.17 inference(scs_inference,[],[17,22])).
% 116.11/116.17 cnf(1987,plain,
% 116.11/116.17 (~P2(a8,a9)+~P2(f3(f3(a6,a8),f5(a6)),f2(a7,a9))),
% 116.11/116.17 inference(scs_inference,[],[1986,20])).
% 116.11/116.17 cnf(2017,plain,
% 116.11/116.17 (~P2(f3(f3(x20171,a8),f5(x20171)),f2(x20172,a9))+~P2(f3(f3(a6,a8),f5(a6)),f2(a7,a9))),
% 116.11/116.17 inference(scs_inference,[],[1987,21])).
% 116.11/116.17 cnf(2081,plain,
% 116.11/116.17 (P2(a8,a9)),
% 116.11/116.17 inference(scs_inference,[],[2017,18])).
% 116.11/116.17 cnf(2097,plain,
% 116.11/116.17 (P2(f3(f5(a8),f3(a8,a8)),f2(a9,a9))),
% 116.11/116.17 inference(scs_inference,[],[2081,16,21,1007,1138,188,463])).
% 116.11/116.17 cnf(2280,plain,
% 116.11/116.17 (~P2(f3(f3(a6,a8),f5(a6)),f2(a7,a9))),
% 116.11/116.17 inference(scs_inference,[],[2097,114,2017])).
% 116.11/116.17 cnf(2559,plain,
% 116.11/116.17 ($false),
% 116.11/116.17 inference(scs_inference,[],[1986,2081,2280,19]),
% 116.11/116.17 ['proof']).
% 116.11/116.17 % SZS output end Proof
% 116.11/116.17 % Total time :115.520000s
%------------------------------------------------------------------------------