TSTP Solution File: SET882+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET882+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 : n032.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 14:31:33 EDT 2023
% Result : Theorem 1.89s 1.99s
% Output : CNFRefutation 1.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET882+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.10/0.32 % Computer : n032.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat Aug 26 16:17:28 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.16/0.55 start to proof:theBenchmark
% 1.89/1.98 %-------------------------------------------
% 1.89/1.98 % File :CSE---1.6
% 1.89/1.98 % Problem :theBenchmark
% 1.89/1.98 % Transform :cnf
% 1.89/1.98 % Format :tptp:raw
% 1.89/1.98 % Command :java -jar mcs_scs.jar %d %s
% 1.89/1.98
% 1.89/1.98 % Result :Theorem 1.370000s
% 1.89/1.98 % Output :CNFRefutation 1.370000s
% 1.89/1.98 %-------------------------------------------
% 1.89/1.99 %------------------------------------------------------------------------------
% 1.89/1.99 % File : SET882+1 : TPTP v8.1.2. Released v3.2.0.
% 1.89/1.99 % Domain : Set theory
% 1.89/1.99 % Problem : A != B => diff(unordered_pair(A,B),singleton(B)) = singleton(A)
% 1.89/1.99 % Version : [Urb06] axioms : Especial.
% 1.89/1.99 % English :
% 1.89/1.99
% 1.89/1.99 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 1.89/1.99 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 1.89/1.99 % Source : [Urb06]
% 1.89/1.99 % Names : zfmisc_1__t23_zfmisc_1 [Urb06]
% 1.89/1.99
% 1.89/1.99 % Status : Theorem
% 1.89/1.99 % Rating : 0.14 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.2.0, 0.28 v6.1.0, 0.27 v6.0.0, 0.22 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.26 v5.2.0, 0.00 v5.0.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.21 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.21 v3.2.0
% 1.89/1.99 % Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% 1.89/1.99 % Number of atoms : 14 ( 7 equ)
% 1.89/1.99 % Maximal formula atoms : 4 ( 2 avg)
% 1.89/1.99 % Number of connectives : 11 ( 4 ~; 1 |; 1 &)
% 1.89/1.99 % ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% 1.89/1.99 % Maximal formula depth : 7 ( 4 avg)
% 1.89/1.99 % Maximal term depth : 3 ( 1 avg)
% 1.89/1.99 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 1.89/1.99 % Number of functors : 3 ( 3 usr; 0 con; 1-2 aty)
% 1.89/1.99 % Number of variables : 14 ( 12 !; 2 ?)
% 1.89/1.99 % SPC : FOF_THM_RFO_SEQ
% 1.89/1.99
% 1.89/1.99 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 1.89/1.99 % library, www.mizar.org
% 1.89/1.99 %------------------------------------------------------------------------------
% 1.89/1.99 fof(antisymmetry_r2_hidden,axiom,
% 1.89/1.99 ! [A,B] :
% 1.89/1.99 ( in(A,B)
% 1.89/1.99 => ~ in(B,A) ) ).
% 1.89/1.99
% 1.89/1.99 fof(commutativity_k2_tarski,axiom,
% 1.89/1.99 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 1.89/1.99
% 1.89/1.99 fof(d1_tarski,axiom,
% 1.89/1.99 ! [A,B] :
% 1.89/1.99 ( B = singleton(A)
% 1.89/1.99 <=> ! [C] :
% 1.89/1.99 ( in(C,B)
% 1.89/1.99 <=> C = A ) ) ).
% 1.89/1.99
% 1.89/1.99 fof(l39_zfmisc_1,axiom,
% 1.89/1.99 ! [A,B,C] :
% 1.89/1.99 ( set_difference(unordered_pair(A,B),C) = singleton(A)
% 1.89/1.99 <=> ( ~ in(A,C)
% 1.89/1.99 & ( in(B,C)
% 1.89/1.99 | A = B ) ) ) ).
% 1.89/1.99
% 1.89/1.99 fof(rc1_xboole_0,axiom,
% 1.89/1.99 ? [A] : empty(A) ).
% 1.89/1.99
% 1.89/1.99 fof(rc2_xboole_0,axiom,
% 1.89/1.99 ? [A] : ~ empty(A) ).
% 1.89/1.99
% 1.89/1.99 fof(t23_zfmisc_1,conjecture,
% 1.89/1.99 ! [A,B] :
% 1.89/1.99 ( A != B
% 1.89/1.99 => set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ) ).
% 1.89/1.99
% 1.89/1.99 %------------------------------------------------------------------------------
% 1.89/1.99 %-------------------------------------------
% 1.89/1.99 % Proof found
% 1.89/1.99 % SZS status Theorem for theBenchmark
% 1.89/1.99 % SZS output start Proof
% 1.89/1.99 %ClaNum:27(EqnAxiom:13)
% 1.89/1.99 %VarNum:66(SingletonVarNum:26)
% 1.89/1.99 %MaxLitNum:3
% 1.89/1.99 %MaxfuncDepth:2
% 1.89/1.99 %SharedTerms:12
% 1.89/1.99 %goalClause: 16 18
% 1.89/1.99 %singleGoalClaCount:2
% 1.89/1.99 [14]P1(a1)
% 1.89/1.99 [16]~E(a4,a6)
% 1.89/1.99 [17]~P1(a5)
% 1.89/1.99 [18]~E(f8(f3(a4,a6),f7(a6)),f7(a4))
% 1.89/1.99 [15]E(f3(x151,x152),f3(x152,x151))
% 1.89/1.99 [21]~P2(x212,x211)+~P2(x211,x212)
% 1.89/1.99 [26]~P2(x261,x263)+~E(f8(f3(x261,x262),x263),f7(x261))
% 1.89/1.99 [22]E(f2(x222,x221),x222)+P2(f2(x222,x221),x221)+E(x221,f7(x222))
% 1.89/1.99 [27]~E(f2(x272,x271),x272)+~P2(f2(x272,x271),x271)+E(x271,f7(x272))
% 1.89/1.99 [19]P2(x191,x192)+~E(x191,x193)+~E(x192,f7(x193))
% 1.89/1.99 [20]~P2(x201,x203)+E(x201,x202)+~E(x203,f7(x202))
% 1.89/1.99 [23]P2(x231,x233)+~E(x231,x232)+E(f8(f3(x231,x232),x233),f7(x231))
% 1.89/1.99 [24]P2(x241,x243)+~P2(x242,x243)+E(f8(f3(x241,x242),x243),f7(x241))
% 1.89/1.99 [25]E(x251,x252)+P2(x251,x253)+~E(f8(f3(x252,x251),x253),f7(x252))
% 1.89/1.99 %EqnAxiom
% 1.89/1.99 [1]E(x11,x11)
% 1.89/1.99 [2]E(x22,x21)+~E(x21,x22)
% 1.89/1.99 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.89/1.99 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 1.89/1.99 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 1.89/1.99 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63))
% 1.89/1.99 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72))
% 1.89/1.99 [8]~E(x81,x82)+E(f7(x81),f7(x82))
% 1.89/1.99 [9]~E(x91,x92)+E(f8(x91,x93),f8(x92,x93))
% 1.89/1.99 [10]~E(x101,x102)+E(f8(x103,x101),f8(x103,x102))
% 1.89/1.99 [11]~P1(x111)+P1(x112)+~E(x111,x112)
% 1.89/1.99 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 1.89/1.99 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 1.89/1.99
% 1.89/1.99 %-------------------------------------------
% 1.89/2.00 cnf(28,plain,
% 1.89/2.00 (~E(a6,a4)),
% 1.89/2.00 inference(scs_inference,[],[16,2])).
% 1.89/2.00 cnf(30,plain,
% 1.89/2.00 (E(f8(f3(x301,x302),x303),f8(f3(x302,x301),x303))),
% 1.89/2.00 inference(scs_inference,[],[16,15,2,10,9])).
% 1.89/2.00 cnf(31,plain,
% 1.89/2.00 (E(f7(f3(x311,x312)),f7(f3(x312,x311)))),
% 1.89/2.00 inference(scs_inference,[],[16,15,2,10,9,8])).
% 1.89/2.00 cnf(36,plain,
% 1.89/2.00 (~E(a1,a5)),
% 1.89/2.00 inference(scs_inference,[],[16,14,17,15,2,10,9,8,7,6,5,4,11])).
% 1.89/2.00 cnf(46,plain,
% 1.89/2.00 (E(f7(f3(x461,x462)),f7(f3(x462,x461)))),
% 1.89/2.00 inference(rename_variables,[],[31])).
% 1.89/2.00 cnf(51,plain,
% 1.89/2.00 (P2(a4,x511)+~E(f8(f3(a6,a4),x511),f7(a6))),
% 1.89/2.00 inference(scs_inference,[],[16,15,31,46,19,13,21,25])).
% 1.89/2.00 cnf(60,plain,
% 1.89/2.00 (~E(a5,a1)),
% 1.89/2.00 inference(scs_inference,[],[36,2])).
% 1.89/2.00 cnf(66,plain,
% 1.89/2.00 (~P2(a6,x661)+~E(x661,f7(a4))),
% 1.89/2.00 inference(scs_inference,[],[28,30,11,20])).
% 1.89/2.00 cnf(69,plain,
% 1.89/2.00 (~P2(a6,f7(a4))),
% 1.89/2.00 inference(equality_inference,[],[66])).
% 1.89/2.00 cnf(71,plain,
% 1.89/2.00 (~E(f8(f3(a4,a6),f7(a4)),f7(a4))),
% 1.89/2.00 inference(scs_inference,[],[28,69,25])).
% 1.89/2.00 cnf(80,plain,
% 1.89/2.00 (~E(a6,x801)+E(f8(f3(a6,x801),f7(a4)),f7(a6))),
% 1.89/2.00 inference(scs_inference,[],[69,23])).
% 1.89/2.00 cnf(86,plain,
% 1.89/2.00 (E(f8(f3(a6,a6),f7(a4)),f7(a6))),
% 1.89/2.00 inference(equality_inference,[],[80])).
% 1.89/2.00 cnf(88,plain,
% 1.89/2.00 (~P2(a4,f8(f3(a6,a6),f7(a4)))),
% 1.89/2.00 inference(scs_inference,[],[86,16,20])).
% 1.89/2.00 cnf(90,plain,
% 1.89/2.00 (E(f7(a6),f8(f3(a6,a6),f7(a4)))),
% 1.89/2.00 inference(scs_inference,[],[86,16,20,2])).
% 1.89/2.00 cnf(91,plain,
% 1.89/2.00 (P2(f8(f3(a6,a6),f7(a4)),x911)+~E(x911,f7(f7(a6)))),
% 1.89/2.00 inference(scs_inference,[],[86,16,20,2,19])).
% 1.89/2.00 cnf(94,plain,
% 1.89/2.00 (P2(f8(f3(a6,a6),f7(a4)),f7(f7(a6)))),
% 1.89/2.00 inference(equality_inference,[],[91])).
% 1.89/2.00 cnf(96,plain,
% 1.89/2.00 (~P2(f7(f7(a6)),f8(f3(a6,a6),f7(a4)))),
% 1.89/2.00 inference(scs_inference,[],[94,21])).
% 1.89/2.00 cnf(98,plain,
% 1.89/2.00 (~P2(a4,f7(a6))),
% 1.89/2.00 inference(scs_inference,[],[94,90,88,21,13])).
% 1.89/2.00 cnf(99,plain,
% 1.89/2.00 (~E(f8(f3(a6,a4),f7(a6)),f7(a6))),
% 1.89/2.00 inference(scs_inference,[],[94,90,88,21,13,51])).
% 1.89/2.00 cnf(101,plain,
% 1.89/2.00 (~P2(a6,f7(a6))),
% 1.89/2.00 inference(scs_inference,[],[94,90,88,18,21,13,51,24])).
% 1.89/2.00 cnf(103,plain,
% 1.89/2.00 (~E(a6,x1031)+~E(f7(a4),f7(x1031))),
% 1.89/2.00 inference(scs_inference,[],[94,90,88,18,69,21,13,51,24,19])).
% 1.89/2.00 cnf(109,plain,
% 1.89/2.00 (~E(f7(f7(a6)),a6)),
% 1.89/2.00 inference(scs_inference,[],[96,86,19])).
% 1.89/2.00 cnf(111,plain,
% 1.89/2.00 (~P2(f8(f3(a6,a4),f7(a6)),x1111)+~E(x1111,f7(f7(a6)))),
% 1.89/2.00 inference(scs_inference,[],[96,99,86,19,20])).
% 1.89/2.00 cnf(114,plain,
% 1.89/2.00 (~P2(f8(f3(a6,a4),f7(a6)),f7(f7(a6)))),
% 1.89/2.00 inference(equality_inference,[],[111])).
% 1.89/2.00 cnf(118,plain,
% 1.89/2.00 (~P2(a6,f8(f3(a6,a6),f7(a4)))),
% 1.89/2.00 inference(scs_inference,[],[114,98,101,94,86,12,19,13])).
% 1.89/2.00 cnf(119,plain,
% 1.89/2.00 (P2(a1,x1191)+~E(f8(f3(a5,a1),x1191),f7(a5))),
% 1.89/2.00 inference(scs_inference,[],[114,98,101,36,94,86,12,19,13,25])).
% 1.89/2.00 cnf(134,plain,
% 1.89/2.00 (~P2(a1,x1341)+~E(x1341,f7(a5))),
% 1.89/2.00 inference(scs_inference,[],[36,20])).
% 1.89/2.00 cnf(139,plain,
% 1.89/2.00 (~P2(a1,f7(a5))),
% 1.89/2.00 inference(equality_inference,[],[134])).
% 1.89/2.00 cnf(142,plain,
% 1.89/2.00 (~E(f8(f3(a5,a1),f7(a5)),f7(a5))),
% 1.89/2.00 inference(scs_inference,[],[139,119])).
% 1.89/2.00 cnf(145,plain,
% 1.89/2.00 (~E(a1,x1451)+E(f8(f3(a1,x1451),f7(a5)),f7(a1))),
% 1.89/2.00 inference(scs_inference,[],[139,118,86,119,19,23])).
% 1.89/2.00 cnf(150,plain,
% 1.89/2.00 (E(f8(f3(a1,a1),f7(a5)),f7(a1))),
% 1.89/2.00 inference(equality_inference,[],[145])).
% 1.89/2.00 cnf(151,plain,
% 1.89/2.00 (E(f7(a1),f8(f3(a1,a1),f7(a5)))),
% 1.89/2.00 inference(scs_inference,[],[150,2])).
% 1.89/2.00 cnf(152,plain,
% 1.89/2.00 (P2(f7(a6),f7(f7(a6)))),
% 1.89/2.00 inference(scs_inference,[],[150,94,86,2,12])).
% 1.89/2.00 cnf(153,plain,
% 1.89/2.00 (~P2(a5,f8(f3(a1,a1),f7(a5)))),
% 1.89/2.00 inference(scs_inference,[],[150,60,94,86,2,12,20])).
% 1.89/2.00 cnf(155,plain,
% 1.89/2.00 (P2(f8(f3(a1,a1),f7(a5)),x1551)+~E(x1551,f7(f7(a1)))),
% 1.89/2.00 inference(scs_inference,[],[150,60,94,86,2,12,20,19])).
% 1.89/2.00 cnf(158,plain,
% 1.89/2.00 (P2(f8(f3(a1,a1),f7(a5)),f7(f7(a1)))),
% 1.89/2.00 inference(equality_inference,[],[155])).
% 1.89/2.00 cnf(163,plain,
% 1.89/2.00 (~P2(a5,f7(a1))),
% 1.89/2.00 inference(scs_inference,[],[158,153,151,109,150,21,2,12,13])).
% 1.89/2.00 cnf(241,plain,
% 1.89/2.00 (~E(f7(x2411),f7(a4))+~E(a6,x2411)),
% 1.89/2.00 inference(scs_inference,[],[103,2])).
% 1.89/2.00 cnf(243,plain,
% 1.89/2.00 (~E(a5,x2431)+E(f8(f3(a5,x2431),f7(a1)),f7(a5))),
% 1.89/2.00 inference(scs_inference,[],[163,118,86,19,23])).
% 1.89/2.00 cnf(246,plain,
% 1.89/2.00 (E(f8(f3(a5,a5),f7(a1)),f7(a5))),
% 1.89/2.00 inference(equality_inference,[],[243])).
% 1.89/2.00 cnf(251,plain,
% 1.89/2.00 (P2(f8(f3(a5,a5),f7(a1)),x2511)+~E(x2511,f7(f7(a5)))),
% 1.89/2.00 inference(scs_inference,[],[246,134,2,19])).
% 1.89/2.00 cnf(253,plain,
% 1.89/2.00 (P2(f8(f3(a5,a5),f7(a1)),f7(f7(a5)))),
% 1.89/2.00 inference(equality_inference,[],[251])).
% 1.89/2.00 cnf(254,plain,
% 1.89/2.00 (~E(f7(f7(a6)),f7(f7(a4)))),
% 1.89/2.00 inference(scs_inference,[],[152,241,20])).
% 1.89/2.00 cnf(259,plain,
% 1.89/2.00 (P2(f7(a5),f7(f7(a5)))),
% 1.89/2.00 inference(scs_inference,[],[71,253,254,246,21,8,2,12])).
% 1.89/2.00 cnf(292,plain,
% 1.89/2.00 (~E(f8(f3(a5,a1),f7(a5)),f8(f3(a5,a5),f7(a1)))),
% 1.89/2.00 inference(scs_inference,[],[142,246,3])).
% 1.89/2.00 cnf(298,plain,
% 1.89/2.00 (~P2(f8(f3(a5,a1),f7(a5)),x2981)+~E(x2981,f7(f7(a5)))),
% 1.89/2.00 inference(scs_inference,[],[292,142,30,3,20])).
% 1.89/2.00 cnf(301,plain,
% 1.89/2.00 (~P2(f8(f3(a5,a1),f7(a5)),f7(f7(a5)))),
% 1.89/2.00 inference(equality_inference,[],[298])).
% 1.89/2.00 cnf(312,plain,
% 1.89/2.00 (~P2(f8(f3(a1,a5),f7(a5)),f7(f7(a5)))),
% 1.89/2.00 inference(scs_inference,[],[301,30,12])).
% 1.89/2.00 cnf(326,plain,
% 1.89/2.00 (~E(a6,x3261)+~E(f7(a6),f7(x3261))),
% 1.89/2.00 inference(scs_inference,[],[101,312,151,259,12,11,19])).
% 1.89/2.00 cnf(331,plain,
% 1.89/2.00 ($false),
% 1.89/2.00 inference(scs_inference,[],[90,86,326,3]),
% 1.89/2.00 ['proof']).
% 1.89/2.00 % SZS output end Proof
% 1.89/2.00 % Total time :1.370000s
%------------------------------------------------------------------------------