TSTP Solution File: SET929+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET929+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 : n026.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 14:31:45 EDT 2023
% Result : Theorem 82.29s 82.48s
% Output : CNFRefutation 82.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET929+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
% 0.14/0.34 % Computer : n026.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 : Sat Aug 26 09:39:18 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.59 start to proof:theBenchmark
% 82.29/82.46 %-------------------------------------------
% 82.29/82.46 % File :CSE---1.6
% 82.29/82.46 % Problem :theBenchmark
% 82.29/82.46 % Transform :cnf
% 82.29/82.46 % Format :tptp:raw
% 82.29/82.46 % Command :java -jar mcs_scs.jar %d %s
% 82.29/82.46
% 82.29/82.46 % Result :Theorem 81.790000s
% 82.29/82.46 % Output :CNFRefutation 81.790000s
% 82.29/82.46 %-------------------------------------------
% 82.29/82.48 %------------------------------------------------------------------------------
% 82.29/82.48 % File : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% 82.29/82.48 % Domain : Set theory
% 82.29/82.48 % Problem : diff(uno_pair(A,B),C) = empty <=> ( in(A,C) & in(B,C) )
% 82.29/82.48 % Version : [Urb06] axioms : Especial.
% 82.29/82.48 % English :
% 82.29/82.48
% 82.29/82.48 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 82.29/82.48 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 82.29/82.48 % Source : [Urb06]
% 82.29/82.48 % Names : zfmisc_1__t73_zfmisc_1 [Urb06]
% 82.29/82.48
% 82.29/82.48 % Status : Theorem
% 82.29/82.48 % Rating : 0.06 v7.4.0, 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.1.0, 0.07 v6.0.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.04 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.05 v3.3.0, 0.07 v3.2.0
% 82.29/82.48 % Syntax : Number of formulae : 9 ( 5 unt; 0 def)
% 82.29/82.48 % Number of atoms : 15 ( 3 equ)
% 82.29/82.48 % Maximal formula atoms : 3 ( 1 avg)
% 82.29/82.48 % Number of connectives : 8 ( 2 ~; 0 |; 2 &)
% 82.29/82.48 % ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% 82.29/82.48 % Maximal formula depth : 6 ( 4 avg)
% 82.29/82.48 % Maximal term depth : 3 ( 1 avg)
% 82.29/82.48 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 82.29/82.48 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 82.29/82.48 % Number of variables : 16 ( 14 !; 2 ?)
% 82.29/82.48 % SPC : FOF_THM_RFO_SEQ
% 82.29/82.48
% 82.29/82.48 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 82.29/82.48 % library, www.mizar.org
% 82.29/82.48 %------------------------------------------------------------------------------
% 82.29/82.48 fof(antisymmetry_r2_hidden,axiom,
% 82.29/82.48 ! [A,B] :
% 82.29/82.48 ( in(A,B)
% 82.29/82.48 => ~ in(B,A) ) ).
% 82.29/82.48
% 82.29/82.48 fof(commutativity_k2_tarski,axiom,
% 82.29/82.48 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 82.29/82.48
% 82.29/82.48 fof(fc1_xboole_0,axiom,
% 82.29/82.48 empty(empty_set) ).
% 82.29/82.48
% 82.29/82.48 fof(rc1_xboole_0,axiom,
% 82.29/82.48 ? [A] : empty(A) ).
% 82.29/82.48
% 82.29/82.48 fof(rc2_xboole_0,axiom,
% 82.29/82.48 ? [A] : ~ empty(A) ).
% 82.29/82.48
% 82.29/82.48 fof(reflexivity_r1_tarski,axiom,
% 82.29/82.48 ! [A,B] : subset(A,A) ).
% 82.29/82.48
% 82.29/82.48 fof(t37_xboole_1,axiom,
% 82.29/82.48 ! [A,B] :
% 82.29/82.48 ( set_difference(A,B) = empty_set
% 82.29/82.48 <=> subset(A,B) ) ).
% 82.29/82.48
% 82.29/82.48 fof(t38_zfmisc_1,axiom,
% 82.29/82.48 ! [A,B,C] :
% 82.29/82.48 ( subset(unordered_pair(A,B),C)
% 82.29/82.48 <=> ( in(A,C)
% 82.29/82.48 & in(B,C) ) ) ).
% 82.29/82.48
% 82.29/82.48 fof(t73_zfmisc_1,conjecture,
% 82.29/82.48 ! [A,B,C] :
% 82.29/82.48 ( set_difference(unordered_pair(A,B),C) = empty_set
% 82.29/82.48 <=> ( in(A,C)
% 82.29/82.48 & in(B,C) ) ) ).
% 82.29/82.48
% 82.29/82.48 %------------------------------------------------------------------------------
% 82.29/82.48 %-------------------------------------------
% 82.29/82.48 % Proof found
% 82.29/82.48 % SZS status Theorem for theBenchmark
% 82.29/82.48 % SZS output start Proof
% 82.29/82.49 %ClaNum:26(EqnAxiom:12)
% 82.29/82.49 %VarNum:35(SingletonVarNum:18)
% 82.29/82.49 %MaxLitNum:3
% 82.29/82.49 %MaxfuncDepth:2
% 82.29/82.49 %SharedTerms:17
% 82.29/82.49 %goalClause: 20 21 26
% 82.29/82.49 [13]P1(a1)
% 82.29/82.49 [14]P1(a2)
% 82.29/82.49 [17]~P1(a4)
% 82.29/82.49 [15]P2(x151,x151)
% 82.29/82.49 [16]E(f3(x161,x162),f3(x162,x161))
% 82.29/82.49 [20]P3(a6,a8)+E(f5(f3(a6,a7),a8),a1)
% 82.29/82.49 [21]P3(a7,a8)+E(f5(f3(a6,a7),a8),a1)
% 82.29/82.49 [22]~P3(x222,x221)+~P3(x221,x222)
% 82.29/82.49 [18]~P2(x181,x182)+E(f5(x181,x182),a1)
% 82.29/82.49 [19]P2(x191,x192)+~E(f5(x191,x192),a1)
% 82.29/82.49 [23]P3(x231,x232)+~P2(f3(x233,x231),x232)
% 82.29/82.49 [24]P3(x241,x242)+~P2(f3(x241,x243),x242)
% 82.29/82.49 [26]~P3(a6,a8)+~P3(a7,a8)+~E(f5(f3(a6,a7),a8),a1)
% 82.29/82.49 [25]~P3(x252,x253)+~P3(x251,x253)+P2(f3(x251,x252),x253)
% 82.29/82.49 %EqnAxiom
% 82.29/82.49 [1]E(x11,x11)
% 82.29/82.49 [2]E(x22,x21)+~E(x21,x22)
% 82.29/82.49 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 82.29/82.49 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 82.29/82.49 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 82.29/82.49 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 82.29/82.49 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 82.29/82.49 [8]~P1(x81)+P1(x82)+~E(x81,x82)
% 82.29/82.49 [9]P3(x92,x93)+~E(x91,x92)+~P3(x91,x93)
% 82.29/82.49 [10]P3(x103,x102)+~E(x101,x102)+~P3(x103,x101)
% 82.29/82.49 [11]P2(x112,x113)+~E(x111,x112)+~P2(x111,x113)
% 82.29/82.49 [12]P2(x123,x122)+~E(x121,x122)+~P2(x123,x121)
% 82.29/82.49
% 82.29/82.49 %-------------------------------------------
% 82.29/82.51 cnf(27,plain,
% 82.29/82.51 (P3(x271,f3(x271,x272))),
% 82.29/82.51 inference(scs_inference,[],[15,24])).
% 82.29/82.51 cnf(28,plain,
% 82.29/82.51 (P2(x281,x281)),
% 82.29/82.51 inference(rename_variables,[],[15])).
% 82.29/82.51 cnf(29,plain,
% 82.29/82.51 (P3(x291,f3(x292,x291))),
% 82.29/82.51 inference(scs_inference,[],[15,28,24,23])).
% 82.29/82.51 cnf(30,plain,
% 82.29/82.51 (P2(x301,x301)),
% 82.29/82.51 inference(rename_variables,[],[15])).
% 82.29/82.51 cnf(32,plain,
% 82.29/82.51 (P2(f3(x321,x322),f3(x322,x321))),
% 82.29/82.51 inference(scs_inference,[],[15,28,30,16,24,23,12])).
% 82.29/82.51 cnf(33,plain,
% 82.29/82.51 (P2(x331,x331)),
% 82.29/82.51 inference(rename_variables,[],[15])).
% 82.29/82.51 cnf(34,plain,
% 82.29/82.51 (P3(f3(x341,x342),f3(f3(x342,x341),x343))),
% 82.29/82.51 inference(scs_inference,[],[15,28,30,16,24,23,12,9])).
% 82.29/82.51 cnf(35,plain,
% 82.29/82.51 (~P3(f3(f3(x351,x352),x353),f3(x351,x352))),
% 82.29/82.51 inference(scs_inference,[],[15,28,30,16,24,23,12,9,22])).
% 82.29/82.51 cnf(37,plain,
% 82.29/82.51 (E(f5(x371,f3(x372,x373)),f5(x371,f3(x373,x372)))),
% 82.29/82.51 inference(scs_inference,[],[15,28,30,16,24,23,12,9,22,7])).
% 82.29/82.51 cnf(38,plain,
% 82.29/82.51 (E(f5(f3(x381,x382),x383),f5(f3(x382,x381),x383))),
% 82.29/82.51 inference(scs_inference,[],[15,28,30,16,24,23,12,9,22,7,6])).
% 82.29/82.51 cnf(41,plain,
% 82.29/82.51 (E(f5(x411,x411),a1)),
% 82.29/82.51 inference(scs_inference,[],[15,28,30,33,16,24,23,12,9,22,7,6,5,4,18])).
% 82.29/82.51 cnf(43,plain,
% 82.29/82.51 (~E(a1,a4)),
% 82.29/82.51 inference(scs_inference,[],[13,15,28,30,33,17,16,24,23,12,9,22,7,6,5,4,18,8])).
% 82.29/82.51 cnf(50,plain,
% 82.29/82.51 (~P3(f3(f3(x501,x502),x503),f3(x502,x501))),
% 82.29/82.51 inference(scs_inference,[],[34,22])).
% 82.29/82.51 cnf(52,plain,
% 82.29/82.51 (P2(f3(f3(x521,x522),f3(x521,x522)),f3(f3(x522,x521),x523))),
% 82.29/82.51 inference(scs_inference,[],[34,22,25])).
% 82.29/82.51 cnf(54,plain,
% 82.29/82.51 (~P3(f3(x541,f3(x542,x543)),f3(x542,x543))),
% 82.29/82.51 inference(scs_inference,[],[16,34,35,22,25,9])).
% 82.29/82.51 cnf(56,plain,
% 82.29/82.51 (E(f3(x561,x562),f3(x562,x561))),
% 82.29/82.51 inference(rename_variables,[],[16])).
% 82.29/82.51 cnf(61,plain,
% 82.29/82.51 (E(f5(f3(x611,x612),f3(x612,x611)),a1)),
% 82.29/82.51 inference(scs_inference,[],[15,16,56,37,34,35,41,43,22,25,9,2,12,8,3])).
% 82.29/82.51 cnf(67,plain,
% 82.29/82.51 (~P3(f3(x671,x672),x671)),
% 82.29/82.51 inference(scs_inference,[],[27,22])).
% 82.29/82.51 cnf(69,plain,
% 82.29/82.51 (~E(f3(x691,f3(x692,x693)),x692)),
% 82.29/82.51 inference(scs_inference,[],[27,29,22,10])).
% 82.29/82.51 cnf(71,plain,
% 82.29/82.51 (P3(a1,f3(f5(x711,x711),x712))),
% 82.29/82.51 inference(scs_inference,[],[27,29,41,22,10,9])).
% 82.29/82.51 cnf(74,plain,
% 82.29/82.51 (E(a1,f5(f3(x741,x742),f3(x742,x741)))),
% 82.29/82.51 inference(scs_inference,[],[14,27,17,29,61,41,22,10,9,8,2])).
% 82.29/82.51 cnf(86,plain,
% 82.29/82.51 (~P3(f3(f5(x861,x861),x862),a1)),
% 82.29/82.51 inference(scs_inference,[],[15,67,69,71,23,24,5,12,22])).
% 82.29/82.51 cnf(93,plain,
% 82.29/82.51 (P1(f5(f3(x931,x932),f3(x932,x931)))),
% 82.29/82.51 inference(scs_inference,[],[15,27,16,50,67,69,74,71,13,23,24,5,12,22,10,9,8])).
% 82.29/82.51 cnf(101,plain,
% 82.29/82.51 (E(f3(x1011,x1012),f3(x1012,x1011))),
% 82.29/82.51 inference(rename_variables,[],[16])).
% 82.29/82.51 cnf(103,plain,
% 82.29/82.51 (E(f3(x1031,x1032),f3(x1032,x1031))),
% 82.29/82.51 inference(rename_variables,[],[16])).
% 82.29/82.51 cnf(109,plain,
% 82.29/82.51 (E(a1,f5(x1091,x1091))),
% 82.29/82.51 inference(scs_inference,[],[29,16,101,103,52,93,54,86,38,41,5,22,12,10,9,8,2])).
% 82.29/82.51 cnf(541,plain,
% 82.29/82.51 (~P3(a8,a6)+E(f5(f3(a6,a7),a8),a1)),
% 82.29/82.51 inference(scs_inference,[],[20,22])).
% 82.29/82.51 cnf(736,plain,
% 82.29/82.51 (~P3(a8,a7)+E(f5(f3(a6,a7),a8),a1)),
% 82.29/82.51 inference(scs_inference,[],[21,22])).
% 82.29/82.51 cnf(740,plain,
% 82.29/82.51 (~P2(f3(x7401,a8),a6)+E(f5(f3(a6,a7),a8),a1)),
% 82.29/82.51 inference(scs_inference,[],[541,23])).
% 82.29/82.51 cnf(747,plain,
% 82.29/82.51 (~P2(f3(a8,x7471),a7)+E(f5(f3(a6,a7),a8),a1)),
% 82.29/82.51 inference(scs_inference,[],[736,24])).
% 82.29/82.51 cnf(777,plain,
% 82.29/82.51 (~E(f5(f3(x7771,a8),a6),a1)+E(f5(f3(a6,a7),a8),a1)),
% 82.29/82.51 inference(scs_inference,[],[740,19])).
% 82.29/82.51 cnf(787,plain,
% 82.29/82.51 (~E(f5(f3(a8,x7871),a7),a1)+E(f5(f3(a6,a7),a8),a1)),
% 82.29/82.51 inference(scs_inference,[],[747,19])).
% 82.29/82.51 cnf(807,plain,
% 82.29/82.51 (~E(a1,f5(f3(x8071,a8),a6))+E(f5(f3(a6,a7),a8),a1)),
% 82.29/82.51 inference(scs_inference,[],[777,2])).
% 82.29/82.51 cnf(815,plain,
% 82.29/82.51 (~E(a1,f5(f3(a8,x8151),a7))+E(f5(f3(a6,a7),a8),a1)),
% 82.29/82.51 inference(scs_inference,[],[787,2])).
% 82.29/82.51 cnf(833,plain,
% 82.29/82.51 (~E(f5(x8331,x8331),f5(f3(a8,x8332),a7))+E(f5(f3(a6,a7),a8),a1)),
% 82.29/82.51 inference(scs_inference,[],[109,815,3])).
% 82.29/82.51 cnf(878,plain,
% 82.29/82.51 (~E(a7,f3(a8,x8781))+E(f5(f3(a6,a7),a8),a1)),
% 82.29/82.51 inference(scs_inference,[],[833,6])).
% 82.29/82.51 cnf(885,plain,
% 82.29/82.51 (~E(f3(a8,x8851),a7)+E(f5(f3(a6,a7),a8),a1)),
% 82.29/82.51 inference(scs_inference,[],[878,2])).
% 82.29/82.51 cnf(1747,plain,
% 82.29/82.51 (~P2(f3(a6,a7),a8)+~P3(a7,a8)+~P3(a6,a8)),
% 82.29/82.51 inference(scs_inference,[],[18,26])).
% 82.29/82.51 cnf(1924,plain,
% 82.29/82.51 (~P2(f3(a6,a7),a8)+~P2(f3(x19241,a7),a8)+~P3(a6,a8)),
% 82.29/82.51 inference(scs_inference,[],[23,1747])).
% 82.29/82.51 cnf(1925,plain,
% 82.29/82.51 (~P2(f3(a6,a7),a8)+~P3(a6,a8)),
% 82.29/82.51 inference(factoring_inference,[],[1924])).
% 82.29/82.51 cnf(2034,plain,
% 82.29/82.51 (~P2(f3(a6,a7),a8)+~P2(f3(a6,x20341),a8)),
% 82.29/82.51 inference(scs_inference,[],[1925,24])).
% 82.29/82.51 cnf(2035,plain,
% 82.29/82.51 (~P2(f3(a6,a7),a8)),
% 82.29/82.51 inference(factoring_inference,[],[2034])).
% 82.29/82.51 cnf(2062,plain,
% 82.29/82.51 ($false),
% 82.29/82.51 inference(scs_inference,[],[109,32,67,16,2035,19,20,21,736,747,777,807,833,885,11,12,3,22,18,23,6,787,815,9,25]),
% 82.29/82.51 ['proof']).
% 82.29/82.51 % SZS output end Proof
% 82.29/82.51 % Total time :81.790000s
%------------------------------------------------------------------------------