TSTP Solution File: SET881+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET881+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 : n011.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 0.20s 0.66s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:09:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % File :CSE---1.6
% 0.20/0.65 % Problem :theBenchmark
% 0.20/0.65 % Transform :cnf
% 0.20/0.65 % Format :tptp:raw
% 0.20/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.65
% 0.20/0.65 % Result :Theorem 0.030000s
% 0.20/0.65 % Output :CNFRefutation 0.030000s
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 % File : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.65 % Domain : Set theory
% 0.20/0.65 % Problem : difference(singleton(A),unordered_pair(A,B)) = empty_set
% 0.20/0.65 % Version : [Urb06] axioms : Especial.
% 0.20/0.65 % English :
% 0.20/0.65
% 0.20/0.65 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.20/0.65 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.20/0.65 % Source : [Urb06]
% 0.20/0.65 % Names : zfmisc_1__t22_zfmisc_1 [Urb06]
% 0.20/0.65
% 0.20/0.65 % Status : Theorem
% 0.20/0.65 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.20 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.19 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 v3.3.0, 0.14 v3.2.0
% 0.20/0.65 % Syntax : Number of formulae : 8 ( 5 unt; 0 def)
% 0.20/0.65 % Number of atoms : 13 ( 6 equ)
% 0.20/0.65 % Maximal formula atoms : 4 ( 1 avg)
% 0.20/0.65 % Number of connectives : 7 ( 2 ~; 1 |; 0 &)
% 0.20/0.65 % ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.65 % Maximal formula depth : 8 ( 4 avg)
% 0.20/0.65 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.65 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.20/0.65 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.20/0.65 % Number of variables : 14 ( 12 !; 2 ?)
% 0.20/0.65 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.65
% 0.20/0.65 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.20/0.65 % library, www.mizar.org
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 fof(antisymmetry_r2_hidden,axiom,
% 0.20/0.65 ! [A,B] :
% 0.20/0.65 ( in(A,B)
% 0.20/0.65 => ~ in(B,A) ) ).
% 0.20/0.65
% 0.20/0.66 fof(commutativity_k2_tarski,axiom,
% 0.20/0.66 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 0.20/0.66
% 0.20/0.66 fof(d2_tarski,axiom,
% 0.20/0.66 ! [A,B,C] :
% 0.20/0.66 ( C = unordered_pair(A,B)
% 0.20/0.66 <=> ! [D] :
% 0.20/0.66 ( in(D,C)
% 0.20/0.66 <=> ( D = A
% 0.20/0.66 | D = B ) ) ) ).
% 0.20/0.66
% 0.20/0.66 fof(fc1_xboole_0,axiom,
% 0.20/0.66 empty(empty_set) ).
% 0.20/0.66
% 0.20/0.66 fof(l36_zfmisc_1,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ( set_difference(singleton(A),B) = empty_set
% 0.20/0.66 <=> in(A,B) ) ).
% 0.20/0.66
% 0.20/0.66 fof(rc1_xboole_0,axiom,
% 0.20/0.66 ? [A] : empty(A) ).
% 0.20/0.66
% 0.20/0.66 fof(rc2_xboole_0,axiom,
% 0.20/0.66 ? [A] : ~ empty(A) ).
% 0.20/0.66
% 0.20/0.66 fof(t22_zfmisc_1,conjecture,
% 0.20/0.66 ! [A,B] : set_difference(singleton(A),unordered_pair(A,B)) = empty_set ).
% 0.20/0.66
% 0.20/0.66 %------------------------------------------------------------------------------
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 % Proof found
% 0.20/0.66 % SZS status Theorem for theBenchmark
% 0.20/0.66 % SZS output start Proof
% 0.20/0.66 %ClaNum:28(EqnAxiom:14)
% 0.20/0.66 %VarNum:76(SingletonVarNum:29)
% 0.20/0.66 %MaxLitNum:4
% 0.20/0.66 %MaxfuncDepth:2
% 0.20/0.66 %SharedTerms:12
% 0.20/0.66 %goalClause: 19
% 0.20/0.66 %singleGoalClaCount:1
% 0.20/0.66 [15]P1(a1)
% 0.20/0.66 [16]P1(a2)
% 0.20/0.66 [18]~P1(a5)
% 0.20/0.66 [19]~E(f9(f7(a6),f4(a6,a8)),a1)
% 0.20/0.66 [17]E(f4(x171,x172),f4(x172,x171))
% 0.20/0.66 [23]~P2(x232,x231)+~P2(x231,x232)
% 0.20/0.66 [22]~P2(x221,x222)+E(f9(f7(x221),x222),a1)
% 0.20/0.66 [24]P2(x241,x242)+~E(f9(f7(x241),x242),a1)
% 0.20/0.66 [27]~E(f3(x272,x273,x271),x273)+~P2(f3(x272,x273,x271),x271)+E(x271,f4(x272,x273))
% 0.20/0.66 [28]~E(f3(x282,x283,x281),x282)+~P2(f3(x282,x283,x281),x281)+E(x281,f4(x282,x283))
% 0.20/0.66 [20]P2(x201,x202)+~E(x201,x203)+~E(x202,f4(x204,x203))
% 0.20/0.66 [21]P2(x211,x212)+~E(x211,x213)+~E(x212,f4(x213,x214))
% 0.20/0.66 [26]E(f3(x262,x263,x261),x263)+E(f3(x262,x263,x261),x262)+P2(f3(x262,x263,x261),x261)+E(x261,f4(x262,x263))
% 0.20/0.66 [25]~P2(x251,x254)+E(x251,x252)+E(x251,x253)+~E(x254,f4(x253,x252))
% 0.20/0.66 %EqnAxiom
% 0.20/0.66 [1]E(x11,x11)
% 0.20/0.66 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.66 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43))
% 0.20/0.66 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52))
% 0.20/0.66 [6]~E(x61,x62)+E(f3(x61,x63,x64),f3(x62,x63,x64))
% 0.20/0.66 [7]~E(x71,x72)+E(f3(x73,x71,x74),f3(x73,x72,x74))
% 0.20/0.66 [8]~E(x81,x82)+E(f3(x83,x84,x81),f3(x83,x84,x82))
% 0.20/0.66 [9]~E(x91,x92)+E(f7(x91),f7(x92))
% 0.20/0.66 [10]~E(x101,x102)+E(f9(x101,x103),f9(x102,x103))
% 0.20/0.66 [11]~E(x111,x112)+E(f9(x113,x111),f9(x113,x112))
% 0.20/0.66 [12]~P1(x121)+P1(x122)+~E(x121,x122)
% 0.20/0.66 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133)
% 0.20/0.66 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141)
% 0.20/0.66
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 cnf(29,plain,
% 0.20/0.66 (~P2(a6,f4(a6,a8))),
% 0.20/0.66 inference(scs_inference,[],[19,22])).
% 0.20/0.66 cnf(31,plain,
% 0.20/0.66 (E(f4(x311,x312),f4(x312,x311))),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(34,plain,
% 0.20/0.66 (E(f4(x341,x342),f4(x342,x341))),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(36,plain,
% 0.20/0.66 (E(f4(x361,x362),f4(x362,x361))),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(45,plain,
% 0.20/0.66 (E(f4(x451,f4(x452,x453)),f4(x451,f4(x453,x452)))),
% 0.20/0.66 inference(scs_inference,[],[19,17,31,34,36,22,21,20,25,2,11,10,9,8,7,6,5])).
% 0.20/0.66 cnf(47,plain,
% 0.20/0.66 (~P2(a6,f4(a8,a6))),
% 0.20/0.66 inference(scs_inference,[],[19,17,31,34,36,22,21,20,25,2,11,10,9,8,7,6,5,4,14])).
% 0.20/0.66 cnf(50,plain,
% 0.20/0.66 (~E(a1,a5)),
% 0.20/0.66 inference(scs_inference,[],[19,15,18,17,31,34,36,22,21,20,25,2,11,10,9,8,7,6,5,4,14,13,12])).
% 0.20/0.66 cnf(69,plain,
% 0.20/0.66 (P2(f4(x691,x692),f4(x693,f4(x691,x692)))),
% 0.20/0.66 inference(scs_inference,[],[17,45,20])).
% 0.20/0.66 cnf(70,plain,
% 0.20/0.66 (E(f4(x701,x702),f4(x702,x701))),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(72,plain,
% 0.20/0.66 (P2(f4(x721,x722),f4(f4(x722,x721),f4(x723,x724)))),
% 0.20/0.66 inference(scs_inference,[],[17,70,45,20,21])).
% 0.20/0.66 cnf(76,plain,
% 0.20/0.66 (E(f4(x761,x762),f4(x762,x761))),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(79,plain,
% 0.20/0.66 (~P2(f4(f4(a5,a5),f4(x791,x792)),f4(x791,x792))),
% 0.20/0.66 inference(scs_inference,[],[17,70,76,45,50,20,21,25,13,23])).
% 0.20/0.66 cnf(85,plain,
% 0.20/0.66 (E(f4(x851,x852),f4(x852,x851))),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(89,plain,
% 0.20/0.66 (E(f4(x891,x892),f4(x892,x891))),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(95,plain,
% 0.20/0.66 ($false),
% 0.20/0.66 inference(scs_inference,[],[29,17,85,89,69,72,79,47,23,20,14,13,4,21]),
% 0.20/0.66 ['proof']).
% 0.20/0.66 % SZS output end Proof
% 0.20/0.66 % Total time :0.030000s
%------------------------------------------------------------------------------