TSTP Solution File: SET874+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET874+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 : 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 14:31:31 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
% 0.13/0.12 % Problem : SET874+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n031.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 16:15:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 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 0.010000s
% 0.20/0.65 % Output :CNFRefutation 0.010000s
% 0.20/0.65 %-------------------------------------------
% 0.20/0.66 %------------------------------------------------------------------------------
% 0.20/0.66 % File : SET874+1 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.66 % Domain : Set theory
% 0.20/0.66 % Problem : union(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B)
% 0.20/0.66 % Version : [Urb06] axioms : Especial.
% 0.20/0.66 % English :
% 0.20/0.66
% 0.20/0.66 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.20/0.66 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.20/0.66 % Source : [Urb06]
% 0.20/0.66 % Names : zfmisc_1__t14_zfmisc_1 [Urb06]
% 0.20/0.66
% 0.20/0.66 % Status : Theorem
% 0.20/0.66 % Rating : 0.08 v7.5.0, 0.09 v7.4.0, 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, 0.13 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.26 v5.2.0, 0.05 v5.0.0, 0.21 v4.1.0, 0.22 v4.0.0, 0.21 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.21 v3.2.0
% 0.20/0.66 % Syntax : Number of formulae : 11 ( 6 unt; 0 def)
% 0.20/0.66 % Number of atoms : 18 ( 8 equ)
% 0.20/0.66 % Maximal formula atoms : 4 ( 1 avg)
% 0.20/0.66 % Number of connectives : 13 ( 6 ~; 1 |; 0 &)
% 0.20/0.66 % ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% 0.20/0.66 % Maximal formula depth : 8 ( 4 avg)
% 0.20/0.66 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.66 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.20/0.66 % Number of functors : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.20/0.66 % Number of variables : 22 ( 20 !; 2 ?)
% 0.20/0.66 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.66
% 0.20/0.66 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.20/0.66 % library, www.mizar.org
% 0.20/0.66 %------------------------------------------------------------------------------
% 0.20/0.66 fof(antisymmetry_r2_hidden,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ( in(A,B)
% 0.20/0.66 => ~ in(B,A) ) ).
% 0.20/0.66
% 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(commutativity_k2_xboole_0,axiom,
% 0.20/0.66 ! [A,B] : set_union2(A,B) = set_union2(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(fc2_xboole_0,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ( ~ empty(A)
% 0.20/0.66 => ~ empty(set_union2(A,B)) ) ).
% 0.20/0.66
% 0.20/0.66 fof(fc3_xboole_0,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ( ~ empty(A)
% 0.20/0.66 => ~ empty(set_union2(B,A)) ) ).
% 0.20/0.66
% 0.20/0.66 fof(idempotence_k2_xboole_0,axiom,
% 0.20/0.66 ! [A,B] : set_union2(A,A) = A ).
% 0.20/0.66
% 0.20/0.66 fof(l23_zfmisc_1,axiom,
% 0.20/0.66 ! [A,B] :
% 0.20/0.66 ( in(A,B)
% 0.20/0.66 => set_union2(singleton(A),B) = 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(t14_zfmisc_1,conjecture,
% 0.20/0.66 ! [A,B] : set_union2(singleton(A),unordered_pair(A,B)) = unordered_pair(A,B) ).
% 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:30(EqnAxiom:14)
% 0.20/0.66 %VarNum:86(SingletonVarNum:34)
% 0.20/0.66 %MaxLitNum:4
% 0.20/0.66 %MaxfuncDepth:2
% 0.20/0.66 %SharedTerms:10
% 0.20/0.66 %goalClause: 20
% 0.20/0.66 %singleGoalClaCount:1
% 0.20/0.66 [15]P1(a1)
% 0.20/0.66 [19]~P1(a4)
% 0.20/0.66 [20]~E(f3(f8(a5),f7(a5,a6)),f7(a5,a6))
% 0.20/0.66 [16]E(f3(x161,x161),x161)
% 0.20/0.66 [17]E(f7(x171,x172),f7(x172,x171))
% 0.20/0.66 [18]E(f3(x181,x182),f3(x182,x181))
% 0.20/0.66 [24]~P2(x242,x241)+~P2(x241,x242)
% 0.20/0.66 [26]P1(x261)+~P1(f3(x262,x261))
% 0.20/0.66 [27]P1(x271)+~P1(f3(x271,x272))
% 0.20/0.66 [23]~P2(x231,x232)+E(f3(f8(x231),x232),x232)
% 0.20/0.66 [29]~E(f2(x292,x293,x291),x293)+~P2(f2(x292,x293,x291),x291)+E(x291,f7(x292,x293))
% 0.20/0.66 [30]~E(f2(x302,x303,x301),x302)+~P2(f2(x302,x303,x301),x301)+E(x301,f7(x302,x303))
% 0.20/0.66 [21]P2(x211,x212)+~E(x211,x213)+~E(x212,f7(x214,x213))
% 0.20/0.66 [22]P2(x221,x222)+~E(x221,x223)+~E(x222,f7(x223,x224))
% 0.20/0.66 [28]E(f2(x282,x283,x281),x283)+E(f2(x282,x283,x281),x282)+P2(f2(x282,x283,x281),x281)+E(x281,f7(x282,x283))
% 0.20/0.66 [25]~P2(x251,x254)+E(x251,x252)+E(x251,x253)+~E(x254,f7(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(f3(x41,x43),f3(x42,x43))
% 0.20/0.66 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.20/0.66 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63))
% 0.20/0.66 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72))
% 0.20/0.66 [8]~E(x81,x82)+E(f2(x81,x83,x84),f2(x82,x83,x84))
% 0.20/0.66 [9]~E(x91,x92)+E(f2(x93,x91,x94),f2(x93,x92,x94))
% 0.20/0.66 [10]~E(x101,x102)+E(f2(x103,x104,x101),f2(x103,x104,x102))
% 0.20/0.66 [11]~E(x111,x112)+E(f8(x111),f8(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(31,plain,
% 0.20/0.66 (E(x311,f3(x311,x311))),
% 0.20/0.66 inference(scs_inference,[],[16,2])).
% 0.20/0.66 cnf(32,plain,
% 0.20/0.66 (~P2(a5,f7(a5,a6))),
% 0.20/0.66 inference(scs_inference,[],[20,16,2,23])).
% 0.20/0.66 cnf(35,plain,
% 0.20/0.66 (E(f3(x351,x351),x351)),
% 0.20/0.66 inference(rename_variables,[],[16])).
% 0.20/0.66 cnf(36,plain,
% 0.20/0.66 (~E(f3(f8(a5),f7(a5,a6)),f3(f7(a5,a6),f7(a5,a6)))),
% 0.20/0.66 inference(scs_inference,[],[20,19,16,35,2,23,12,3])).
% 0.20/0.66 cnf(37,plain,
% 0.20/0.66 (E(f3(x371,x371),x371)),
% 0.20/0.66 inference(rename_variables,[],[16])).
% 0.20/0.66 cnf(39,plain,
% 0.20/0.66 (E(f7(x391,x392),f7(x392,x391))),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(42,plain,
% 0.20/0.66 (E(f7(x421,x422),f7(x422,x421))),
% 0.20/0.66 inference(rename_variables,[],[17])).
% 0.20/0.66 cnf(43,plain,
% 0.20/0.66 (~P2(f3(f8(a5),f7(a5,a6)),f7(f7(a5,a6),f7(a5,a6)))),
% 0.20/0.66 inference(scs_inference,[],[20,19,16,35,17,39,42,2,23,12,3,22,21,25])).
% 0.20/0.66 cnf(57,plain,
% 0.20/0.66 (E(f3(f3(x571,x571),x572),f3(x571,x572))),
% 0.20/0.66 inference(scs_inference,[],[20,19,16,35,37,17,39,42,2,23,12,3,22,21,25,27,26,11,10,9,8,7,6,5,4])).
% 0.20/0.66 cnf(58,plain,
% 0.20/0.66 (~P2(a5,f3(f7(a5,a6),f7(a5,a6)))),
% 0.20/0.66 inference(scs_inference,[],[20,19,16,35,37,17,39,42,2,23,12,3,22,21,25,27,26,11,10,9,8,7,6,5,4,14])).
% 0.20/0.66 cnf(59,plain,
% 0.20/0.66 (~P2(x591,f7(a5,a6))+~E(x591,a5)),
% 0.20/0.67 inference(scs_inference,[],[20,19,16,35,37,17,39,42,2,23,12,3,22,21,25,27,26,11,10,9,8,7,6,5,4,14,13])).
% 0.20/0.67 cnf(68,plain,
% 0.20/0.67 (E(f3(x681,x682),f3(x682,x681))),
% 0.20/0.67 inference(rename_variables,[],[18])).
% 0.20/0.67 cnf(73,plain,
% 0.20/0.67 (E(x731,f3(x731,x731))),
% 0.20/0.67 inference(rename_variables,[],[31])).
% 0.20/0.67 cnf(76,plain,
% 0.20/0.67 (E(x761,f3(x761,x761))),
% 0.20/0.67 inference(rename_variables,[],[31])).
% 0.20/0.67 cnf(79,plain,
% 0.20/0.67 ($false),
% 0.20/0.67 inference(scs_inference,[],[20,15,18,68,16,19,31,73,76,57,43,32,36,58,59,2,4,14,13,12,3,22,21,7,6]),
% 0.20/0.67 ['proof']).
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67 % Total time :0.010000s
%------------------------------------------------------------------------------