TSTP Solution File: SET873+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET873+1 : 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 : n012.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 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET873+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n012.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 08:56:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % File :CSE---1.6
% 0.19/0.63 % Problem :theBenchmark
% 0.19/0.63 % Transform :cnf
% 0.19/0.63 % Format :tptp:raw
% 0.19/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.63
% 0.19/0.63 % Result :Theorem 0.020000s
% 0.19/0.63 % Output :CNFRefutation 0.020000s
% 0.19/0.63 %-------------------------------------------
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 % File : SET873+1 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.64 % Domain : Set theory
% 0.19/0.64 % Problem : union(singleton(A),singleton(B)) = singleton(A) => A = B
% 0.19/0.64 % Version : [Urb06] axioms : Especial.
% 0.19/0.64 % English :
% 0.19/0.64
% 0.19/0.64 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.19/0.64 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.19/0.64 % Source : [Urb06]
% 0.19/0.64 % Names : zfmisc_1__t13_zfmisc_1 [Urb06]
% 0.19/0.64
% 0.19/0.64 % Status : Theorem
% 0.19/0.64 % Rating : 0.11 v7.5.0, 0.12 v7.4.0, 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, 0.17 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.22 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 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, 0.14 v3.2.0
% 0.19/0.64 % Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% 0.19/0.64 % Number of atoms : 18 ( 6 equ)
% 0.19/0.64 % Maximal formula atoms : 3 ( 1 avg)
% 0.19/0.64 % Number of connectives : 13 ( 6 ~; 0 |; 0 &)
% 0.19/0.64 % ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% 0.19/0.64 % Maximal formula depth : 6 ( 4 avg)
% 0.19/0.64 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.64 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.19/0.64 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.19/0.64 % Number of variables : 21 ( 19 !; 2 ?)
% 0.19/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.64
% 0.19/0.64 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.64 % library, www.mizar.org
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 fof(antisymmetry_r2_hidden,axiom,
% 0.19/0.64 ! [A,B] :
% 0.19/0.64 ( in(A,B)
% 0.19/0.64 => ~ in(B,A) ) ).
% 0.19/0.64
% 0.19/0.64 fof(commutativity_k2_xboole_0,axiom,
% 0.19/0.64 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.19/0.64
% 0.19/0.64 fof(d1_tarski,axiom,
% 0.19/0.64 ! [A,B] :
% 0.19/0.64 ( B = singleton(A)
% 0.19/0.64 <=> ! [C] :
% 0.19/0.64 ( in(C,B)
% 0.19/0.64 <=> C = A ) ) ).
% 0.19/0.64
% 0.19/0.64 fof(fc2_xboole_0,axiom,
% 0.19/0.64 ! [A,B] :
% 0.19/0.64 ( ~ empty(A)
% 0.19/0.64 => ~ empty(set_union2(A,B)) ) ).
% 0.19/0.64
% 0.19/0.64 fof(fc3_xboole_0,axiom,
% 0.19/0.64 ! [A,B] :
% 0.19/0.64 ( ~ empty(A)
% 0.19/0.64 => ~ empty(set_union2(B,A)) ) ).
% 0.19/0.64
% 0.19/0.64 fof(idempotence_k2_xboole_0,axiom,
% 0.19/0.64 ! [A,B] : set_union2(A,A) = A ).
% 0.19/0.64
% 0.19/0.64 fof(l21_zfmisc_1,axiom,
% 0.19/0.64 ! [A,B] :
% 0.19/0.64 ( subset(set_union2(singleton(A),B),B)
% 0.19/0.64 => in(A,B) ) ).
% 0.19/0.64
% 0.19/0.64 fof(rc1_xboole_0,axiom,
% 0.19/0.64 ? [A] : empty(A) ).
% 0.19/0.64
% 0.19/0.64 fof(rc2_xboole_0,axiom,
% 0.19/0.64 ? [A] : ~ empty(A) ).
% 0.19/0.64
% 0.19/0.64 fof(reflexivity_r1_tarski,axiom,
% 0.19/0.64 ! [A,B] : subset(A,A) ).
% 0.19/0.64
% 0.19/0.64 fof(t13_zfmisc_1,conjecture,
% 0.19/0.64 ! [A,B] :
% 0.19/0.64 ( set_union2(singleton(A),singleton(B)) = singleton(A)
% 0.19/0.64 => A = B ) ).
% 0.19/0.64
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 % Proof found
% 0.19/0.64 % SZS status Theorem for theBenchmark
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 %ClaNum:28(EqnAxiom:13)
% 0.19/0.64 %VarNum:52(SingletonVarNum:22)
% 0.19/0.64 %MaxLitNum:3
% 0.19/0.64 %MaxfuncDepth:2
% 0.19/0.64 %SharedTerms:11
% 0.19/0.64 %goalClause: 17 19
% 0.19/0.64 %singleGoalClaCount:2
% 0.19/0.64 [14]P1(a1)
% 0.19/0.64 [19]~E(a6,a4)
% 0.19/0.64 [20]~P1(a5)
% 0.19/0.64 [17]E(f3(f7(a4),f7(a6)),f7(a4))
% 0.19/0.64 [15]P2(x151,x151)
% 0.19/0.64 [16]E(f3(x161,x161),x161)
% 0.19/0.64 [18]E(f3(x181,x182),f3(x182,x181))
% 0.19/0.64 [23]~P3(x232,x231)+~P3(x231,x232)
% 0.19/0.64 [24]P1(x241)+~P1(f3(x242,x241))
% 0.19/0.64 [25]P1(x251)+~P1(f3(x251,x252))
% 0.19/0.64 [28]P3(x281,x282)+~P2(f3(f7(x281),x282),x282)
% 0.19/0.64 [26]E(f2(x262,x261),x262)+P3(f2(x262,x261),x261)+E(x261,f7(x262))
% 0.19/0.64 [27]~E(f2(x272,x271),x272)+~P3(f2(x272,x271),x271)+E(x271,f7(x272))
% 0.19/0.64 [21]P3(x211,x212)+~E(x211,x213)+~E(x212,f7(x213))
% 0.19/0.64 [22]~P3(x221,x223)+E(x221,x222)+~E(x223,f7(x222))
% 0.19/0.64 %EqnAxiom
% 0.19/0.64 [1]E(x11,x11)
% 0.19/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.64 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.19/0.64 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.19/0.64 [6]~E(x61,x62)+E(f7(x61),f7(x62))
% 0.19/0.64 [7]~E(x71,x72)+E(f2(x71,x73),f2(x72,x73))
% 0.19/0.64 [8]~E(x81,x82)+E(f2(x83,x81),f2(x83,x82))
% 0.19/0.64 [9]~P1(x91)+P1(x92)+~E(x91,x92)
% 0.19/0.64 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103)
% 0.19/0.64 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111)
% 0.19/0.64 [12]P3(x122,x123)+~E(x121,x122)+~P3(x121,x123)
% 0.19/0.64 [13]P3(x133,x132)+~E(x131,x132)+~P3(x133,x131)
% 0.19/0.64
% 0.19/0.64 %-------------------------------------------
% 0.19/0.65 cnf(29,plain,
% 0.19/0.65 (E(f7(a4),f3(f7(a4),f7(a6)))),
% 0.19/0.65 inference(scs_inference,[],[17,2])).
% 0.19/0.65 cnf(30,plain,
% 0.19/0.65 (P2(f3(f7(a4),f7(a6)),f7(a4))),
% 0.19/0.65 inference(scs_inference,[],[17,15,2,11])).
% 0.19/0.65 cnf(31,plain,
% 0.19/0.65 (P2(x311,x311)),
% 0.19/0.65 inference(rename_variables,[],[15])).
% 0.19/0.65 cnf(32,plain,
% 0.19/0.65 (P2(f7(a4),f3(f7(a4),f7(a6)))),
% 0.19/0.65 inference(scs_inference,[],[17,15,31,2,11,10])).
% 0.19/0.65 cnf(35,plain,
% 0.19/0.65 (E(f3(x351,x351),x351)),
% 0.19/0.65 inference(rename_variables,[],[16])).
% 0.19/0.65 cnf(37,plain,
% 0.19/0.65 (E(f3(x371,x371),x371)),
% 0.19/0.65 inference(rename_variables,[],[16])).
% 0.19/0.65 cnf(38,plain,
% 0.19/0.65 (~P3(a6,f3(f7(a4),f7(a6)))),
% 0.19/0.65 inference(scs_inference,[],[17,15,31,19,20,16,35,2,11,10,9,3,22])).
% 0.19/0.65 cnf(40,plain,
% 0.19/0.65 (~P1(f3(a5,x401))),
% 0.19/0.65 inference(scs_inference,[],[17,15,31,19,20,16,35,2,11,10,9,3,22,25])).
% 0.19/0.65 cnf(46,plain,
% 0.19/0.65 (E(f7(f3(x461,x461)),f7(x461))),
% 0.19/0.65 inference(scs_inference,[],[17,15,31,19,20,16,35,37,2,11,10,9,3,22,25,24,8,7,6])).
% 0.19/0.65 cnf(49,plain,
% 0.19/0.65 (~P3(f3(a6,a6),f3(f7(a4),f7(a6)))),
% 0.19/0.65 inference(scs_inference,[],[17,15,31,19,20,16,35,37,2,11,10,9,3,22,25,24,8,7,6,5,4,12])).
% 0.19/0.65 cnf(50,plain,
% 0.19/0.65 (~E(f3(f7(a4),f7(a6)),f7(a6))),
% 0.19/0.65 inference(scs_inference,[],[17,15,31,19,20,16,35,37,2,11,10,9,3,22,25,24,8,7,6,5,4,12,21])).
% 0.19/0.65 cnf(52,plain,
% 0.19/0.65 (~P3(x521,f3(f7(a4),f7(a6)))+P3(x521,f7(a4))),
% 0.19/0.65 inference(scs_inference,[],[17,15,31,19,20,16,35,37,2,11,10,9,3,22,25,24,8,7,6,5,4,12,21,13])).
% 0.19/0.65 cnf(53,plain,
% 0.19/0.65 (~E(a4,a6)),
% 0.19/0.65 inference(scs_inference,[],[19,2])).
% 0.19/0.65 cnf(54,plain,
% 0.19/0.65 (~E(f7(a4),f7(a6))),
% 0.19/0.65 inference(scs_inference,[],[17,19,50,2,3])).
% 0.19/0.65 cnf(55,plain,
% 0.19/0.65 (P3(f3(a4,a4),f3(f7(a4),f7(a6)))),
% 0.19/0.65 inference(scs_inference,[],[17,16,19,50,2,3,21])).
% 0.19/0.65 cnf(56,plain,
% 0.19/0.65 (E(f3(x561,x561),x561)),
% 0.19/0.65 inference(rename_variables,[],[16])).
% 0.19/0.65 cnf(58,plain,
% 0.19/0.65 (P3(f3(a4,a4),f7(a4))),
% 0.19/0.65 inference(scs_inference,[],[17,16,19,50,2,3,21,13])).
% 0.19/0.65 cnf(59,plain,
% 0.19/0.65 (P3(a4,f3(f7(a4),f7(a6)))),
% 0.19/0.65 inference(scs_inference,[],[17,16,56,19,50,2,3,21,13,12])).
% 0.19/0.65 cnf(60,plain,
% 0.19/0.65 (E(f3(x601,x601),x601)),
% 0.19/0.65 inference(rename_variables,[],[16])).
% 0.19/0.65 cnf(66,plain,
% 0.19/0.65 (P2(x661,x661)),
% 0.19/0.65 inference(rename_variables,[],[15])).
% 0.19/0.65 cnf(68,plain,
% 0.19/0.65 (E(f3(x681,x681),x681)),
% 0.19/0.65 inference(rename_variables,[],[16])).
% 0.19/0.65 cnf(70,plain,
% 0.19/0.65 (P2(f3(x701,x701),x701)),
% 0.19/0.65 inference(scs_inference,[],[17,14,18,15,66,16,56,60,68,19,20,50,2,3,21,13,12,9,52,23,10,22,11])).
% 0.19/0.65 cnf(72,plain,
% 0.19/0.65 (P3(x721,f7(x721))),
% 0.19/0.65 inference(scs_inference,[],[70,28])).
% 0.19/0.65 cnf(75,plain,
% 0.19/0.65 (~P3(f7(a4),f3(a4,a4))),
% 0.19/0.65 inference(scs_inference,[],[70,58,28,23])).
% 0.19/0.65 cnf(77,plain,
% 0.19/0.65 (E(x771,f3(x771,x771))),
% 0.19/0.65 inference(scs_inference,[],[16,70,58,28,23,2])).
% 0.19/0.65 cnf(81,plain,
% 0.19/0.65 (~P3(a6,f7(a4))),
% 0.19/0.65 inference(scs_inference,[],[29,18,16,70,55,58,38,28,23,2,12,3,13])).
% 0.19/0.65 cnf(88,plain,
% 0.19/0.65 (~E(f3(a4,a4),f3(f7(f7(a4)),f3(a4,a4)))),
% 0.19/0.65 inference(scs_inference,[],[15,72,75,49,17,28,21,23,10])).
% 0.19/0.65 cnf(89,plain,
% 0.19/0.65 (P2(x891,x891)),
% 0.19/0.65 inference(rename_variables,[],[15])).
% 0.19/0.65 cnf(94,plain,
% 0.19/0.65 (E(f3(x941,x941),x941)),
% 0.19/0.65 inference(rename_variables,[],[16])).
% 0.19/0.65 cnf(97,plain,
% 0.19/0.65 (P3(a4,f3(f7(a6),f7(a4)))),
% 0.19/0.65 inference(scs_inference,[],[15,89,29,18,16,94,72,54,75,49,59,17,28,21,23,10,2,11,3,12,13])).
% 0.19/0.65 cnf(106,plain,
% 0.19/0.65 (E(x1061,f3(x1061,x1061))),
% 0.19/0.65 inference(rename_variables,[],[77])).
% 0.19/0.65 cnf(109,plain,
% 0.19/0.65 (E(f3(x1091,x1091),x1091)),
% 0.19/0.65 inference(rename_variables,[],[16])).
% 0.19/0.65 cnf(125,plain,
% 0.19/0.65 ($false),
% 0.19/0.65 inference(scs_inference,[],[30,29,18,16,109,46,77,106,53,88,32,40,81,97,72,23,21,22,10,2,3,11,12,13,25,24,5,4,28]),
% 0.19/0.65 ['proof']).
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65 % Total time :0.020000s
%------------------------------------------------------------------------------