TSTP Solution File: NUM395+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM395+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 : n006.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 10:21:55 EDT 2023
% Result : Theorem 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM395+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
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 14:25:07 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % File :CSE---1.6
% 0.20/0.62 % Problem :theBenchmark
% 0.20/0.62 % Transform :cnf
% 0.20/0.62 % Format :tptp:raw
% 0.20/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.62
% 0.20/0.62 % Result :Theorem 0.000000s
% 0.20/0.62 % Output :CNFRefutation 0.000000s
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 %------------------------------------------------------------------------------
% 0.20/0.62 % File : NUM395+1 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.62 % Domain : Number Theory (Ordinals)
% 0.20/0.62 % Problem : Ordinal numbers, theorem 27
% 0.20/0.62 % Version : [Urb06] axioms : Especial.
% 0.20/0.62 % English :
% 0.20/0.62
% 0.20/0.62 % Refs : [Ban90] Bancerek (1990), The Ordinal Numbers
% 0.20/0.62 % [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.20/0.62 % Source : [Urb06]
% 0.20/0.62 % Names : ordinal1__t27_ordinal1 [Urb06]
% 0.20/0.62
% 0.20/0.62 % Status : Theorem
% 0.20/0.62 % Rating : 0.06 v8.1.0, 0.03 v7.4.0, 0.00 v6.3.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.00 v3.2.0
% 0.20/0.62 % Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% 0.20/0.62 % Number of atoms : 68 ( 2 equ)
% 0.20/0.62 % Maximal formula atoms : 6 ( 2 avg)
% 0.20/0.62 % Number of connectives : 45 ( 6 ~; 1 |; 28 &)
% 0.20/0.62 % ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% 0.20/0.62 % Maximal formula depth : 7 ( 4 avg)
% 0.20/0.62 % Maximal term depth : 1 ( 1 avg)
% 0.20/0.62 % Number of predicates : 12 ( 11 usr; 0 prp; 1-2 aty)
% 0.20/0.62 % Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% 0.20/0.62 % Number of variables : 30 ( 18 !; 12 ?)
% 0.20/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.62
% 0.20/0.62 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.20/0.62 % library, www.mizar.org
% 0.20/0.62 %------------------------------------------------------------------------------
% 0.20/0.62 fof(existence_m1_subset_1,axiom,
% 0.20/0.62 ! [A] :
% 0.20/0.62 ? [B] : element(B,A) ).
% 0.20/0.62
% 0.20/0.62 fof(t2_subset,axiom,
% 0.20/0.62 ! [A,B] :
% 0.20/0.62 ( element(A,B)
% 0.20/0.62 => ( empty(B)
% 0.20/0.62 | in(A,B) ) ) ).
% 0.20/0.62
% 0.20/0.62 fof(antisymmetry_r2_hidden,axiom,
% 0.20/0.62 ! [A,B] :
% 0.20/0.62 ( in(A,B)
% 0.20/0.62 => ~ in(B,A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(t1_subset,axiom,
% 0.20/0.62 ! [A,B] :
% 0.20/0.62 ( in(A,B)
% 0.20/0.62 => element(A,B) ) ).
% 0.20/0.62
% 0.20/0.62 fof(cc1_funct_1,axiom,
% 0.20/0.62 ! [A] :
% 0.20/0.62 ( empty(A)
% 0.20/0.62 => function(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(cc2_funct_1,axiom,
% 0.20/0.62 ! [A] :
% 0.20/0.62 ( ( relation(A)
% 0.20/0.62 & empty(A)
% 0.20/0.62 & function(A) )
% 0.20/0.62 => ( relation(A)
% 0.20/0.62 & function(A)
% 0.20/0.62 & one_to_one(A) ) ) ).
% 0.20/0.62
% 0.20/0.62 fof(cc1_relat_1,axiom,
% 0.20/0.62 ! [A] :
% 0.20/0.62 ( empty(A)
% 0.20/0.62 => relation(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(t7_boole,axiom,
% 0.20/0.62 ! [A,B] :
% 0.20/0.62 ~ ( in(A,B)
% 0.20/0.62 & empty(B) ) ).
% 0.20/0.62
% 0.20/0.62 fof(t8_boole,axiom,
% 0.20/0.62 ! [A,B] :
% 0.20/0.62 ~ ( empty(A)
% 0.20/0.62 & A != B
% 0.20/0.62 & empty(B) ) ).
% 0.20/0.62
% 0.20/0.62 fof(cc1_ordinal1,axiom,
% 0.20/0.62 ! [A] :
% 0.20/0.62 ( ordinal(A)
% 0.20/0.62 => ( epsilon_transitive(A)
% 0.20/0.62 & epsilon_connected(A) ) ) ).
% 0.20/0.62
% 0.20/0.62 fof(cc2_ordinal1,axiom,
% 0.20/0.62 ! [A] :
% 0.20/0.62 ( ( epsilon_transitive(A)
% 0.20/0.62 & epsilon_connected(A) )
% 0.20/0.62 => ordinal(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(rc1_ordinal1,axiom,
% 0.20/0.62 ? [A] :
% 0.20/0.62 ( epsilon_transitive(A)
% 0.20/0.62 & epsilon_connected(A)
% 0.20/0.62 & ordinal(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(rc1_funct_1,axiom,
% 0.20/0.62 ? [A] :
% 0.20/0.62 ( relation(A)
% 0.20/0.62 & function(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(rc2_funct_1,axiom,
% 0.20/0.62 ? [A] :
% 0.20/0.62 ( relation(A)
% 0.20/0.62 & empty(A)
% 0.20/0.62 & function(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(rc3_funct_1,axiom,
% 0.20/0.62 ? [A] :
% 0.20/0.62 ( relation(A)
% 0.20/0.62 & function(A)
% 0.20/0.62 & one_to_one(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(rc4_funct_1,axiom,
% 0.20/0.62 ? [A] :
% 0.20/0.62 ( relation(A)
% 0.20/0.62 & relation_empty_yielding(A)
% 0.20/0.62 & function(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(rc5_funct_1,axiom,
% 0.20/0.62 ? [A] :
% 0.20/0.62 ( relation(A)
% 0.20/0.62 & relation_non_empty(A)
% 0.20/0.62 & function(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(fc4_relat_1,axiom,
% 0.20/0.62 ( empty(empty_set)
% 0.20/0.62 & relation(empty_set) ) ).
% 0.20/0.62
% 0.20/0.62 fof(fc12_relat_1,axiom,
% 0.20/0.62 ( empty(empty_set)
% 0.20/0.62 & relation(empty_set)
% 0.20/0.62 & relation_empty_yielding(empty_set) ) ).
% 0.20/0.62
% 0.20/0.62 fof(rc1_relat_1,axiom,
% 0.20/0.62 ? [A] :
% 0.20/0.62 ( empty(A)
% 0.20/0.62 & relation(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(rc2_relat_1,axiom,
% 0.20/0.62 ? [A] :
% 0.20/0.62 ( ~ empty(A)
% 0.20/0.62 & relation(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(rc3_relat_1,axiom,
% 0.20/0.62 ? [A] :
% 0.20/0.62 ( relation(A)
% 0.20/0.62 & relation_empty_yielding(A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(fc1_xboole_0,axiom,
% 0.20/0.62 empty(empty_set) ).
% 0.20/0.62
% 0.20/0.62 fof(rc1_xboole_0,axiom,
% 0.20/0.62 ? [A] : empty(A) ).
% 0.20/0.62
% 0.20/0.62 fof(rc2_xboole_0,axiom,
% 0.20/0.62 ? [A] : ~ empty(A) ).
% 0.20/0.62
% 0.20/0.62 fof(t6_boole,axiom,
% 0.20/0.62 ! [A] :
% 0.20/0.62 ( empty(A)
% 0.20/0.62 => A = empty_set ) ).
% 0.20/0.62
% 0.20/0.62 fof(t27_ordinal1,conjecture,
% 0.20/0.62 ordinal(empty_set) ).
% 0.20/0.62
% 0.20/0.62 fof(d4_ordinal1,axiom,
% 0.20/0.62 ! [A] :
% 0.20/0.62 ( ordinal(A)
% 0.20/0.62 <=> ( epsilon_transitive(A)
% 0.20/0.62 & epsilon_connected(A) ) ) ).
% 0.20/0.62
% 0.20/0.63 fof(l18_ordinal1,axiom,
% 0.20/0.63 ( epsilon_transitive(empty_set)
% 0.20/0.63 & epsilon_connected(empty_set) ) ).
% 0.20/0.63
% 0.20/0.63 %------------------------------------------------------------------------------
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark
% 0.20/0.63 % SZS output start Proof
% 0.20/0.63 %ClaNum:67(EqnAxiom:17)
% 0.20/0.63 %VarNum:39(SingletonVarNum:18)
% 0.20/0.63 %MaxLitNum:4
% 0.20/0.63 %MaxfuncDepth:1
% 0.20/0.63 %SharedTerms:43
% 0.20/0.63 %goalClause: 52
% 0.20/0.63 %singleGoalClaCount:1
% 0.20/0.63 [20]P1(a1)
% 0.20/0.63 [21]P1(a2)
% 0.20/0.63 [22]P1(a9)
% 0.20/0.63 [23]P1(a3)
% 0.20/0.63 [24]P3(a5)
% 0.20/0.63 [25]P3(a2)
% 0.20/0.63 [26]P3(a10)
% 0.20/0.63 [27]P3(a11)
% 0.20/0.63 [28]P3(a12)
% 0.20/0.63 [30]P6(a1)
% 0.20/0.63 [31]P6(a5)
% 0.20/0.63 [32]P6(a2)
% 0.20/0.63 [33]P6(a10)
% 0.20/0.63 [34]P6(a11)
% 0.20/0.63 [35]P6(a12)
% 0.20/0.63 [36]P6(a9)
% 0.20/0.63 [37]P6(a13)
% 0.20/0.63 [38]P6(a4)
% 0.20/0.63 [39]P7(a10)
% 0.20/0.63 [40]P9(a6)
% 0.20/0.63 [41]P4(a1)
% 0.20/0.63 [42]P4(a6)
% 0.20/0.63 [43]P5(a1)
% 0.20/0.63 [44]P5(a6)
% 0.20/0.63 [45]P10(a1)
% 0.20/0.63 [46]P10(a11)
% 0.20/0.63 [47]P10(a4)
% 0.20/0.63 [48]P11(a12)
% 0.20/0.63 [50]~P1(a13)
% 0.20/0.63 [51]~P1(a8)
% 0.20/0.63 [52]~P9(a1)
% 0.20/0.63 [49]P2(f7(x491),x491)
% 0.20/0.63 [53]~P1(x531)+E(x531,a1)
% 0.20/0.63 [54]~P1(x541)+P3(x541)
% 0.20/0.63 [55]~P1(x551)+P6(x551)
% 0.20/0.63 [57]~P9(x571)+P4(x571)
% 0.20/0.63 [59]~P9(x591)+P5(x591)
% 0.20/0.63 [64]~P1(x641)+~P8(x642,x641)
% 0.20/0.63 [65]~P8(x651,x652)+P2(x651,x652)
% 0.20/0.63 [67]~P8(x672,x671)+~P8(x671,x672)
% 0.20/0.63 [62]~P4(x621)+~P5(x621)+P9(x621)
% 0.20/0.63 [60]~P1(x602)+~P1(x601)+E(x601,x602)
% 0.20/0.63 [66]~P2(x662,x661)+P1(x661)+P8(x662,x661)
% 0.20/0.63 [63]~P1(x631)+~P3(x631)+~P6(x631)+P7(x631)
% 0.20/0.63 %EqnAxiom
% 0.20/0.63 [1]E(x11,x11)
% 0.20/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.63 [4]~E(x41,x42)+E(f7(x41),f7(x42))
% 0.20/0.63 [5]~P1(x51)+P1(x52)+~E(x51,x52)
% 0.20/0.63 [6]P8(x62,x63)+~E(x61,x62)+~P8(x61,x63)
% 0.20/0.63 [7]P8(x73,x72)+~E(x71,x72)+~P8(x73,x71)
% 0.20/0.63 [8]~P9(x81)+P9(x82)+~E(x81,x82)
% 0.20/0.63 [9]P2(x92,x93)+~E(x91,x92)+~P2(x91,x93)
% 0.20/0.63 [10]P2(x103,x102)+~E(x101,x102)+~P2(x103,x101)
% 0.20/0.63 [11]~P5(x111)+P5(x112)+~E(x111,x112)
% 0.20/0.63 [12]~P4(x121)+P4(x122)+~E(x121,x122)
% 0.20/0.63 [13]~P3(x131)+P3(x132)+~E(x131,x132)
% 0.20/0.63 [14]~P11(x141)+P11(x142)+~E(x141,x142)
% 0.20/0.63 [15]~P10(x151)+P10(x152)+~E(x151,x152)
% 0.20/0.63 [16]~P6(x161)+P6(x162)+~E(x161,x162)
% 0.20/0.63 [17]~P7(x171)+P7(x172)+~E(x171,x172)
% 0.20/0.63
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 cnf(68,plain,
% 0.20/0.63 ($false),
% 0.20/0.63 inference(scs_inference,[],[41,43,52,62]),
% 0.20/0.63 ['proof']).
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time :0.000000s
%------------------------------------------------------------------------------