TSTP Solution File: NUM387+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM387+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 : n021.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 10:21:54 EDT 2023
% Result : Theorem 0.18s 0.67s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM387+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.15/0.33 % Computer : n021.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Fri Aug 25 09:05:56 EDT 2023
% 0.15/0.33 % CPUTime :
% 0.18/0.57 start to proof:theBenchmark
% 0.18/0.66 %-------------------------------------------
% 0.18/0.66 % File :CSE---1.6
% 0.18/0.66 % Problem :theBenchmark
% 0.18/0.66 % Transform :cnf
% 0.18/0.66 % Format :tptp:raw
% 0.18/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.18/0.66
% 0.18/0.66 % Result :Theorem 0.010000s
% 0.18/0.66 % Output :CNFRefutation 0.010000s
% 0.18/0.66 %-------------------------------------------
% 0.18/0.66 %------------------------------------------------------------------------------
% 0.18/0.66 % File : NUM387+1 : TPTP v8.1.2. Released v3.2.0.
% 0.18/0.66 % Domain : Number Theory (Ordinals)
% 0.18/0.66 % Problem : Ordinal numbers, theorem 14
% 0.18/0.66 % Version : [Urb06] axioms : Especial.
% 0.18/0.66 % English :
% 0.18/0.66
% 0.18/0.66 % Refs : [Ban90] Bancerek (1990), The Ordinal Numbers
% 0.18/0.66 % [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.18/0.66 % Source : [Urb06]
% 0.18/0.66 % Names : ordinal1__t14_ordinal1 [Urb06]
% 0.18/0.66
% 0.18/0.66 % Status : Theorem
% 0.18/0.66 % Rating : 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.2.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.22 v5.4.0, 0.21 v5.3.0, 0.22 v5.2.0, 0.00 v5.0.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.00 v3.4.0, 0.05 v3.3.0, 0.14 v3.2.0
% 0.18/0.66 % Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% 0.18/0.66 % Number of atoms : 67 ( 7 equ)
% 0.18/0.66 % Maximal formula atoms : 6 ( 2 avg)
% 0.18/0.66 % Number of connectives : 46 ( 12 ~; 1 |; 23 &)
% 0.18/0.66 % ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% 0.18/0.66 % Maximal formula depth : 7 ( 4 avg)
% 0.18/0.66 % Maximal term depth : 3 ( 1 avg)
% 0.18/0.66 % Number of predicates : 9 ( 8 usr; 0 prp; 1-2 aty)
% 0.18/0.66 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.18/0.66 % Number of variables : 41 ( 30 !; 11 ?)
% 0.18/0.66 % SPC : FOF_THM_RFO_SEQ
% 0.18/0.66
% 0.18/0.66 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.18/0.66 % library, www.mizar.org
% 0.18/0.66 %------------------------------------------------------------------------------
% 0.18/0.66 fof(antisymmetry_r2_hidden,axiom,
% 0.18/0.66 ! [A,B] :
% 0.18/0.66 ( in(A,B)
% 0.18/0.66 => ~ in(B,A) ) ).
% 0.18/0.66
% 0.18/0.66 fof(cc1_funct_1,axiom,
% 0.18/0.66 ! [A] :
% 0.18/0.66 ( empty(A)
% 0.18/0.66 => function(A) ) ).
% 0.18/0.66
% 0.18/0.66 fof(cc1_relat_1,axiom,
% 0.18/0.66 ! [A] :
% 0.18/0.66 ( empty(A)
% 0.18/0.66 => relation(A) ) ).
% 0.18/0.66
% 0.18/0.66 fof(cc2_funct_1,axiom,
% 0.18/0.66 ! [A] :
% 0.18/0.66 ( ( relation(A)
% 0.18/0.66 & empty(A)
% 0.18/0.66 & function(A) )
% 0.18/0.66 => ( relation(A)
% 0.18/0.66 & function(A)
% 0.18/0.66 & one_to_one(A) ) ) ).
% 0.18/0.66
% 0.18/0.66 fof(commutativity_k2_xboole_0,axiom,
% 0.18/0.66 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.18/0.66
% 0.18/0.66 fof(d1_ordinal1,axiom,
% 0.18/0.66 ! [A] : succ(A) = set_union2(A,singleton(A)) ).
% 0.18/0.66
% 0.18/0.66 fof(existence_m1_subset_1,axiom,
% 0.18/0.66 ! [A] :
% 0.18/0.66 ? [B] : element(B,A) ).
% 0.18/0.66
% 0.18/0.66 fof(fc12_relat_1,axiom,
% 0.18/0.66 ( empty(empty_set)
% 0.18/0.66 & relation(empty_set)
% 0.18/0.66 & relation_empty_yielding(empty_set) ) ).
% 0.18/0.66
% 0.18/0.66 fof(fc1_ordinal1,axiom,
% 0.18/0.66 ! [A] : ~ empty(succ(A)) ).
% 0.18/0.66
% 0.18/0.66 fof(fc1_xboole_0,axiom,
% 0.18/0.66 empty(empty_set) ).
% 0.18/0.66
% 0.18/0.66 fof(fc2_relat_1,axiom,
% 0.18/0.66 ! [A,B] :
% 0.18/0.66 ( ( relation(A)
% 0.18/0.66 & relation(B) )
% 0.18/0.66 => relation(set_union2(A,B)) ) ).
% 0.18/0.66
% 0.18/0.66 fof(fc2_xboole_0,axiom,
% 0.18/0.66 ! [A,B] :
% 0.18/0.66 ( ~ empty(A)
% 0.18/0.66 => ~ empty(set_union2(A,B)) ) ).
% 0.18/0.66
% 0.18/0.66 fof(fc3_xboole_0,axiom,
% 0.18/0.66 ! [A,B] :
% 0.18/0.66 ( ~ empty(A)
% 0.18/0.66 => ~ empty(set_union2(B,A)) ) ).
% 0.18/0.66
% 0.18/0.66 fof(fc4_relat_1,axiom,
% 0.18/0.66 ( empty(empty_set)
% 0.18/0.66 & relation(empty_set) ) ).
% 0.18/0.66
% 0.18/0.66 fof(idempotence_k2_xboole_0,axiom,
% 0.18/0.66 ! [A,B] : set_union2(A,A) = A ).
% 0.18/0.66
% 0.18/0.66 fof(rc1_funct_1,axiom,
% 0.18/0.66 ? [A] :
% 0.18/0.66 ( relation(A)
% 0.18/0.66 & function(A) ) ).
% 0.18/0.66
% 0.18/0.66 fof(rc1_relat_1,axiom,
% 0.18/0.66 ? [A] :
% 0.18/0.66 ( empty(A)
% 0.18/0.66 & relation(A) ) ).
% 0.18/0.66
% 0.18/0.66 fof(rc1_xboole_0,axiom,
% 0.18/0.66 ? [A] : empty(A) ).
% 0.18/0.66
% 0.18/0.66 fof(rc2_funct_1,axiom,
% 0.18/0.66 ? [A] :
% 0.18/0.66 ( relation(A)
% 0.18/0.66 & empty(A)
% 0.18/0.66 & function(A) ) ).
% 0.18/0.66
% 0.18/0.66 fof(rc2_relat_1,axiom,
% 0.18/0.66 ? [A] :
% 0.18/0.66 ( ~ empty(A)
% 0.18/0.66 & relation(A) ) ).
% 0.18/0.66
% 0.18/0.66 fof(rc2_xboole_0,axiom,
% 0.18/0.66 ? [A] : ~ empty(A) ).
% 0.18/0.66
% 0.18/0.66 fof(rc3_funct_1,axiom,
% 0.18/0.66 ? [A] :
% 0.18/0.66 ( relation(A)
% 0.18/0.66 & function(A)
% 0.18/0.67 & one_to_one(A) ) ).
% 0.18/0.67
% 0.18/0.67 fof(rc3_relat_1,axiom,
% 0.18/0.67 ? [A] :
% 0.18/0.67 ( relation(A)
% 0.18/0.67 & relation_empty_yielding(A) ) ).
% 0.18/0.67
% 0.18/0.67 fof(rc4_funct_1,axiom,
% 0.18/0.67 ? [A] :
% 0.18/0.67 ( relation(A)
% 0.18/0.67 & relation_empty_yielding(A)
% 0.18/0.67 & function(A) ) ).
% 0.18/0.67
% 0.18/0.67 fof(rc5_funct_1,axiom,
% 0.18/0.67 ? [A] :
% 0.18/0.67 ( relation(A)
% 0.18/0.67 & relation_non_empty(A)
% 0.18/0.67 & function(A) ) ).
% 0.18/0.67
% 0.18/0.67 fof(t10_ordinal1,axiom,
% 0.18/0.67 ! [A] : in(A,succ(A)) ).
% 0.18/0.67
% 0.18/0.67 fof(t14_ordinal1,conjecture,
% 0.18/0.67 ! [A] : A != succ(A) ).
% 0.18/0.67
% 0.18/0.67 fof(t1_boole,axiom,
% 0.18/0.67 ! [A] : set_union2(A,empty_set) = A ).
% 0.18/0.67
% 0.18/0.67 fof(t1_subset,axiom,
% 0.18/0.67 ! [A,B] :
% 0.18/0.67 ( in(A,B)
% 0.18/0.67 => element(A,B) ) ).
% 0.18/0.67
% 0.18/0.67 fof(t2_subset,axiom,
% 0.18/0.67 ! [A,B] :
% 0.18/0.67 ( element(A,B)
% 0.18/0.67 => ( empty(B)
% 0.18/0.67 | in(A,B) ) ) ).
% 0.18/0.67
% 0.18/0.67 fof(t6_boole,axiom,
% 0.18/0.67 ! [A] :
% 0.18/0.67 ( empty(A)
% 0.18/0.67 => A = empty_set ) ).
% 0.18/0.67
% 0.18/0.67 fof(t7_boole,axiom,
% 0.18/0.67 ! [A,B] :
% 0.18/0.67 ~ ( in(A,B)
% 0.18/0.67 & empty(B) ) ).
% 0.18/0.67
% 0.18/0.67 fof(t8_boole,axiom,
% 0.18/0.67 ! [A,B] :
% 0.18/0.67 ~ ( empty(A)
% 0.18/0.67 & A != B
% 0.18/0.67 & empty(B) ) ).
% 0.18/0.67
% 0.18/0.67 %------------------------------------------------------------------------------
% 0.18/0.67 %-------------------------------------------
% 0.18/0.67 % Proof found
% 0.18/0.67 % SZS status Theorem for theBenchmark
% 0.18/0.67 % SZS output start Proof
% 0.18/0.67 %ClaNum:64(EqnAxiom:17)
% 0.18/0.67 %VarNum:56(SingletonVarNum:27)
% 0.18/0.67 %MaxLitNum:4
% 0.18/0.67 %MaxfuncDepth:2
% 0.18/0.67 %SharedTerms:40
% 0.18/0.67 %goalClause: 46
% 0.18/0.67 %singleGoalClaCount:1
% 0.18/0.67 [20]P1(a1)
% 0.18/0.67 [21]P1(a2)
% 0.18/0.67 [22]P1(a8)
% 0.18/0.67 [23]P1(a9)
% 0.18/0.67 [24]P3(a3)
% 0.18/0.67 [25]P3(a9)
% 0.18/0.67 [26]P3(a10)
% 0.18/0.67 [27]P3(a4)
% 0.18/0.67 [28]P3(a5)
% 0.18/0.67 [30]P4(a1)
% 0.18/0.67 [31]P4(a3)
% 0.18/0.67 [32]P4(a2)
% 0.18/0.67 [33]P4(a9)
% 0.18/0.67 [34]P4(a11)
% 0.18/0.67 [35]P4(a10)
% 0.18/0.67 [36]P4(a13)
% 0.18/0.67 [37]P4(a4)
% 0.18/0.67 [38]P4(a5)
% 0.18/0.67 [39]P5(a10)
% 0.18/0.67 [40]P7(a1)
% 0.18/0.67 [41]P7(a13)
% 0.18/0.67 [42]P7(a4)
% 0.18/0.67 [43]P8(a5)
% 0.18/0.67 [50]~P1(a11)
% 0.18/0.67 [51]~P1(a12)
% 0.18/0.67 [46]E(f14(a6,f15(a6)),a6)
% 0.18/0.67 [44]E(f14(x441,a1),x441)
% 0.18/0.67 [45]E(f14(x451,x451),x451)
% 0.18/0.67 [47]P2(f7(x471),x471)
% 0.18/0.67 [49]P6(x491,f14(x491,f15(x491)))
% 0.18/0.67 [52]~P1(f14(x521,f15(x521)))
% 0.18/0.67 [48]E(f14(x481,x482),f14(x482,x481))
% 0.18/0.67 [53]~P1(x531)+E(x531,a1)
% 0.18/0.67 [54]~P1(x541)+P3(x541)
% 0.18/0.67 [55]~P1(x551)+P4(x551)
% 0.18/0.67 [58]~P1(x581)+~P6(x582,x581)
% 0.18/0.67 [59]~P6(x591,x592)+P2(x591,x592)
% 0.18/0.67 [62]~P6(x622,x621)+~P6(x621,x622)
% 0.18/0.67 [63]P1(x631)+~P1(f14(x632,x631))
% 0.18/0.67 [64]P1(x641)+~P1(f14(x641,x642))
% 0.18/0.67 [56]~P1(x562)+~P1(x561)+E(x561,x562)
% 0.18/0.67 [60]~P2(x602,x601)+P1(x601)+P6(x602,x601)
% 0.18/0.67 [61]~P4(x612)+~P4(x611)+P4(f14(x611,x612))
% 0.18/0.67 [57]~P1(x571)+~P3(x571)+~P4(x571)+P5(x571)
% 0.18/0.67 %EqnAxiom
% 0.18/0.67 [1]E(x11,x11)
% 0.18/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.67 [4]~E(x41,x42)+E(f14(x41,x43),f14(x42,x43))
% 0.18/0.67 [5]~E(x51,x52)+E(f14(x53,x51),f14(x53,x52))
% 0.18/0.67 [6]~E(x61,x62)+E(f15(x61),f15(x62))
% 0.18/0.67 [7]~E(x71,x72)+E(f7(x71),f7(x72))
% 0.18/0.67 [8]~P1(x81)+P1(x82)+~E(x81,x82)
% 0.18/0.67 [9]P6(x92,x93)+~E(x91,x92)+~P6(x91,x93)
% 0.18/0.67 [10]P6(x103,x102)+~E(x101,x102)+~P6(x103,x101)
% 0.18/0.67 [11]~P5(x111)+P5(x112)+~E(x111,x112)
% 0.18/0.67 [12]~P4(x121)+P4(x122)+~E(x121,x122)
% 0.18/0.67 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133)
% 0.18/0.67 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141)
% 0.18/0.67 [15]~P3(x151)+P3(x152)+~E(x151,x152)
% 0.18/0.67 [16]~P7(x161)+P7(x162)+~E(x161,x162)
% 0.18/0.67 [17]~P8(x171)+P8(x172)+~E(x171,x172)
% 0.18/0.67
% 0.18/0.67 %-------------------------------------------
% 0.18/0.67 cnf(66,plain,
% 0.18/0.67 (~P6(f14(x661,f15(x661)),x661)),
% 0.18/0.67 inference(scs_inference,[],[46,49,2,62])).
% 0.18/0.67 cnf(71,plain,
% 0.18/0.67 (P6(x711,f14(x711,f15(x711)))),
% 0.18/0.67 inference(rename_variables,[],[49])).
% 0.18/0.67 cnf(73,plain,
% 0.18/0.67 (E(f14(x731,x731),x731)),
% 0.18/0.67 inference(rename_variables,[],[45])).
% 0.18/0.67 cnf(74,plain,
% 0.18/0.67 (~E(f14(x741,f15(x741)),f14(a1,a1))),
% 0.18/0.67 inference(scs_inference,[],[46,20,50,45,73,49,2,62,58,10,8,3])).
% 0.18/0.67 cnf(75,plain,
% 0.18/0.67 (E(f14(x751,x751),x751)),
% 0.18/0.67 inference(rename_variables,[],[45])).
% 0.18/0.67 cnf(84,plain,
% 0.18/0.67 (P3(a1)),
% 0.18/0.67 inference(scs_inference,[],[46,20,22,23,25,33,50,45,73,49,71,2,62,58,10,8,3,60,57,59,55,54])).
% 0.18/0.67 cnf(97,plain,
% 0.18/0.67 (~P2(f14(a11,f15(a11)),f14(a11,a11))),
% 0.18/0.67 inference(scs_inference,[],[46,20,21,22,23,25,33,43,50,45,73,75,49,71,2,62,58,10,8,3,60,57,59,55,54,53,64,63,7,6,5,4,17,14])).
% 0.18/0.67 cnf(100,plain,
% 0.18/0.67 (P2(f14(a6,f15(a6)),f14(a6,f15(a6)))),
% 0.18/0.67 inference(scs_inference,[],[46,20,21,22,23,25,30,33,43,50,45,73,75,49,71,2,62,58,10,8,3,60,57,59,55,54,53,64,63,7,6,5,4,17,14,61,13])).
% 0.18/0.67 cnf(111,plain,
% 0.18/0.67 (~E(f14(x1111,f15(x1111)),f14(a1,a1))),
% 0.18/0.67 inference(rename_variables,[],[74])).
% 0.18/0.67 cnf(118,plain,
% 0.18/0.67 ($false),
% 0.18/0.67 inference(scs_inference,[],[46,31,51,47,44,52,21,30,20,66,97,74,111,100,84,59,61,57,2,5,14,10,8,3,60]),
% 0.18/0.67 ['proof']).
% 0.18/0.67 % SZS output end Proof
% 0.18/0.67 % Total time :0.010000s
%------------------------------------------------------------------------------