TSTP Solution File: SEU200+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU200+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n023.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 16:18:20 EDT 2023
% Result : Theorem 0.52s 0.68s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU200+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n023.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 : Thu Aug 24 01:54:27 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.46/0.57 start to proof:theBenchmark
% 0.52/0.67 %-------------------------------------------
% 0.52/0.67 % File :CSE---1.6
% 0.52/0.67 % Problem :theBenchmark
% 0.52/0.67 % Transform :cnf
% 0.52/0.67 % Format :tptp:raw
% 0.52/0.67 % Command :java -jar mcs_scs.jar %d %s
% 0.52/0.67
% 0.52/0.67 % Result :Theorem 0.050000s
% 0.52/0.67 % Output :CNFRefutation 0.050000s
% 0.52/0.67 %-------------------------------------------
% 0.52/0.68 %------------------------------------------------------------------------------
% 0.52/0.68 % File : SEU200+1 : TPTP v8.1.2. Released v3.3.0.
% 0.52/0.68 % Domain : Set theory
% 0.52/0.68 % Problem : MPTP bushy problem t118_relat_1
% 0.52/0.68 % Version : [Urb07] axioms : Especial.
% 0.52/0.68 % English :
% 0.52/0.68
% 0.52/0.68 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% 0.52/0.68 % : [Urb07] Urban (2006), Email to G. Sutcliffe
% 0.52/0.68 % Source : [Urb07]
% 0.52/0.68 % Names : bushy-t118_relat_1 [Urb07]
% 0.52/0.68
% 0.52/0.68 % Status : Theorem
% 0.52/0.68 % Rating : 0.03 v8.1.0, 0.00 v6.4.0, 0.04 v6.1.0, 0.07 v6.0.0, 0.04 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.1.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.1, 0.17 v4.0.0, 0.21 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0
% 0.52/0.68 % Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% 0.52/0.68 % Number of atoms : 69 ( 2 equ)
% 0.52/0.68 % Maximal formula atoms : 5 ( 2 avg)
% 0.52/0.68 % Number of connectives : 49 ( 14 ~; 1 |; 16 &)
% 0.52/0.68 % ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% 0.52/0.68 % Maximal formula depth : 7 ( 4 avg)
% 0.52/0.68 % Maximal term depth : 3 ( 1 avg)
% 0.52/0.68 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% 0.52/0.68 % Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% 0.52/0.68 % Number of variables : 45 ( 38 !; 7 ?)
% 0.52/0.68 % SPC : FOF_THM_RFO_SEQ
% 0.52/0.68
% 0.52/0.68 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.52/0.68 % library, www.mizar.org
% 0.52/0.68 %------------------------------------------------------------------------------
% 0.52/0.68 fof(antisymmetry_r2_hidden,axiom,
% 0.52/0.68 ! [A,B] :
% 0.52/0.68 ( in(A,B)
% 0.52/0.68 => ~ in(B,A) ) ).
% 0.52/0.68
% 0.52/0.68 fof(cc1_relat_1,axiom,
% 0.52/0.68 ! [A] :
% 0.52/0.68 ( empty(A)
% 0.52/0.68 => relation(A) ) ).
% 0.52/0.68
% 0.52/0.68 fof(dt_k1_relat_1,axiom,
% 0.52/0.68 $true ).
% 0.52/0.68
% 0.52/0.68 fof(dt_k1_xboole_0,axiom,
% 0.52/0.68 $true ).
% 0.52/0.68
% 0.52/0.68 fof(dt_k1_zfmisc_1,axiom,
% 0.52/0.68 $true ).
% 0.52/0.68
% 0.52/0.68 fof(dt_k2_relat_1,axiom,
% 0.52/0.68 $true ).
% 0.52/0.68
% 0.52/0.68 fof(dt_k8_relat_1,axiom,
% 0.52/0.68 ! [A,B] :
% 0.52/0.68 ( relation(B)
% 0.52/0.68 => relation(relation_rng_restriction(A,B)) ) ).
% 0.52/0.68
% 0.52/0.68 fof(dt_m1_subset_1,axiom,
% 0.52/0.68 $true ).
% 0.52/0.68
% 0.52/0.68 fof(existence_m1_subset_1,axiom,
% 0.52/0.68 ! [A] :
% 0.52/0.68 ? [B] : element(B,A) ).
% 0.52/0.68
% 0.52/0.68 fof(fc1_subset_1,axiom,
% 0.52/0.68 ! [A] : ~ empty(powerset(A)) ).
% 0.52/0.68
% 0.52/0.68 fof(fc1_xboole_0,axiom,
% 0.52/0.68 empty(empty_set) ).
% 0.52/0.68
% 0.52/0.68 fof(fc4_relat_1,axiom,
% 0.52/0.68 ( empty(empty_set)
% 0.52/0.68 & relation(empty_set) ) ).
% 0.52/0.68
% 0.52/0.68 fof(fc5_relat_1,axiom,
% 0.52/0.68 ! [A] :
% 0.52/0.68 ( ( ~ empty(A)
% 0.52/0.68 & relation(A) )
% 0.52/0.68 => ~ empty(relation_dom(A)) ) ).
% 0.52/0.68
% 0.52/0.68 fof(fc6_relat_1,axiom,
% 0.52/0.68 ! [A] :
% 0.52/0.68 ( ( ~ empty(A)
% 0.52/0.68 & relation(A) )
% 0.52/0.68 => ~ empty(relation_rng(A)) ) ).
% 0.52/0.68
% 0.52/0.68 fof(fc7_relat_1,axiom,
% 0.52/0.68 ! [A] :
% 0.52/0.68 ( empty(A)
% 0.52/0.68 => ( empty(relation_dom(A))
% 0.52/0.68 & relation(relation_dom(A)) ) ) ).
% 0.52/0.68
% 0.52/0.68 fof(fc8_relat_1,axiom,
% 0.52/0.68 ! [A] :
% 0.52/0.68 ( empty(A)
% 0.52/0.68 => ( empty(relation_rng(A))
% 0.52/0.68 & relation(relation_rng(A)) ) ) ).
% 0.52/0.68
% 0.52/0.68 fof(rc1_relat_1,axiom,
% 0.52/0.68 ? [A] :
% 0.52/0.68 ( empty(A)
% 0.52/0.68 & relation(A) ) ).
% 0.52/0.68
% 0.52/0.68 fof(rc1_subset_1,axiom,
% 0.52/0.68 ! [A] :
% 0.52/0.68 ( ~ empty(A)
% 0.52/0.68 => ? [B] :
% 0.52/0.68 ( element(B,powerset(A))
% 0.52/0.68 & ~ empty(B) ) ) ).
% 0.52/0.68
% 0.52/0.68 fof(rc1_xboole_0,axiom,
% 0.52/0.68 ? [A] : empty(A) ).
% 0.52/0.68
% 0.52/0.68 fof(rc2_relat_1,axiom,
% 0.52/0.68 ? [A] :
% 0.52/0.68 ( ~ empty(A)
% 0.52/0.68 & relation(A) ) ).
% 0.52/0.68
% 0.52/0.68 fof(rc2_subset_1,axiom,
% 0.52/0.68 ! [A] :
% 0.52/0.68 ? [B] :
% 0.52/0.68 ( element(B,powerset(A))
% 0.52/0.68 & empty(B) ) ).
% 0.52/0.68
% 0.52/0.68 fof(rc2_xboole_0,axiom,
% 0.52/0.68 ? [A] : ~ empty(A) ).
% 0.52/0.68
% 0.52/0.68 fof(reflexivity_r1_tarski,axiom,
% 0.52/0.68 ! [A,B] : subset(A,A) ).
% 0.52/0.68
% 0.52/0.68 fof(t117_relat_1,axiom,
% 0.52/0.68 ! [A,B] :
% 0.52/0.68 ( relation(B)
% 0.52/0.68 => subset(relation_rng_restriction(A,B),B) ) ).
% 0.52/0.68
% 0.52/0.68 fof(t118_relat_1,conjecture,
% 0.52/0.68 ! [A,B] :
% 0.52/0.68 ( relation(B)
% 0.52/0.68 => subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ) ).
% 0.52/0.68
% 0.52/0.68 fof(t1_subset,axiom,
% 0.52/0.68 ! [A,B] :
% 0.52/0.68 ( in(A,B)
% 0.52/0.68 => element(A,B) ) ).
% 0.52/0.68
% 0.52/0.68 fof(t25_relat_1,axiom,
% 0.52/0.68 ! [A] :
% 0.52/0.68 ( relation(A)
% 0.52/0.68 => ! [B] :
% 0.52/0.68 ( relation(B)
% 0.52/0.68 => ( subset(A,B)
% 0.52/0.68 => ( subset(relation_dom(A),relation_dom(B))
% 0.52/0.68 & subset(relation_rng(A),relation_rng(B)) ) ) ) ) ).
% 0.52/0.68
% 0.52/0.68 fof(t2_subset,axiom,
% 0.52/0.68 ! [A,B] :
% 0.52/0.68 ( element(A,B)
% 0.52/0.68 => ( empty(B)
% 0.52/0.68 | in(A,B) ) ) ).
% 0.52/0.68
% 0.52/0.68 fof(t3_subset,axiom,
% 0.52/0.68 ! [A,B] :
% 0.52/0.68 ( element(A,powerset(B))
% 0.52/0.68 <=> subset(A,B) ) ).
% 0.52/0.68
% 0.52/0.68 fof(t4_subset,axiom,
% 0.52/0.68 ! [A,B,C] :
% 0.52/0.68 ( ( in(A,B)
% 0.52/0.68 & element(B,powerset(C)) )
% 0.52/0.68 => element(A,C) ) ).
% 0.52/0.68
% 0.52/0.68 fof(t5_subset,axiom,
% 0.52/0.68 ! [A,B,C] :
% 0.52/0.68 ~ ( in(A,B)
% 0.52/0.68 & element(B,powerset(C))
% 0.52/0.68 & empty(C) ) ).
% 0.52/0.68
% 0.52/0.68 fof(t6_boole,axiom,
% 0.52/0.68 ! [A] :
% 0.52/0.68 ( empty(A)
% 0.52/0.68 => A = empty_set ) ).
% 0.52/0.68
% 0.52/0.68 fof(t7_boole,axiom,
% 0.52/0.68 ! [A,B] :
% 0.52/0.68 ~ ( in(A,B)
% 0.52/0.68 & empty(B) ) ).
% 0.52/0.68
% 0.52/0.68 fof(t8_boole,axiom,
% 0.52/0.68 ! [A,B] :
% 0.52/0.68 ~ ( empty(A)
% 0.52/0.68 & A != B
% 0.52/0.68 & empty(B) ) ).
% 0.52/0.68
% 0.52/0.68 %------------------------------------------------------------------------------
% 0.52/0.68 %-------------------------------------------
% 0.52/0.68 % Proof found
% 0.52/0.68 % SZS status Theorem for theBenchmark
% 0.52/0.68 % SZS output start Proof
% 0.52/0.68 %ClaNum:58(EqnAxiom:19)
% 0.52/0.68 %VarNum:89(SingletonVarNum:43)
% 0.52/0.68 %MaxLitNum:4
% 0.52/0.68 %MaxfuncDepth:2
% 0.52/0.68 %SharedTerms:20
% 0.52/0.68 %goalClause: 27 35
% 0.52/0.68 %singleGoalClaCount:2
% 0.52/0.68 [21]P1(a1)
% 0.52/0.68 [22]P1(a2)
% 0.52/0.68 [23]P1(a4)
% 0.52/0.68 [24]P3(a1)
% 0.52/0.68 [25]P3(a2)
% 0.52/0.68 [26]P3(a6)
% 0.52/0.68 [27]P3(a7)
% 0.52/0.68 [32]~P1(a6)
% 0.52/0.68 [33]~P1(a9)
% 0.52/0.68 [35]~P5(f13(f12(a10,a7)),f13(a7))
% 0.52/0.68 [29]P5(x291,x291)
% 0.52/0.68 [28]P1(f8(x281))
% 0.52/0.68 [30]P2(f3(x301),x301)
% 0.52/0.68 [31]P2(f8(x311),f11(x311))
% 0.52/0.68 [34]~P1(f11(x341))
% 0.52/0.68 [36]~P1(x361)+E(x361,a1)
% 0.52/0.68 [37]~P1(x371)+P3(x371)
% 0.52/0.68 [39]~P1(x391)+P1(f14(x391))
% 0.52/0.68 [40]~P1(x401)+P1(f13(x401))
% 0.52/0.68 [41]~P1(x411)+P3(f14(x411))
% 0.52/0.68 [42]~P1(x421)+P3(f13(x421))
% 0.52/0.68 [43]P1(x431)+~P1(f5(x431))
% 0.52/0.68 [47]P1(x471)+P2(f5(x471),f11(x471))
% 0.52/0.68 [46]~P1(x461)+~P4(x462,x461)
% 0.52/0.68 [48]~P4(x481,x482)+P2(x481,x482)
% 0.52/0.68 [52]~P4(x522,x521)+~P4(x521,x522)
% 0.52/0.68 [49]~P3(x492)+P3(f12(x491,x492))
% 0.52/0.68 [51]~P5(x511,x512)+P2(x511,f11(x512))
% 0.52/0.68 [53]P5(x531,x532)+~P2(x531,f11(x532))
% 0.52/0.68 [54]~P3(x542)+P5(f12(x541,x542),x542)
% 0.52/0.68 [44]~P3(x441)+P1(x441)+~P1(f14(x441))
% 0.52/0.68 [45]~P3(x451)+P1(x451)+~P1(f13(x451))
% 0.52/0.68 [38]~P1(x382)+~P1(x381)+E(x381,x382)
% 0.52/0.68 [50]~P2(x502,x501)+P1(x501)+P4(x502,x501)
% 0.52/0.68 [55]~P1(x551)+~P4(x552,x553)+~P2(x553,f11(x551))
% 0.52/0.68 [58]P2(x581,x582)+~P4(x581,x583)+~P2(x583,f11(x582))
% 0.52/0.68 [56]~P3(x562)+~P3(x561)+~P5(x561,x562)+P5(f14(x561),f14(x562))
% 0.52/0.68 [57]~P3(x572)+~P3(x571)+~P5(x571,x572)+P5(f13(x571),f13(x572))
% 0.52/0.68 %EqnAxiom
% 0.52/0.68 [1]E(x11,x11)
% 0.52/0.68 [2]E(x22,x21)+~E(x21,x22)
% 0.52/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.52/0.69 [4]~E(x41,x42)+E(f8(x41),f8(x42))
% 0.52/0.69 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 0.52/0.69 [6]~E(x61,x62)+E(f11(x61),f11(x62))
% 0.52/0.69 [7]~E(x71,x72)+E(f13(x71),f13(x72))
% 0.52/0.69 [8]~E(x81,x82)+E(f12(x81,x83),f12(x82,x83))
% 0.52/0.69 [9]~E(x91,x92)+E(f12(x93,x91),f12(x93,x92))
% 0.52/0.69 [10]~E(x101,x102)+E(f14(x101),f14(x102))
% 0.52/0.69 [11]~E(x111,x112)+E(f5(x111),f5(x112))
% 0.52/0.69 [12]~P1(x121)+P1(x122)+~E(x121,x122)
% 0.52/0.69 [13]P2(x132,x133)+~E(x131,x132)+~P2(x131,x133)
% 0.52/0.69 [14]P2(x143,x142)+~E(x141,x142)+~P2(x143,x141)
% 0.52/0.69 [15]P4(x152,x153)+~E(x151,x152)+~P4(x151,x153)
% 0.52/0.69 [16]P4(x163,x162)+~E(x161,x162)+~P4(x163,x161)
% 0.52/0.69 [17]~P3(x171)+P3(x172)+~E(x171,x172)
% 0.52/0.69 [18]P5(x182,x183)+~E(x181,x182)+~P5(x181,x183)
% 0.52/0.69 [19]P5(x193,x192)+~E(x191,x192)+~P5(x193,x191)
% 0.52/0.69
% 0.52/0.69 %-------------------------------------------
% 0.52/0.69 cnf(61,plain,
% 0.52/0.69 (P2(f3(x611),x611)),
% 0.52/0.69 inference(rename_variables,[],[30])).
% 0.52/0.69 cnf(63,plain,
% 0.52/0.69 (~E(f13(f12(a10,a7)),f13(a7))),
% 0.52/0.69 inference(scs_inference,[],[29,21,35,30,46,53,19])).
% 0.52/0.69 cnf(64,plain,
% 0.52/0.69 (P5(x641,x641)),
% 0.52/0.69 inference(rename_variables,[],[29])).
% 0.52/0.69 cnf(66,plain,
% 0.52/0.69 (P5(x661,x661)),
% 0.52/0.69 inference(rename_variables,[],[29])).
% 0.52/0.69 cnf(67,plain,
% 0.52/0.69 (P4(f3(a6),a6)),
% 0.52/0.69 inference(scs_inference,[],[29,64,21,32,35,30,61,46,53,19,18,50])).
% 0.52/0.69 cnf(68,plain,
% 0.52/0.69 (P2(f3(x681),x681)),
% 0.52/0.69 inference(rename_variables,[],[30])).
% 0.52/0.69 cnf(70,plain,
% 0.52/0.69 (~P4(x701,f3(f11(a1)))),
% 0.52/0.69 inference(scs_inference,[],[29,64,21,32,35,30,61,68,46,53,19,18,50,55])).
% 0.52/0.69 cnf(73,plain,
% 0.52/0.69 (~P4(a6,f3(a6))),
% 0.52/0.69 inference(scs_inference,[],[29,64,21,32,35,30,61,68,46,53,19,18,50,55,52])).
% 0.52/0.69 cnf(79,plain,
% 0.52/0.69 (P5(f12(x791,a7),a7)),
% 0.52/0.69 inference(scs_inference,[],[27,29,64,21,22,23,32,35,30,61,68,46,53,19,18,50,55,52,37,36,54])).
% 0.52/0.69 cnf(81,plain,
% 0.52/0.69 (P2(x811,f11(x811))),
% 0.52/0.69 inference(scs_inference,[],[27,29,64,66,21,22,23,32,35,30,61,68,46,53,19,18,50,55,52,37,36,54,51])).
% 0.52/0.69 cnf(83,plain,
% 0.52/0.69 (P3(f12(x831,a7))),
% 0.52/0.69 inference(scs_inference,[],[27,29,64,66,21,22,23,32,35,30,61,68,46,53,19,18,50,55,52,37,36,54,51,49])).
% 0.52/0.69 cnf(95,plain,
% 0.52/0.69 (E(f5(a2),f5(a1))),
% 0.52/0.69 inference(scs_inference,[],[27,29,64,66,21,22,23,32,35,30,61,68,46,53,19,18,50,55,52,37,36,54,51,49,43,42,41,40,39,11])).
% 0.52/0.69 cnf(97,plain,
% 0.52/0.69 (E(f12(x971,a2),f12(x971,a1))),
% 0.52/0.69 inference(scs_inference,[],[27,29,64,66,21,22,23,32,35,30,61,68,46,53,19,18,50,55,52,37,36,54,51,49,43,42,41,40,39,11,10,9])).
% 0.52/0.69 cnf(98,plain,
% 0.52/0.69 (E(f12(a2,x981),f12(a1,x981))),
% 0.52/0.69 inference(scs_inference,[],[27,29,64,66,21,22,23,32,35,30,61,68,46,53,19,18,50,55,52,37,36,54,51,49,43,42,41,40,39,11,10,9,8])).
% 0.52/0.69 cnf(100,plain,
% 0.52/0.69 (E(f11(a2),f11(a1))),
% 0.52/0.69 inference(scs_inference,[],[27,29,64,66,21,22,23,32,35,30,61,68,46,53,19,18,50,55,52,37,36,54,51,49,43,42,41,40,39,11,10,9,8,7,6])).
% 0.52/0.69 cnf(107,plain,
% 0.52/0.69 (~E(a1,a6)),
% 0.52/0.69 inference(scs_inference,[],[27,29,64,66,21,22,23,32,35,30,61,68,46,53,19,18,50,55,52,37,36,54,51,49,43,42,41,40,39,11,10,9,8,7,6,5,4,47,17,16,12])).
% 0.52/0.69 cnf(123,plain,
% 0.52/0.69 (~P4(x1231,f3(f11(a1)))),
% 0.52/0.69 inference(rename_variables,[],[70])).
% 0.52/0.69 cnf(133,plain,
% 0.52/0.69 (P2(f8(x1331),f11(x1331))),
% 0.52/0.69 inference(rename_variables,[],[31])).
% 0.52/0.69 cnf(141,plain,
% 0.52/0.69 (P5(x1411,x1411)),
% 0.52/0.69 inference(rename_variables,[],[29])).
% 0.52/0.69 cnf(152,plain,
% 0.52/0.69 (~E(f8(f13(a7)),f13(f12(a10,a7)))),
% 0.52/0.69 inference(scs_inference,[],[27,33,28,31,133,29,141,30,35,81,70,123,63,83,95,97,98,100,79,67,73,107,50,55,53,51,14,3,58,18,12,7,2,15,48,57,19,16,13])).
% 0.52/0.69 cnf(165,plain,
% 0.52/0.69 ($false),
% 0.52/0.69 inference(scs_inference,[],[35,28,152,79,83,27,38,40,57]),
% 0.52/0.69 ['proof']).
% 0.52/0.69 % SZS output end Proof
% 0.52/0.69 % Total time :0.050000s
%------------------------------------------------------------------------------