TSTP Solution File: SEU263+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU263+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n028.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 16:18:50 EDT 2023
% Result : Theorem 0.59s 0.73s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU263+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 18:48:34 EDT 2023
% 0.22/0.36 % CPUTime :
% 0.22/0.65 start to proof:theBenchmark
% 0.59/0.72 %-------------------------------------------
% 0.59/0.72 % File :CSE---1.6
% 0.59/0.72 % Problem :theBenchmark
% 0.59/0.72 % Transform :cnf
% 0.59/0.72 % Format :tptp:raw
% 0.59/0.72 % Command :java -jar mcs_scs.jar %d %s
% 0.59/0.72
% 0.59/0.72 % Result :Theorem 0.010000s
% 0.59/0.72 % Output :CNFRefutation 0.010000s
% 0.59/0.72 %-------------------------------------------
% 0.59/0.72 %------------------------------------------------------------------------------
% 0.59/0.72 % File : SEU263+1 : TPTP v8.1.2. Released v3.3.0.
% 0.59/0.72 % Domain : Set theory
% 0.59/0.72 % Problem : MPTP bushy problem t14_relset_1
% 0.59/0.72 % Version : [Urb07] axioms : Especial.
% 0.59/0.72 % English :
% 0.59/0.72
% 0.59/0.72 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% 0.59/0.72 % : [Urb07] Urban (2006), Email to G. Sutcliffe
% 0.59/0.72 % Source : [Urb07]
% 0.59/0.72 % Names : bushy-t14_relset_1 [Urb07]
% 0.59/0.72
% 0.59/0.72 % Status : Theorem
% 0.59/0.72 % Rating : 0.00 v8.1.0, 0.07 v7.5.0, 0.10 v7.4.0, 0.00 v7.0.0, 0.07 v6.3.0, 0.15 v6.2.0, 0.09 v6.1.0, 0.16 v6.0.0, 0.25 v5.5.0, 0.21 v5.4.0, 0.26 v5.3.0, 0.30 v5.2.0, 0.07 v5.0.0, 0.15 v4.1.0, 0.17 v4.0.1, 0.26 v4.0.0, 0.25 v3.7.0, 0.14 v3.5.0, 0.25 v3.4.0, 0.00 v3.3.0
% 0.59/0.72 % Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% 0.59/0.72 % Number of atoms : 34 ( 0 equ)
% 0.59/0.72 % Maximal formula atoms : 3 ( 1 avg)
% 0.59/0.72 % Number of connectives : 14 ( 0 ~; 0 |; 3 &)
% 0.59/0.72 % ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% 0.59/0.72 % Maximal formula depth : 7 ( 4 avg)
% 0.59/0.72 % Maximal term depth : 3 ( 1 avg)
% 0.59/0.72 % Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% 0.59/0.72 % Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% 0.59/0.72 % Number of variables : 39 ( 36 !; 3 ?)
% 0.59/0.72 % SPC : FOF_THM_RFO_NEQ
% 0.59/0.72
% 0.59/0.72 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.59/0.72 % library, www.mizar.org
% 0.59/0.72 %------------------------------------------------------------------------------
% 0.59/0.72 fof(cc1_relset_1,axiom,
% 0.59/0.72 ! [A,B,C] :
% 0.59/0.72 ( element(C,powerset(cartesian_product2(A,B)))
% 0.59/0.72 => relation(C) ) ).
% 0.59/0.72
% 0.59/0.72 fof(d1_relset_1,axiom,
% 0.59/0.72 ! [A,B,C] :
% 0.59/0.72 ( relation_of2(C,A,B)
% 0.59/0.72 <=> subset(C,cartesian_product2(A,B)) ) ).
% 0.59/0.72
% 0.59/0.72 fof(dt_k1_relat_1,axiom,
% 0.59/0.72 $true ).
% 0.59/0.72
% 0.59/0.72 fof(dt_k1_zfmisc_1,axiom,
% 0.59/0.72 $true ).
% 0.59/0.72
% 0.59/0.72 fof(dt_k2_relat_1,axiom,
% 0.59/0.72 $true ).
% 0.59/0.72
% 0.59/0.72 fof(dt_k2_zfmisc_1,axiom,
% 0.59/0.72 $true ).
% 0.59/0.72
% 0.59/0.72 fof(dt_m1_relset_1,axiom,
% 0.59/0.72 $true ).
% 0.59/0.72
% 0.59/0.72 fof(dt_m1_subset_1,axiom,
% 0.59/0.72 $true ).
% 0.59/0.72
% 0.59/0.72 fof(dt_m2_relset_1,axiom,
% 0.59/0.72 ! [A,B,C] :
% 0.59/0.72 ( relation_of2_as_subset(C,A,B)
% 0.59/0.72 => element(C,powerset(cartesian_product2(A,B))) ) ).
% 0.59/0.72
% 0.59/0.72 fof(existence_m1_relset_1,axiom,
% 0.59/0.72 ! [A,B] :
% 0.59/0.72 ? [C] : relation_of2(C,A,B) ).
% 0.59/0.72
% 0.59/0.72 fof(existence_m1_subset_1,axiom,
% 0.59/0.72 ! [A] :
% 0.59/0.72 ? [B] : element(B,A) ).
% 0.59/0.72
% 0.59/0.72 fof(existence_m2_relset_1,axiom,
% 0.59/0.72 ! [A,B] :
% 0.59/0.72 ? [C] : relation_of2_as_subset(C,A,B) ).
% 0.59/0.72
% 0.59/0.72 fof(redefinition_m2_relset_1,axiom,
% 0.59/0.72 ! [A,B,C] :
% 0.59/0.72 ( relation_of2_as_subset(C,A,B)
% 0.59/0.72 <=> relation_of2(C,A,B) ) ).
% 0.59/0.72
% 0.59/0.72 fof(reflexivity_r1_tarski,axiom,
% 0.59/0.72 ! [A,B] : subset(A,A) ).
% 0.59/0.72
% 0.59/0.72 fof(t119_zfmisc_1,axiom,
% 0.59/0.72 ! [A,B,C,D] :
% 0.59/0.72 ( ( subset(A,B)
% 0.59/0.72 & subset(C,D) )
% 0.59/0.72 => subset(cartesian_product2(A,C),cartesian_product2(B,D)) ) ).
% 0.59/0.72
% 0.59/0.72 fof(t12_relset_1,axiom,
% 0.59/0.72 ! [A,B,C] :
% 0.59/0.72 ( relation_of2_as_subset(C,A,B)
% 0.59/0.72 => ( subset(relation_dom(C),A)
% 0.59/0.72 & subset(relation_rng(C),B) ) ) ).
% 0.59/0.72
% 0.59/0.72 fof(t14_relset_1,conjecture,
% 0.59/0.72 ! [A,B,C,D] :
% 0.59/0.72 ( relation_of2_as_subset(D,C,A)
% 0.59/0.72 => ( subset(relation_rng(D),B)
% 0.59/0.72 => relation_of2_as_subset(D,C,B) ) ) ).
% 0.59/0.72
% 0.59/0.72 fof(t1_xboole_1,axiom,
% 0.59/0.73 ! [A,B,C] :
% 0.59/0.73 ( ( subset(A,B)
% 0.59/0.73 & subset(B,C) )
% 0.59/0.73 => subset(A,C) ) ).
% 0.59/0.73
% 0.59/0.73 fof(t21_relat_1,axiom,
% 0.59/0.73 ! [A] :
% 0.59/0.73 ( relation(A)
% 0.59/0.73 => subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ) ).
% 0.59/0.73
% 0.59/0.73 fof(t3_subset,axiom,
% 0.59/0.73 ! [A,B] :
% 0.59/0.73 ( element(A,powerset(B))
% 0.59/0.73 <=> subset(A,B) ) ).
% 0.59/0.73
% 0.59/0.73 %------------------------------------------------------------------------------
% 0.59/0.73 %-------------------------------------------
% 0.59/0.73 % Proof found
% 0.59/0.73 % SZS status Theorem for theBenchmark
% 0.59/0.73 % SZS output start Proof
% 0.59/0.73 %ClaNum:20(EqnAxiom:0)
% 0.59/0.73 %VarNum:82(SingletonVarNum:42)
% 0.59/0.73 %MaxLitNum:3
% 0.59/0.73 %MaxfuncDepth:2
% 0.59/0.73 %SharedTerms:8
% 0.59/0.73 %goalClause: 2 4 7
% 0.59/0.73 %singleGoalClaCount:3
% 0.59/0.73 [4]P3(a1,a8,a6)
% 0.59/0.73 [7]~P3(a1,a8,a2)
% 0.59/0.73 [2]P1(f9(a1),a2)
% 0.59/0.73 [1]P1(x11,x11)
% 0.59/0.73 [3]P2(f3(x31),x31)
% 0.59/0.73 [5]P4(f4(x51,x52),x51,x52)
% 0.59/0.73 [6]P3(f7(x61,x62),x61,x62)
% 0.59/0.73 [11]~P5(x111)+P1(x111,f5(f11(x111),f9(x111)))
% 0.59/0.73 [8]~P1(x81,x82)+P2(x81,f10(x82))
% 0.59/0.73 [9]P1(x91,x92)+~P2(x91,f10(x92))
% 0.59/0.73 [18]~P3(x181,x182,x183)+P4(x181,x182,x183)
% 0.59/0.73 [19]~P4(x191,x192,x193)+P3(x191,x192,x193)
% 0.59/0.73 [12]~P3(x121,x122,x123)+P1(f11(x121),x122)
% 0.59/0.73 [13]~P3(x131,x133,x132)+P1(f9(x131),x132)
% 0.59/0.73 [16]P4(x161,x162,x163)+~P1(x161,f5(x162,x163))
% 0.59/0.73 [17]~P4(x171,x172,x173)+P1(x171,f5(x172,x173))
% 0.59/0.73 [15]P5(x151)+~P2(x151,f10(f5(x152,x153)))
% 0.59/0.73 [20]~P3(x201,x202,x203)+P2(x201,f10(f5(x202,x203)))
% 0.59/0.73 [10]~P1(x101,x103)+P1(x101,x102)+~P1(x103,x102)
% 0.59/0.73 [14]~P1(x142,x144)+~P1(x141,x143)+P1(f5(x141,x142),f5(x143,x144))
% 0.59/0.73 %EqnAxiom
% 0.59/0.73
% 0.59/0.73 %-------------------------------------------
% 0.59/0.73 cnf(21,plain,
% 0.59/0.73 (~P4(a1,a8,a2)),
% 0.59/0.73 inference(scs_inference,[],[7,19])).
% 0.59/0.73 cnf(30,plain,
% 0.59/0.73 (P1(f11(a1),a8)),
% 0.59/0.73 inference(scs_inference,[],[1,4,7,3,19,9,16,18,13,12])).
% 0.59/0.73 cnf(34,plain,
% 0.59/0.73 (P2(a1,f10(f5(a8,a6)))),
% 0.59/0.73 inference(scs_inference,[],[2,1,4,7,3,19,9,16,18,13,12,8,20])).
% 0.59/0.73 cnf(38,plain,
% 0.59/0.73 (P1(f5(f9(a1),f9(a1)),f5(a2,a2))),
% 0.59/0.73 inference(scs_inference,[],[2,1,4,7,5,3,19,9,16,18,13,12,8,20,17,14])).
% 0.59/0.73 cnf(40,plain,
% 0.59/0.73 (P5(a1)),
% 0.59/0.73 inference(scs_inference,[],[2,1,4,7,5,3,19,9,16,18,13,12,8,20,17,14,15])).
% 0.59/0.73 cnf(50,plain,
% 0.59/0.73 (~P1(f5(f11(a1),f9(a1)),f5(a8,a2))),
% 0.59/0.73 inference(scs_inference,[],[2,1,5,21,40,11,19,16,14,10])).
% 0.59/0.73 cnf(64,plain,
% 0.59/0.73 ($false),
% 0.59/0.73 inference(scs_inference,[],[6,38,50,30,34,2,9,18,16,14]),
% 0.59/0.73 ['proof']).
% 0.59/0.73 % SZS output end Proof
% 0.59/0.73 % Total time :0.010000s
%------------------------------------------------------------------------------