TSTP Solution File: SEU010+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU010+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 : n016.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 16:17:11 EDT 2023
% Result : Theorem 0.21s 0.64s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU010+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.17/0.36 % Computer : n016.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Wed Aug 23 20:04:08 EDT 2023
% 0.17/0.36 % CPUTime :
% 0.21/0.55 start to proof:theBenchmark
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 % File :CSE---1.6
% 0.21/0.62 % Problem :theBenchmark
% 0.21/0.62 % Transform :cnf
% 0.21/0.62 % Format :tptp:raw
% 0.21/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.62
% 0.21/0.62 % Result :Theorem 0.010000s
% 0.21/0.62 % Output :CNFRefutation 0.010000s
% 0.21/0.62 %-------------------------------------------
% 0.21/0.63 %------------------------------------------------------------------------------
% 0.21/0.63 % File : SEU010+1 : TPTP v8.1.2. Released v3.2.0.
% 0.21/0.63 % Domain : Set theory
% 0.21/0.63 % Problem : Functions and their basic properties, theorem 42
% 0.21/0.63 % Version : [Urb06] axioms : Especial.
% 0.21/0.63 % English :
% 0.21/0.63
% 0.21/0.63 % Refs : [Byl90] Bylinski (1990), Functions and Their Basic Properties
% 0.21/0.63 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.21/0.63 % Source : [Urb06]
% 0.21/0.63 % Names : funct_1__t42_funct_1 [Urb06]
% 0.21/0.63
% 0.21/0.63 % Status : Theorem
% 0.21/0.63 % Rating : 0.11 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.03 v7.3.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.27 v6.0.0, 0.22 v5.5.0, 0.30 v5.4.0, 0.32 v5.3.0, 0.37 v5.2.0, 0.20 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.30 v4.0.1, 0.26 v4.0.0, 0.25 v3.7.0, 0.15 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.14 v3.2.0
% 0.21/0.63 % Syntax : Number of formulae : 38 ( 7 unt; 0 def)
% 0.21/0.63 % Number of atoms : 92 ( 6 equ)
% 0.21/0.63 % Maximal formula atoms : 6 ( 2 avg)
% 0.21/0.63 % Number of connectives : 68 ( 14 ~; 1 |; 31 &)
% 0.21/0.63 % ( 1 <=>; 21 =>; 0 <=; 0 <~>)
% 0.21/0.63 % Maximal formula depth : 7 ( 4 avg)
% 0.21/0.63 % Maximal term depth : 4 ( 1 avg)
% 0.21/0.63 % Number of predicates : 8 ( 7 usr; 0 prp; 1-2 aty)
% 0.21/0.63 % Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% 0.21/0.63 % Number of variables : 55 ( 46 !; 9 ?)
% 0.21/0.63 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.63
% 0.21/0.63 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.21/0.63 % library, www.mizar.org
% 0.21/0.63 %------------------------------------------------------------------------------
% 0.21/0.63 fof(antisymmetry_r2_hidden,axiom,
% 0.21/0.63 ! [A,B] :
% 0.21/0.63 ( in(A,B)
% 0.21/0.63 => ~ in(B,A) ) ).
% 0.21/0.63
% 0.21/0.63 fof(fc4_relat_1,axiom,
% 0.21/0.63 ( empty(empty_set)
% 0.21/0.63 & relation(empty_set) ) ).
% 0.21/0.63
% 0.21/0.63 fof(fc12_relat_1,axiom,
% 0.21/0.63 ( empty(empty_set)
% 0.21/0.63 & relation(empty_set)
% 0.21/0.63 & relation_empty_yielding(empty_set) ) ).
% 0.21/0.63
% 0.21/0.63 fof(fc1_xboole_0,axiom,
% 0.21/0.63 empty(empty_set) ).
% 0.21/0.63
% 0.21/0.63 fof(t1_subset,axiom,
% 0.21/0.63 ! [A,B] :
% 0.21/0.63 ( in(A,B)
% 0.21/0.63 => element(A,B) ) ).
% 0.21/0.63
% 0.21/0.63 fof(t4_subset,axiom,
% 0.21/0.63 ! [A,B,C] :
% 0.21/0.63 ( ( in(A,B)
% 0.21/0.63 & element(B,powerset(C)) )
% 0.21/0.63 => element(A,C) ) ).
% 0.21/0.63
% 0.21/0.63 fof(t5_subset,axiom,
% 0.21/0.63 ! [A,B,C] :
% 0.21/0.63 ~ ( in(A,B)
% 0.21/0.63 & element(B,powerset(C))
% 0.21/0.63 & empty(C) ) ).
% 0.21/0.63
% 0.21/0.63 fof(existence_m1_subset_1,axiom,
% 0.21/0.63 ! [A] :
% 0.21/0.63 ? [B] : element(B,A) ).
% 0.21/0.63
% 0.21/0.63 fof(cc1_funct_1,axiom,
% 0.21/0.63 ! [A] :
% 0.21/0.63 ( empty(A)
% 0.21/0.63 => function(A) ) ).
% 0.21/0.63
% 0.21/0.63 fof(fc1_subset_1,axiom,
% 0.21/0.63 ! [A] : ~ empty(powerset(A)) ).
% 0.21/0.63
% 0.21/0.63 fof(fc5_relat_1,axiom,
% 0.21/0.63 ! [A] :
% 0.21/0.63 ( ( ~ empty(A)
% 0.21/0.63 & relation(A) )
% 0.21/0.63 => ~ empty(relation_dom(A)) ) ).
% 0.21/0.63
% 0.21/0.63 fof(fc6_relat_1,axiom,
% 0.21/0.63 ! [A] :
% 0.21/0.63 ( ( ~ empty(A)
% 0.21/0.63 & relation(A) )
% 0.21/0.63 => ~ empty(relation_rng(A)) ) ).
% 0.21/0.63
% 0.21/0.63 fof(fc7_relat_1,axiom,
% 0.21/0.63 ! [A] :
% 0.21/0.63 ( empty(A)
% 0.21/0.63 => ( empty(relation_dom(A))
% 0.21/0.63 & relation(relation_dom(A)) ) ) ).
% 0.21/0.63
% 0.21/0.63 fof(fc8_relat_1,axiom,
% 0.21/0.63 ! [A] :
% 0.21/0.63 ( empty(A)
% 0.21/0.63 => ( empty(relation_rng(A))
% 0.21/0.63 & relation(relation_rng(A)) ) ) ).
% 0.21/0.63
% 0.21/0.63 fof(fc9_relat_1,axiom,
% 0.21/0.63 ! [A,B] :
% 0.21/0.63 ( ( empty(A)
% 0.21/0.63 & relation(B) )
% 0.21/0.63 => ( empty(relation_composition(A,B))
% 0.21/0.63 & relation(relation_composition(A,B)) ) ) ).
% 0.21/0.63
% 0.21/0.63 fof(fc10_relat_1,axiom,
% 0.21/0.63 ! [A,B] :
% 0.21/0.63 ( ( empty(A)
% 0.21/0.63 & relation(B) )
% 0.21/0.63 => ( empty(relation_composition(B,A))
% 0.21/0.63 & relation(relation_composition(B,A)) ) ) ).
% 0.21/0.63
% 0.21/0.63 fof(cc1_relat_1,axiom,
% 0.21/0.63 ! [A] :
% 0.21/0.63 ( empty(A)
% 0.21/0.63 => relation(A) ) ).
% 0.21/0.63
% 0.21/0.63 fof(t2_subset,axiom,
% 0.21/0.63 ! [A,B] :
% 0.21/0.63 ( element(A,B)
% 0.21/0.63 => ( empty(B)
% 0.21/0.63 | in(A,B) ) ) ).
% 0.21/0.63
% 0.21/0.63 fof(t6_boole,axiom,
% 0.21/0.63 ! [A] :
% 0.21/0.63 ( empty(A)
% 0.21/0.63 => A = empty_set ) ).
% 0.21/0.63
% 0.21/0.63 fof(t7_boole,axiom,
% 0.21/0.63 ! [A,B] :
% 0.21/0.63 ~ ( in(A,B)
% 0.21/0.63 & empty(B) ) ).
% 0.21/0.63
% 0.21/0.63 fof(t8_boole,axiom,
% 0.21/0.63 ! [A,B] :
% 0.21/0.63 ~ ( empty(A)
% 0.21/0.63 & A != B
% 0.21/0.63 & empty(B) ) ).
% 0.21/0.63
% 0.21/0.63 fof(reflexivity_r1_tarski,axiom,
% 0.21/0.63 ! [A,B] : subset(A,A) ).
% 0.21/0.63
% 0.21/0.63 fof(dt_k5_relat_1,axiom,
% 0.21/0.63 ! [A,B] :
% 0.21/0.63 ( ( relation(A)
% 0.21/0.63 & relation(B) )
% 0.21/0.63 => relation(relation_composition(A,B)) ) ).
% 0.21/0.63
% 0.21/0.63 fof(dt_k6_relat_1,axiom,
% 0.21/0.63 ! [A] : relation(identity_relation(A)) ).
% 0.21/0.63
% 0.21/0.63 fof(fc1_funct_1,axiom,
% 0.21/0.63 ! [A,B] :
% 0.21/0.63 ( ( relation(A)
% 0.21/0.63 & function(A)
% 0.21/0.63 & relation(B)
% 0.21/0.63 & function(B) )
% 0.21/0.63 => ( relation(relation_composition(A,B))
% 0.21/0.63 & function(relation_composition(A,B)) ) ) ).
% 0.21/0.63
% 0.21/0.63 fof(fc2_funct_1,axiom,
% 0.21/0.63 ! [A] :
% 0.21/0.63 ( relation(identity_relation(A))
% 0.21/0.63 & function(identity_relation(A)) ) ).
% 0.21/0.63
% 0.21/0.63 fof(rc1_funct_1,axiom,
% 0.21/0.63 ? [A] :
% 0.21/0.63 ( relation(A)
% 0.21/0.63 & function(A) ) ).
% 0.21/0.63
% 0.21/0.63 fof(rc1_subset_1,axiom,
% 0.21/0.63 ! [A] :
% 0.21/0.63 ( ~ empty(A)
% 0.21/0.63 => ? [B] :
% 0.21/0.63 ( element(B,powerset(A))
% 0.21/0.63 & ~ empty(B) ) ) ).
% 0.21/0.63
% 0.21/0.63 fof(rc2_subset_1,axiom,
% 0.21/0.63 ! [A] :
% 0.21/0.63 ? [B] :
% 0.21/0.63 ( element(B,powerset(A))
% 0.21/0.63 & empty(B) ) ).
% 0.21/0.63
% 0.21/0.63 fof(rc1_relat_1,axiom,
% 0.21/0.63 ? [A] :
% 0.21/0.63 ( empty(A)
% 0.21/0.63 & relation(A) ) ).
% 0.21/0.63
% 0.21/0.63 fof(rc2_relat_1,axiom,
% 0.21/0.63 ? [A] :
% 0.21/0.63 ( ~ empty(A)
% 0.21/0.63 & relation(A) ) ).
% 0.21/0.63
% 0.21/0.63 fof(rc3_relat_1,axiom,
% 0.21/0.63 ? [A] :
% 0.21/0.63 ( relation(A)
% 0.21/0.63 & relation_empty_yielding(A) ) ).
% 0.21/0.63
% 0.21/0.63 fof(rc1_xboole_0,axiom,
% 0.21/0.63 ? [A] : empty(A) ).
% 0.21/0.63
% 0.21/0.63 fof(rc2_xboole_0,axiom,
% 0.21/0.63 ? [A] : ~ empty(A) ).
% 0.21/0.63
% 0.21/0.63 fof(t3_subset,axiom,
% 0.21/0.64 ! [A,B] :
% 0.21/0.64 ( element(A,powerset(B))
% 0.21/0.64 <=> subset(A,B) ) ).
% 0.21/0.64
% 0.21/0.64 fof(t42_funct_1,conjecture,
% 0.21/0.64 ! [A] :
% 0.21/0.64 ( ( relation(A)
% 0.21/0.64 & function(A) )
% 0.21/0.64 => ( relation_composition(identity_relation(relation_dom(A)),A) = A
% 0.21/0.64 & relation_composition(A,identity_relation(relation_rng(A))) = A ) ) ).
% 0.21/0.64
% 0.21/0.64 fof(t77_relat_1,axiom,
% 0.21/0.64 ! [A,B] :
% 0.21/0.64 ( relation(B)
% 0.21/0.64 => ( subset(relation_dom(B),A)
% 0.21/0.64 => relation_composition(identity_relation(A),B) = B ) ) ).
% 0.21/0.64
% 0.21/0.64 fof(t79_relat_1,axiom,
% 0.21/0.64 ! [A,B] :
% 0.21/0.64 ( relation(B)
% 0.21/0.64 => ( subset(relation_rng(B),A)
% 0.21/0.64 => relation_composition(B,identity_relation(A)) = B ) ) ).
% 0.21/0.64
% 0.21/0.64 %------------------------------------------------------------------------------
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 % Proof found
% 0.21/0.64 % SZS status Theorem for theBenchmark
% 0.21/0.64 % SZS output start Proof
% 0.21/0.64 %ClaNum:78(EqnAxiom:22)
% 0.21/0.64 %VarNum:112(SingletonVarNum:54)
% 0.21/0.64 %MaxLitNum:5
% 0.21/0.64 %MaxfuncDepth:3
% 0.21/0.64 %SharedTerms:31
% 0.21/0.64 %goalClause: 34 38 78
% 0.21/0.64 %singleGoalClaCount:2
% 0.21/0.64 [25]P1(a1)
% 0.21/0.64 [26]P1(a2)
% 0.21/0.64 [27]P1(a8)
% 0.21/0.64 [29]P3(a1)
% 0.21/0.64 [30]P3(a3)
% 0.21/0.64 [31]P3(a2)
% 0.21/0.64 [32]P3(a9)
% 0.21/0.64 [33]P3(a10)
% 0.21/0.64 [34]P3(a4)
% 0.21/0.64 [35]P6(a1)
% 0.21/0.64 [36]P6(a10)
% 0.21/0.64 [37]P4(a3)
% 0.21/0.64 [38]P4(a4)
% 0.21/0.64 [46]~P1(a9)
% 0.21/0.64 [47]~P1(a12)
% 0.21/0.64 [43]P7(x431,x431)
% 0.21/0.64 [39]P1(f6(x391))
% 0.21/0.64 [41]P3(f11(x411))
% 0.21/0.64 [42]P4(f11(x421))
% 0.21/0.64 [44]P2(f5(x441),x441)
% 0.21/0.64 [45]P2(f6(x451),f13(x451))
% 0.21/0.64 [48]~P1(f13(x481))
% 0.21/0.64 [78]~E(f15(a4,f11(f16(a4))),a4)+~E(f15(f11(f14(a4)),a4),a4)
% 0.21/0.64 [49]~P1(x491)+E(x491,a1)
% 0.21/0.64 [50]~P1(x501)+P3(x501)
% 0.21/0.64 [51]~P1(x511)+P4(x511)
% 0.21/0.64 [53]~P1(x531)+P1(f14(x531))
% 0.21/0.64 [54]~P1(x541)+P1(f16(x541))
% 0.21/0.64 [55]~P1(x551)+P3(f14(x551))
% 0.21/0.64 [56]~P1(x561)+P3(f16(x561))
% 0.21/0.64 [57]P1(x571)+~P1(f7(x571))
% 0.21/0.64 [61]P1(x611)+P2(f7(x611),f13(x611))
% 0.21/0.64 [60]~P1(x601)+~P5(x602,x601)
% 0.21/0.64 [62]~P5(x621,x622)+P2(x621,x622)
% 0.21/0.64 [70]~P5(x702,x701)+~P5(x701,x702)
% 0.21/0.64 [64]~P7(x641,x642)+P2(x641,f13(x642))
% 0.21/0.64 [71]P7(x711,x712)+~P2(x711,f13(x712))
% 0.21/0.64 [58]~P3(x581)+P1(x581)+~P1(f14(x581))
% 0.21/0.64 [59]~P3(x591)+P1(x591)+~P1(f16(x591))
% 0.21/0.64 [52]~P1(x522)+~P1(x521)+E(x521,x522)
% 0.21/0.64 [63]~P2(x632,x631)+P1(x631)+P5(x632,x631)
% 0.21/0.64 [65]~P1(x652)+~P3(x651)+P1(f15(x651,x652))
% 0.21/0.64 [66]~P1(x661)+~P3(x662)+P1(f15(x661,x662))
% 0.21/0.64 [67]~P1(x672)+~P3(x671)+P3(f15(x671,x672))
% 0.21/0.64 [68]~P1(x681)+~P3(x682)+P3(f15(x681,x682))
% 0.21/0.64 [69]~P3(x692)+~P3(x691)+P3(f15(x691,x692))
% 0.21/0.64 [74]~P3(x741)+~P7(f16(x741),x742)+E(f15(x741,f11(x742)),x741)
% 0.21/0.64 [75]~P3(x752)+~P7(f14(x752),x751)+E(f15(f11(x751),x752),x752)
% 0.21/0.64 [76]~P1(x761)+~P5(x762,x763)+~P2(x763,f13(x761))
% 0.21/0.64 [77]P2(x771,x772)+~P5(x771,x773)+~P2(x773,f13(x772))
% 0.21/0.64 [73]~P3(x732)+~P3(x731)+~P4(x732)+~P4(x731)+P4(f15(x731,x732))
% 0.21/0.64 %EqnAxiom
% 0.21/0.64 [1]E(x11,x11)
% 0.21/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.64 [4]~E(x41,x42)+E(f6(x41),f6(x42))
% 0.21/0.64 [5]~E(x51,x52)+E(f11(x51),f11(x52))
% 0.21/0.64 [6]~E(x61,x62)+E(f14(x61),f14(x62))
% 0.21/0.64 [7]~E(x71,x72)+E(f15(x71,x73),f15(x72,x73))
% 0.21/0.64 [8]~E(x81,x82)+E(f15(x83,x81),f15(x83,x82))
% 0.21/0.64 [9]~E(x91,x92)+E(f5(x91),f5(x92))
% 0.21/0.64 [10]~E(x101,x102)+E(f16(x101),f16(x102))
% 0.21/0.64 [11]~E(x111,x112)+E(f13(x111),f13(x112))
% 0.21/0.64 [12]~E(x121,x122)+E(f7(x121),f7(x122))
% 0.21/0.64 [13]~P1(x131)+P1(x132)+~E(x131,x132)
% 0.21/0.64 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143)
% 0.21/0.64 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151)
% 0.21/0.64 [16]P5(x162,x163)+~E(x161,x162)+~P5(x161,x163)
% 0.21/0.64 [17]P5(x173,x172)+~E(x171,x172)+~P5(x173,x171)
% 0.21/0.64 [18]~P3(x181)+P3(x182)+~E(x181,x182)
% 0.21/0.64 [19]P7(x192,x193)+~E(x191,x192)+~P7(x191,x193)
% 0.21/0.64 [20]P7(x203,x202)+~E(x201,x202)+~P7(x203,x201)
% 0.21/0.64 [21]~P4(x211)+P4(x212)+~E(x211,x212)
% 0.21/0.64 [22]~P6(x221)+P6(x222)+~E(x221,x222)
% 0.21/0.64
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 cnf(81,plain,
% 0.21/0.64 (P2(f5(x811),x811)),
% 0.21/0.64 inference(rename_variables,[],[44])).
% 0.21/0.64 cnf(84,plain,
% 0.21/0.64 (P2(f5(x841),x841)),
% 0.21/0.64 inference(rename_variables,[],[44])).
% 0.21/0.64 cnf(87,plain,
% 0.21/0.64 (P2(f5(x871),x871)),
% 0.21/0.64 inference(rename_variables,[],[44])).
% 0.21/0.64 cnf(150,plain,
% 0.21/0.64 (~P7(f16(a4),f16(a4))),
% 0.21/0.64 inference(scs_inference,[],[34,43,38,25,26,27,32,35,46,44,81,84,87,60,71,63,76,70,51,50,49,64,57,56,55,54,53,12,11,10,9,8,7,6,5,4,61,22,17,13,69,68,67,66,65,59,58,75,73,2,78,20,19,15,14,3,77,74])).
% 0.21/0.64 cnf(154,plain,
% 0.21/0.64 ($false),
% 0.21/0.64 inference(scs_inference,[],[43,150]),
% 0.21/0.64 ['proof']).
% 0.21/0.64 % SZS output end Proof
% 0.21/0.64 % Total time :0.010000s
%------------------------------------------------------------------------------