TSTP Solution File: SEU080+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU080+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 16:17:26 EDT 2023
% Result : Theorem 0.19s 0.63s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU080+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
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 23 20:00:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % File :CSE---1.6
% 0.19/0.62 % Problem :theBenchmark
% 0.19/0.62 % Transform :cnf
% 0.19/0.62 % Format :tptp:raw
% 0.19/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.62
% 0.19/0.62 % Result :Theorem 0.010000s
% 0.19/0.62 % Output :CNFRefutation 0.010000s
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 %------------------------------------------------------------------------------
% 0.19/0.62 % File : SEU080+1 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.62 % Domain : Set theory
% 0.19/0.62 % Problem : Functions and their basic properties, theorem 161
% 0.19/0.62 % Version : [Urb06] axioms : Especial.
% 0.19/0.62 % English :
% 0.19/0.62
% 0.19/0.62 % Refs : [Byl90] Bylinski (1990), Functions and Their Basic Properties
% 0.19/0.62 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.19/0.62 % Source : [Urb06]
% 0.19/0.62 % Names : funct_1__t161_funct_1 [Urb06]
% 0.19/0.62
% 0.19/0.62 % Status : Theorem
% 0.19/0.62 % Rating : 0.11 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.21 v6.2.0, 0.24 v6.1.0, 0.23 v6.0.0, 0.30 v5.5.0, 0.22 v5.4.0, 0.25 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.19 v5.0.0, 0.17 v4.1.0, 0.22 v4.0.0, 0.21 v3.7.0, 0.05 v3.4.0, 0.16 v3.3.0, 0.07 v3.2.0
% 0.19/0.62 % Syntax : Number of formulae : 33 ( 6 unt; 0 def)
% 0.19/0.62 % Number of atoms : 82 ( 5 equ)
% 0.19/0.62 % Maximal formula atoms : 6 ( 2 avg)
% 0.19/0.62 % Number of connectives : 61 ( 12 ~; 1 |; 31 &)
% 0.19/0.62 % ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% 0.19/0.62 % Maximal formula depth : 8 ( 4 avg)
% 0.19/0.62 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.62 % Number of predicates : 9 ( 8 usr; 0 prp; 1-2 aty)
% 0.19/0.62 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.19/0.62 % Number of variables : 49 ( 38 !; 11 ?)
% 0.19/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.62
% 0.19/0.62 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.62 % library, www.mizar.org
% 0.19/0.62 %------------------------------------------------------------------------------
% 0.19/0.62 fof(antisymmetry_r2_hidden,axiom,
% 0.19/0.62 ! [A,B] :
% 0.19/0.62 ( in(A,B)
% 0.19/0.62 => ~ in(B,A) ) ).
% 0.19/0.62
% 0.19/0.62 fof(cc1_funct_1,axiom,
% 0.19/0.62 ! [A] :
% 0.19/0.62 ( empty(A)
% 0.19/0.62 => function(A) ) ).
% 0.19/0.62
% 0.19/0.63 fof(cc1_relat_1,axiom,
% 0.19/0.63 ! [A] :
% 0.19/0.63 ( empty(A)
% 0.19/0.63 => relation(A) ) ).
% 0.19/0.63
% 0.19/0.63 fof(cc2_funct_1,axiom,
% 0.19/0.63 ! [A] :
% 0.19/0.63 ( ( relation(A)
% 0.19/0.63 & empty(A)
% 0.19/0.63 & function(A) )
% 0.19/0.63 => ( relation(A)
% 0.19/0.63 & function(A)
% 0.19/0.63 & one_to_one(A) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(d10_xboole_0,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ( A = B
% 0.19/0.63 <=> ( subset(A,B)
% 0.19/0.63 & subset(B,A) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(existence_m1_subset_1,axiom,
% 0.19/0.63 ! [A] :
% 0.19/0.63 ? [B] : element(B,A) ).
% 0.19/0.63
% 0.19/0.63 fof(fc12_relat_1,axiom,
% 0.19/0.63 ( empty(empty_set)
% 0.19/0.63 & relation(empty_set)
% 0.19/0.63 & relation_empty_yielding(empty_set) ) ).
% 0.19/0.63
% 0.19/0.63 fof(fc1_subset_1,axiom,
% 0.19/0.63 ! [A] : ~ empty(powerset(A)) ).
% 0.19/0.63
% 0.19/0.63 fof(fc1_xboole_0,axiom,
% 0.19/0.63 empty(empty_set) ).
% 0.19/0.63
% 0.19/0.63 fof(fc4_relat_1,axiom,
% 0.19/0.63 ( empty(empty_set)
% 0.19/0.63 & relation(empty_set) ) ).
% 0.19/0.63
% 0.19/0.63 fof(fc6_relat_1,axiom,
% 0.19/0.63 ! [A] :
% 0.19/0.63 ( ( ~ empty(A)
% 0.19/0.63 & relation(A) )
% 0.19/0.63 => ~ empty(relation_rng(A)) ) ).
% 0.19/0.63
% 0.19/0.63 fof(fc8_relat_1,axiom,
% 0.19/0.63 ! [A] :
% 0.19/0.63 ( empty(A)
% 0.19/0.63 => ( empty(relation_rng(A))
% 0.19/0.63 & relation(relation_rng(A)) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(rc1_funct_1,axiom,
% 0.19/0.63 ? [A] :
% 0.19/0.63 ( relation(A)
% 0.19/0.63 & function(A) ) ).
% 0.19/0.63
% 0.19/0.63 fof(rc1_relat_1,axiom,
% 0.19/0.63 ? [A] :
% 0.19/0.63 ( empty(A)
% 0.19/0.63 & relation(A) ) ).
% 0.19/0.63
% 0.19/0.63 fof(rc1_subset_1,axiom,
% 0.19/0.63 ! [A] :
% 0.19/0.63 ( ~ empty(A)
% 0.19/0.63 => ? [B] :
% 0.19/0.63 ( element(B,powerset(A))
% 0.19/0.63 & ~ empty(B) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(rc1_xboole_0,axiom,
% 0.19/0.63 ? [A] : empty(A) ).
% 0.19/0.63
% 0.19/0.63 fof(rc2_funct_1,axiom,
% 0.19/0.63 ? [A] :
% 0.19/0.63 ( relation(A)
% 0.19/0.63 & empty(A)
% 0.19/0.63 & function(A) ) ).
% 0.19/0.63
% 0.19/0.63 fof(rc2_relat_1,axiom,
% 0.19/0.63 ? [A] :
% 0.19/0.63 ( ~ empty(A)
% 0.19/0.63 & relation(A) ) ).
% 0.19/0.63
% 0.19/0.63 fof(rc2_subset_1,axiom,
% 0.19/0.63 ! [A] :
% 0.19/0.63 ? [B] :
% 0.19/0.63 ( element(B,powerset(A))
% 0.19/0.63 & empty(B) ) ).
% 0.19/0.63
% 0.19/0.63 fof(rc2_xboole_0,axiom,
% 0.19/0.63 ? [A] : ~ empty(A) ).
% 0.19/0.63
% 0.19/0.63 fof(rc3_funct_1,axiom,
% 0.19/0.63 ? [A] :
% 0.19/0.63 ( relation(A)
% 0.19/0.63 & function(A)
% 0.19/0.63 & one_to_one(A) ) ).
% 0.19/0.63
% 0.19/0.63 fof(rc3_relat_1,axiom,
% 0.19/0.63 ? [A] :
% 0.19/0.63 ( relation(A)
% 0.19/0.63 & relation_empty_yielding(A) ) ).
% 0.19/0.63
% 0.19/0.63 fof(reflexivity_r1_tarski,axiom,
% 0.19/0.63 ! [A,B] : subset(A,A) ).
% 0.19/0.63
% 0.19/0.63 fof(t158_funct_1,axiom,
% 0.19/0.63 ! [A,B,C] :
% 0.19/0.63 ( ( relation(C)
% 0.19/0.63 & function(C) )
% 0.19/0.63 => ( ( subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
% 0.19/0.63 & subset(A,relation_rng(C)) )
% 0.19/0.63 => subset(A,B) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t161_funct_1,conjecture,
% 0.19/0.63 ! [A,B,C] :
% 0.19/0.63 ( ( relation(C)
% 0.19/0.63 & function(C) )
% 0.19/0.63 => ( ( relation_inverse_image(C,A) = relation_inverse_image(C,B)
% 0.19/0.63 & subset(A,relation_rng(C))
% 0.19/0.63 & subset(B,relation_rng(C)) )
% 0.19/0.63 => A = B ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t1_subset,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ( in(A,B)
% 0.19/0.63 => element(A,B) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t2_subset,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ( element(A,B)
% 0.19/0.63 => ( empty(B)
% 0.19/0.63 | in(A,B) ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t3_subset,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ( element(A,powerset(B))
% 0.19/0.63 <=> subset(A,B) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t4_subset,axiom,
% 0.19/0.63 ! [A,B,C] :
% 0.19/0.63 ( ( in(A,B)
% 0.19/0.63 & element(B,powerset(C)) )
% 0.19/0.63 => element(A,C) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t5_subset,axiom,
% 0.19/0.63 ! [A,B,C] :
% 0.19/0.63 ~ ( in(A,B)
% 0.19/0.63 & element(B,powerset(C))
% 0.19/0.63 & empty(C) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t6_boole,axiom,
% 0.19/0.63 ! [A] :
% 0.19/0.63 ( empty(A)
% 0.19/0.63 => A = empty_set ) ).
% 0.19/0.63
% 0.19/0.63 fof(t7_boole,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ~ ( in(A,B)
% 0.19/0.63 & empty(B) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t8_boole,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ~ ( empty(A)
% 0.19/0.63 & A != B
% 0.19/0.63 & empty(B) ) ).
% 0.19/0.63
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % Proof found
% 0.19/0.63 % SZS status Theorem for theBenchmark
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 %ClaNum:76(EqnAxiom:21)
% 0.19/0.63 %VarNum:89(SingletonVarNum:41)
% 0.19/0.63 %MaxLitNum:5
% 0.19/0.63 %MaxfuncDepth:1
% 0.19/0.63 %SharedTerms:40
% 0.19/0.63 %goalClause: 31 40 46 47 49 51
% 0.19/0.63 %singleGoalClaCount:6
% 0.19/0.63 [24]P1(a1)
% 0.19/0.63 [25]P1(a2)
% 0.19/0.63 [26]P1(a10)
% 0.19/0.63 [27]P1(a12)
% 0.19/0.63 [28]P3(a3)
% 0.19/0.63 [29]P3(a12)
% 0.19/0.63 [30]P3(a4)
% 0.19/0.63 [31]P3(a5)
% 0.19/0.63 [33]P4(a1)
% 0.19/0.63 [34]P4(a3)
% 0.19/0.63 [35]P4(a2)
% 0.19/0.63 [36]P4(a12)
% 0.19/0.63 [37]P4(a13)
% 0.19/0.63 [38]P4(a4)
% 0.19/0.63 [39]P4(a6)
% 0.19/0.63 [40]P4(a5)
% 0.19/0.63 [41]P5(a4)
% 0.19/0.63 [42]P7(a1)
% 0.19/0.63 [43]P7(a6)
% 0.19/0.63 [51]~E(a8,a7)
% 0.19/0.63 [52]~P1(a13)
% 0.19/0.63 [53]~P1(a18)
% 0.19/0.63 [46]P8(a7,f15(a5))
% 0.19/0.63 [47]P8(a8,f15(a5))
% 0.19/0.63 [49]E(f16(a5,a8),f16(a5,a7))
% 0.19/0.63 [45]P8(x451,x451)
% 0.19/0.63 [44]P1(f14(x441))
% 0.19/0.63 [48]P2(f9(x481),x481)
% 0.19/0.63 [50]P2(f14(x501),f17(x501))
% 0.19/0.63 [54]~P1(f17(x541))
% 0.19/0.63 [55]~P1(x551)+E(x551,a1)
% 0.19/0.63 [56]~P1(x561)+P3(x561)
% 0.19/0.63 [57]~P1(x571)+P4(x571)
% 0.19/0.63 [59]~P1(x591)+P1(f15(x591))
% 0.19/0.63 [60]~P1(x601)+P4(f15(x601))
% 0.19/0.63 [63]P1(x631)+~P1(f11(x631))
% 0.19/0.63 [67]P1(x671)+P2(f11(x671),f17(x671))
% 0.19/0.63 [62]~E(x621,x622)+P8(x621,x622)
% 0.19/0.63 [66]~P1(x661)+~P6(x662,x661)
% 0.19/0.63 [68]~P6(x681,x682)+P2(x681,x682)
% 0.19/0.63 [71]~P6(x712,x711)+~P6(x711,x712)
% 0.19/0.63 [70]~P8(x701,x702)+P2(x701,f17(x702))
% 0.19/0.63 [72]P8(x721,x722)+~P2(x721,f17(x722))
% 0.19/0.63 [65]~P4(x651)+P1(x651)+~P1(f15(x651))
% 0.19/0.63 [58]~P1(x582)+~P1(x581)+E(x581,x582)
% 0.19/0.63 [69]~P2(x692,x691)+P1(x691)+P6(x692,x691)
% 0.19/0.63 [73]~P8(x732,x731)+~P8(x731,x732)+E(x731,x732)
% 0.19/0.63 [74]~P1(x741)+~P6(x742,x743)+~P2(x743,f17(x741))
% 0.19/0.63 [75]P2(x751,x752)+~P6(x751,x753)+~P2(x753,f17(x752))
% 0.19/0.63 [64]~P1(x641)+~P3(x641)+~P4(x641)+P5(x641)
% 0.19/0.63 [76]~P4(x763)+P8(x761,x762)+~P3(x763)+~P8(x761,f15(x763))+~P8(f16(x763,x761),f16(x763,x762))
% 0.19/0.63 %EqnAxiom
% 0.19/0.63 [1]E(x11,x11)
% 0.19/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.63 [4]~E(x41,x42)+E(f14(x41),f14(x42))
% 0.19/0.63 [5]~E(x51,x52)+E(f15(x51),f15(x52))
% 0.19/0.63 [6]~E(x61,x62)+E(f16(x61,x63),f16(x62,x63))
% 0.19/0.63 [7]~E(x71,x72)+E(f16(x73,x71),f16(x73,x72))
% 0.19/0.63 [8]~E(x81,x82)+E(f9(x81),f9(x82))
% 0.19/0.63 [9]~E(x91,x92)+E(f17(x91),f17(x92))
% 0.19/0.63 [10]~E(x101,x102)+E(f11(x101),f11(x102))
% 0.19/0.63 [11]~P1(x111)+P1(x112)+~E(x111,x112)
% 0.19/0.63 [12]P8(x122,x123)+~E(x121,x122)+~P8(x121,x123)
% 0.19/0.63 [13]P8(x133,x132)+~E(x131,x132)+~P8(x133,x131)
% 0.19/0.63 [14]P6(x142,x143)+~E(x141,x142)+~P6(x141,x143)
% 0.19/0.63 [15]P6(x153,x152)+~E(x151,x152)+~P6(x153,x151)
% 0.19/0.63 [16]~P4(x161)+P4(x162)+~E(x161,x162)
% 0.19/0.63 [17]~P3(x171)+P3(x172)+~E(x171,x172)
% 0.19/0.63 [18]P2(x182,x183)+~E(x181,x182)+~P2(x181,x183)
% 0.19/0.63 [19]P2(x193,x192)+~E(x191,x192)+~P2(x193,x191)
% 0.19/0.63 [20]~P5(x201)+P5(x202)+~E(x201,x202)
% 0.19/0.63 [21]~P7(x211)+P7(x212)+~E(x211,x212)
% 0.19/0.63
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 cnf(81,plain,
% 0.19/0.63 (P2(f9(x811),x811)),
% 0.19/0.64 inference(rename_variables,[],[48])).
% 0.19/0.64 cnf(84,plain,
% 0.19/0.64 (P2(f9(x841),x841)),
% 0.19/0.64 inference(rename_variables,[],[48])).
% 0.19/0.64 cnf(86,plain,
% 0.19/0.64 (P8(x861,x861)),
% 0.19/0.64 inference(rename_variables,[],[45])).
% 0.19/0.64 cnf(87,plain,
% 0.19/0.64 (P8(f16(a5,a7),f16(a5,a8))),
% 0.19/0.64 inference(scs_inference,[],[45,86,24,49,48,81,2,66,72,19,13,12])).
% 0.19/0.64 cnf(88,plain,
% 0.19/0.64 (P8(x881,x881)),
% 0.19/0.64 inference(rename_variables,[],[45])).
% 0.19/0.64 cnf(90,plain,
% 0.19/0.64 (P2(f9(x901),x901)),
% 0.19/0.64 inference(rename_variables,[],[48])).
% 0.19/0.64 cnf(92,plain,
% 0.19/0.64 (~P6(x921,f9(f17(a1)))),
% 0.19/0.64 inference(scs_inference,[],[45,86,24,52,49,48,81,84,90,2,66,72,19,13,12,69,74])).
% 0.19/0.64 cnf(100,plain,
% 0.19/0.64 (P3(a1)),
% 0.19/0.64 inference(scs_inference,[],[45,86,24,26,27,29,36,52,49,48,81,84,90,2,66,72,19,13,12,69,74,64,71,57,56])).
% 0.19/0.64 cnf(115,plain,
% 0.19/0.64 (E(f16(x1151,a2),f16(x1151,a1))),
% 0.19/0.64 inference(scs_inference,[],[45,86,88,24,25,26,27,29,36,52,49,48,81,84,90,2,66,72,19,13,12,69,74,64,71,57,56,55,70,63,60,59,10,9,8,7])).
% 0.19/0.64 cnf(126,plain,
% 0.19/0.64 (P8(a8,a7)),
% 0.19/0.64 inference(scs_inference,[],[31,45,86,88,40,24,25,26,27,29,36,37,42,52,47,49,48,81,84,90,2,66,72,19,13,12,69,74,64,71,57,56,55,70,63,60,59,10,9,8,7,6,5,4,67,21,15,11,65,76])).
% 0.19/0.64 cnf(146,plain,
% 0.19/0.64 ($false),
% 0.19/0.64 inference(scs_inference,[],[31,51,33,40,46,48,24,92,87,115,100,126,62,69,73,64,76]),
% 0.19/0.64 ['proof']).
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64 % Total time :0.010000s
%------------------------------------------------------------------------------