TSTP Solution File: SEU123+2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU123+2 : 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 : n002.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 16:17:36 EDT 2023
% Result : Theorem 0.21s 0.65s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU123+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 17:53:16 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof:theBenchmark
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 % File :CSE---1.6
% 0.21/0.64 % Problem :theBenchmark
% 0.21/0.64 % Transform :cnf
% 0.21/0.64 % Format :tptp:raw
% 0.21/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.64
% 0.21/0.64 % Result :Theorem 0.000000s
% 0.21/0.64 % Output :CNFRefutation 0.000000s
% 0.21/0.64 %-------------------------------------------
% 0.21/0.64 %------------------------------------------------------------------------------
% 0.21/0.64 % File : SEU123+2 : TPTP v8.1.2. Released v3.3.0.
% 0.21/0.64 % Domain : Set theory
% 0.21/0.64 % Problem : MPTP chainy problem t3_xboole_1
% 0.21/0.64 % Version : [Urb07] axioms : Especial.
% 0.21/0.64 % English :
% 0.21/0.64
% 0.21/0.64 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% 0.21/0.64 % : [Urb07] Urban (2006), Email to G. Sutcliffe
% 0.21/0.64 % Source : [Urb07]
% 0.21/0.64 % Names : chainy-t3_xboole_1 [Urb07]
% 0.21/0.64
% 0.21/0.64 % Status : Theorem
% 0.21/0.64 % Rating : 0.03 v8.1.0, 0.00 v6.3.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.07 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.00 v5.0.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0
% 0.21/0.64 % Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% 0.21/0.64 % Number of atoms : 49 ( 9 equ)
% 0.21/0.64 % Maximal formula atoms : 6 ( 2 avg)
% 0.21/0.64 % Number of connectives : 40 ( 14 ~; 0 |; 14 &)
% 0.21/0.64 % ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% 0.21/0.64 % Maximal formula depth : 9 ( 4 avg)
% 0.21/0.64 % Maximal term depth : 2 ( 1 avg)
% 0.21/0.64 % Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% 0.21/0.64 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.21/0.64 % Number of variables : 43 ( 39 !; 4 ?)
% 0.21/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.64
% 0.21/0.64 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.21/0.64 % library, www.mizar.org
% 0.21/0.64 %------------------------------------------------------------------------------
% 0.21/0.64 fof(antisymmetry_r2_hidden,axiom,
% 0.21/0.64 ! [A,B] :
% 0.21/0.65 ( in(A,B)
% 0.21/0.65 => ~ in(B,A) ) ).
% 0.21/0.65
% 0.21/0.65 fof(commutativity_k3_xboole_0,axiom,
% 0.21/0.65 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
% 0.21/0.65
% 0.21/0.65 fof(d10_xboole_0,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( A = B
% 0.21/0.65 <=> ( subset(A,B)
% 0.21/0.65 & subset(B,A) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(d1_xboole_0,axiom,
% 0.21/0.65 ! [A] :
% 0.21/0.65 ( A = empty_set
% 0.21/0.65 <=> ! [B] : ~ in(B,A) ) ).
% 0.21/0.65
% 0.21/0.65 fof(d3_tarski,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( subset(A,B)
% 0.21/0.65 <=> ! [C] :
% 0.21/0.65 ( in(C,A)
% 0.21/0.65 => in(C,B) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(d3_xboole_0,axiom,
% 0.21/0.65 ! [A,B,C] :
% 0.21/0.65 ( C = set_intersection2(A,B)
% 0.21/0.65 <=> ! [D] :
% 0.21/0.65 ( in(D,C)
% 0.21/0.65 <=> ( in(D,A)
% 0.21/0.65 & in(D,B) ) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(d7_xboole_0,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( disjoint(A,B)
% 0.21/0.65 <=> set_intersection2(A,B) = empty_set ) ).
% 0.21/0.65
% 0.21/0.65 fof(dt_k1_xboole_0,axiom,
% 0.21/0.65 $true ).
% 0.21/0.65
% 0.21/0.65 fof(dt_k3_xboole_0,axiom,
% 0.21/0.65 $true ).
% 0.21/0.65
% 0.21/0.65 fof(fc1_xboole_0,axiom,
% 0.21/0.65 empty(empty_set) ).
% 0.21/0.65
% 0.21/0.65 fof(idempotence_k3_xboole_0,axiom,
% 0.21/0.65 ! [A,B] : set_intersection2(A,A) = A ).
% 0.21/0.65
% 0.21/0.65 fof(rc1_xboole_0,axiom,
% 0.21/0.65 ? [A] : empty(A) ).
% 0.21/0.65
% 0.21/0.65 fof(rc2_xboole_0,axiom,
% 0.21/0.65 ? [A] : ~ empty(A) ).
% 0.21/0.65
% 0.21/0.65 fof(reflexivity_r1_tarski,axiom,
% 0.21/0.65 ! [A,B] : subset(A,A) ).
% 0.21/0.65
% 0.21/0.65 fof(symmetry_r1_xboole_0,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( disjoint(A,B)
% 0.21/0.65 => disjoint(B,A) ) ).
% 0.21/0.65
% 0.21/0.65 fof(t1_xboole_1,lemma,
% 0.21/0.65 ! [A,B,C] :
% 0.21/0.65 ( ( subset(A,B)
% 0.21/0.65 & subset(B,C) )
% 0.21/0.65 => subset(A,C) ) ).
% 0.21/0.65
% 0.21/0.65 fof(t2_xboole_1,lemma,
% 0.21/0.65 ! [A] : subset(empty_set,A) ).
% 0.21/0.65
% 0.21/0.65 fof(t3_xboole_0,lemma,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( ~ ( ~ disjoint(A,B)
% 0.21/0.65 & ! [C] :
% 0.21/0.65 ~ ( in(C,A)
% 0.21/0.65 & in(C,B) ) )
% 0.21/0.65 & ~ ( ? [C] :
% 0.21/0.65 ( in(C,A)
% 0.21/0.65 & in(C,B) )
% 0.21/0.65 & disjoint(A,B) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(t3_xboole_1,conjecture,
% 0.21/0.65 ! [A] :
% 0.21/0.65 ( subset(A,empty_set)
% 0.21/0.65 => A = empty_set ) ).
% 0.21/0.65
% 0.21/0.65 fof(t4_xboole_0,lemma,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( ~ ( ~ disjoint(A,B)
% 0.21/0.65 & ! [C] : ~ in(C,set_intersection2(A,B)) )
% 0.21/0.65 & ~ ( ? [C] : in(C,set_intersection2(A,B))
% 0.21/0.65 & disjoint(A,B) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(t6_boole,axiom,
% 0.21/0.65 ! [A] :
% 0.21/0.65 ( empty(A)
% 0.21/0.65 => A = empty_set ) ).
% 0.21/0.65
% 0.21/0.65 fof(t7_boole,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ~ ( in(A,B)
% 0.21/0.65 & empty(B) ) ).
% 0.21/0.65
% 0.21/0.65 fof(t8_boole,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ~ ( empty(A)
% 0.21/0.65 & A != B
% 0.21/0.65 & empty(B) ) ).
% 0.21/0.65
% 0.21/0.65 %------------------------------------------------------------------------------
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 % Proof found
% 0.21/0.65 % SZS status Theorem for theBenchmark
% 0.21/0.65 % SZS output start Proof
% 0.21/0.65 %ClaNum:58(EqnAxiom:22)
% 0.21/0.65 %VarNum:160(SingletonVarNum:68)
% 0.21/0.65 %MaxLitNum:4
% 0.21/0.65 %MaxfuncDepth:1
% 0.21/0.65 %SharedTerms:9
% 0.21/0.65 %goalClause: 25 30
% 0.21/0.65 %singleGoalClaCount:2
% 0.21/0.65 [23]P1(a1)
% 0.21/0.65 [24]P1(a2)
% 0.21/0.65 [25]P3(a6,a1)
% 0.21/0.65 [30]~E(a6,a1)
% 0.21/0.65 [31]~P1(a7)
% 0.21/0.65 [26]P3(a1,x261)
% 0.21/0.65 [27]P3(x271,x271)
% 0.21/0.65 [28]E(f9(x281,x281),x281)
% 0.21/0.65 [29]E(f9(x291,x292),f9(x292,x291))
% 0.21/0.65 [32]~P1(x321)+E(x321,a1)
% 0.21/0.65 [36]P4(f3(x361),x361)+E(x361,a1)
% 0.21/0.65 [35]~E(x351,x352)+P3(x351,x352)
% 0.21/0.65 [37]~P4(x372,x371)+~E(x371,a1)
% 0.21/0.65 [38]~P1(x381)+~P4(x382,x381)
% 0.21/0.65 [41]~P2(x412,x411)+P2(x411,x412)
% 0.21/0.65 [42]~P4(x422,x421)+~P4(x421,x422)
% 0.21/0.65 [39]~P2(x391,x392)+E(f9(x391,x392),a1)
% 0.21/0.65 [40]P2(x401,x402)+~E(f9(x401,x402),a1)
% 0.21/0.65 [44]P3(x441,x442)+P4(f4(x441,x442),x441)
% 0.21/0.65 [45]P2(x451,x452)+P4(f8(x451,x452),x452)
% 0.21/0.65 [46]P2(x461,x462)+P4(f8(x461,x462),x461)
% 0.21/0.65 [52]P3(x521,x522)+~P4(f4(x521,x522),x522)
% 0.21/0.65 [53]P2(x531,x532)+P4(f10(x531,x532),f9(x531,x532))
% 0.21/0.65 [55]~P2(x551,x552)+~P4(x553,f9(x551,x552))
% 0.21/0.65 [33]~P1(x332)+~P1(x331)+E(x331,x332)
% 0.21/0.65 [43]~P3(x432,x431)+~P3(x431,x432)+E(x431,x432)
% 0.21/0.65 [47]~P3(x473,x472)+P4(x471,x472)+~P4(x471,x473)
% 0.21/0.65 [48]~P3(x481,x483)+P3(x481,x482)+~P3(x483,x482)
% 0.21/0.65 [51]~P2(x513,x512)+~P4(x511,x512)+~P4(x511,x513)
% 0.21/0.65 [56]P4(f5(x562,x563,x561),x561)+P4(f5(x562,x563,x561),x563)+E(x561,f9(x562,x563))
% 0.21/0.65 [57]P4(f5(x572,x573,x571),x571)+P4(f5(x572,x573,x571),x572)+E(x571,f9(x572,x573))
% 0.21/0.65 [49]~P4(x491,x493)+P4(x491,x492)+~E(x493,f9(x494,x492))
% 0.21/0.65 [50]~P4(x501,x503)+P4(x501,x502)+~E(x503,f9(x502,x504))
% 0.21/0.65 [58]~P4(f5(x582,x583,x581),x581)+~P4(f5(x582,x583,x581),x583)+~P4(f5(x582,x583,x581),x582)+E(x581,f9(x582,x583))
% 0.21/0.65 [54]~P4(x541,x544)+~P4(x541,x543)+P4(x541,x542)+~E(x542,f9(x543,x544))
% 0.21/0.65 %EqnAxiom
% 0.21/0.65 [1]E(x11,x11)
% 0.21/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.65 [4]~E(x41,x42)+E(f9(x41,x43),f9(x42,x43))
% 0.21/0.65 [5]~E(x51,x52)+E(f9(x53,x51),f9(x53,x52))
% 0.21/0.65 [6]~E(x61,x62)+E(f5(x61,x63,x64),f5(x62,x63,x64))
% 0.21/0.65 [7]~E(x71,x72)+E(f5(x73,x71,x74),f5(x73,x72,x74))
% 0.21/0.65 [8]~E(x81,x82)+E(f5(x83,x84,x81),f5(x83,x84,x82))
% 0.21/0.65 [9]~E(x91,x92)+E(f10(x91,x93),f10(x92,x93))
% 0.21/0.65 [10]~E(x101,x102)+E(f10(x103,x101),f10(x103,x102))
% 0.21/0.65 [11]~E(x111,x112)+E(f3(x111),f3(x112))
% 0.21/0.65 [12]~E(x121,x122)+E(f4(x121,x123),f4(x122,x123))
% 0.21/0.65 [13]~E(x131,x132)+E(f4(x133,x131),f4(x133,x132))
% 0.21/0.65 [14]~E(x141,x142)+E(f8(x141,x143),f8(x142,x143))
% 0.21/0.65 [15]~E(x151,x152)+E(f8(x153,x151),f8(x153,x152))
% 0.21/0.65 [16]~P1(x161)+P1(x162)+~E(x161,x162)
% 0.21/0.65 [17]P4(x172,x173)+~E(x171,x172)+~P4(x171,x173)
% 0.21/0.65 [18]P4(x183,x182)+~E(x181,x182)+~P4(x183,x181)
% 0.21/0.65 [19]P3(x192,x193)+~E(x191,x192)+~P3(x191,x193)
% 0.21/0.65 [20]P3(x203,x202)+~E(x201,x202)+~P3(x203,x201)
% 0.21/0.65 [21]P2(x212,x213)+~E(x211,x212)+~P2(x211,x213)
% 0.21/0.65 [22]P2(x223,x222)+~E(x221,x222)+~P2(x223,x221)
% 0.21/0.65
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 cnf(63,plain,
% 0.21/0.65 (E(f9(x631,x631),x631)),
% 0.21/0.65 inference(rename_variables,[],[28])).
% 0.21/0.65 cnf(84,plain,
% 0.21/0.65 ($false),
% 0.21/0.65 inference(scs_inference,[],[25,26,30,23,28,63,2,38,37,32,36,46,45,22,21,20,19,16,3,48,47,43]),
% 0.21/0.65 ['proof']).
% 0.21/0.65 % SZS output end Proof
% 0.21/0.65 % Total time :0.000000s
%------------------------------------------------------------------------------