TSTP Solution File: SEU126+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU126+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 : n018.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 16:17:37 EDT 2023
% Result : Theorem 0.19s 0.67s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU126+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n018.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 : Wed Aug 23 19:21:57 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.58 start to proof:theBenchmark
% 0.19/0.66 %-------------------------------------------
% 0.19/0.66 % File :CSE---1.6
% 0.19/0.66 % Problem :theBenchmark
% 0.19/0.66 % Transform :cnf
% 0.19/0.66 % Format :tptp:raw
% 0.19/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.66
% 0.19/0.66 % Result :Theorem 0.020000s
% 0.19/0.66 % Output :CNFRefutation 0.020000s
% 0.19/0.66 %-------------------------------------------
% 0.19/0.66 %------------------------------------------------------------------------------
% 0.19/0.66 % File : SEU126+1 : TPTP v8.1.2. Released v3.3.0.
% 0.19/0.66 % Domain : Set theory
% 0.19/0.66 % Problem : MPTP bushy problem t12_xboole_1
% 0.19/0.66 % Version : [Urb07] axioms : Especial.
% 0.19/0.66 % English :
% 0.19/0.66
% 0.19/0.66 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% 0.19/0.66 % : [Urb07] Urban (2006), Email to G. Sutcliffe
% 0.19/0.66 % Source : [Urb07]
% 0.19/0.66 % Names : bushy-t12_xboole_1 [Urb07]
% 0.19/0.66
% 0.19/0.66 % Status : Theorem
% 0.19/0.66 % Rating : 0.22 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.13 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.12 v6.1.0, 0.13 v6.0.0, 0.17 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 v3.4.0, 0.26 v3.3.0
% 0.19/0.66 % Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% 0.19/0.66 % Number of atoms : 34 ( 8 equ)
% 0.19/0.66 % Maximal formula atoms : 4 ( 1 avg)
% 0.19/0.66 % Number of connectives : 24 ( 9 ~; 1 |; 4 &)
% 0.19/0.66 % ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.66 % Maximal formula depth : 8 ( 4 avg)
% 0.19/0.66 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.66 % Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% 0.19/0.66 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.19/0.66 % Number of variables : 31 ( 29 !; 2 ?)
% 0.19/0.66 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.66
% 0.19/0.66 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.66 % library, www.mizar.org
% 0.19/0.66 %------------------------------------------------------------------------------
% 0.19/0.66 fof(antisymmetry_r2_hidden,axiom,
% 0.19/0.66 ! [A,B] :
% 0.19/0.66 ( in(A,B)
% 0.19/0.66 => ~ in(B,A) ) ).
% 0.19/0.66
% 0.19/0.66 fof(commutativity_k2_xboole_0,axiom,
% 0.19/0.66 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.19/0.66
% 0.19/0.66 fof(d10_xboole_0,axiom,
% 0.19/0.66 ! [A,B] :
% 0.19/0.66 ( A = B
% 0.19/0.66 <=> ( subset(A,B)
% 0.19/0.66 & subset(B,A) ) ) ).
% 0.19/0.66
% 0.19/0.66 fof(d2_xboole_0,axiom,
% 0.19/0.66 ! [A,B,C] :
% 0.19/0.66 ( C = set_union2(A,B)
% 0.19/0.66 <=> ! [D] :
% 0.19/0.66 ( in(D,C)
% 0.19/0.66 <=> ( in(D,A)
% 0.19/0.66 | in(D,B) ) ) ) ).
% 0.19/0.66
% 0.19/0.66 fof(d3_tarski,axiom,
% 0.19/0.66 ! [A,B] :
% 0.19/0.66 ( subset(A,B)
% 0.19/0.66 <=> ! [C] :
% 0.19/0.66 ( in(C,A)
% 0.19/0.66 => in(C,B) ) ) ).
% 0.19/0.66
% 0.19/0.66 fof(dt_k1_xboole_0,axiom,
% 0.19/0.66 $true ).
% 0.19/0.66
% 0.19/0.66 fof(dt_k2_xboole_0,axiom,
% 0.19/0.66 $true ).
% 0.19/0.66
% 0.19/0.66 fof(fc1_xboole_0,axiom,
% 0.19/0.66 empty(empty_set) ).
% 0.19/0.66
% 0.19/0.66 fof(fc2_xboole_0,axiom,
% 0.19/0.67 ! [A,B] :
% 0.19/0.67 ( ~ empty(A)
% 0.19/0.67 => ~ empty(set_union2(A,B)) ) ).
% 0.19/0.67
% 0.19/0.67 fof(fc3_xboole_0,axiom,
% 0.19/0.67 ! [A,B] :
% 0.19/0.67 ( ~ empty(A)
% 0.19/0.67 => ~ empty(set_union2(B,A)) ) ).
% 0.19/0.67
% 0.19/0.67 fof(idempotence_k2_xboole_0,axiom,
% 0.19/0.67 ! [A,B] : set_union2(A,A) = A ).
% 0.19/0.67
% 0.19/0.67 fof(rc1_xboole_0,axiom,
% 0.19/0.67 ? [A] : empty(A) ).
% 0.19/0.67
% 0.19/0.67 fof(rc2_xboole_0,axiom,
% 0.19/0.67 ? [A] : ~ empty(A) ).
% 0.19/0.67
% 0.19/0.67 fof(reflexivity_r1_tarski,axiom,
% 0.19/0.67 ! [A,B] : subset(A,A) ).
% 0.19/0.67
% 0.19/0.67 fof(t12_xboole_1,conjecture,
% 0.19/0.67 ! [A,B] :
% 0.19/0.67 ( subset(A,B)
% 0.19/0.67 => set_union2(A,B) = B ) ).
% 0.19/0.67
% 0.19/0.67 fof(t1_boole,axiom,
% 0.19/0.67 ! [A] : set_union2(A,empty_set) = A ).
% 0.19/0.67
% 0.19/0.67 fof(t6_boole,axiom,
% 0.19/0.67 ! [A] :
% 0.19/0.67 ( empty(A)
% 0.19/0.67 => A = empty_set ) ).
% 0.19/0.67
% 0.19/0.67 fof(t7_boole,axiom,
% 0.19/0.67 ! [A,B] :
% 0.19/0.67 ~ ( in(A,B)
% 0.19/0.67 & empty(B) ) ).
% 0.19/0.67
% 0.19/0.67 fof(t8_boole,axiom,
% 0.19/0.67 ! [A,B] :
% 0.19/0.67 ~ ( empty(A)
% 0.19/0.67 & A != B
% 0.19/0.67 & empty(B) ) ).
% 0.19/0.67
% 0.19/0.67 %------------------------------------------------------------------------------
% 0.19/0.67 %-------------------------------------------
% 0.19/0.67 % Proof found
% 0.19/0.67 % SZS status Theorem for theBenchmark
% 0.19/0.67 % SZS output start Proof
% 0.19/0.67 %ClaNum:42(EqnAxiom:15)
% 0.19/0.67 %VarNum:116(SingletonVarNum:48)
% 0.19/0.67 %MaxLitNum:4
% 0.19/0.67 %MaxfuncDepth:1
% 0.19/0.67 %SharedTerms:11
% 0.19/0.67 %goalClause: 18 24
% 0.19/0.67 %singleGoalClaCount:2
% 0.19/0.67 [16]P1(a1)
% 0.19/0.67 [17]P1(a2)
% 0.19/0.67 [18]P2(a5,a7)
% 0.19/0.67 [23]~P1(a6)
% 0.19/0.67 [24]~E(f8(a5,a7),a7)
% 0.19/0.67 [20]P2(x201,x201)
% 0.19/0.67 [19]E(f8(x191,a1),x191)
% 0.19/0.67 [21]E(f8(x211,x211),x211)
% 0.19/0.67 [22]E(f8(x221,x222),f8(x222,x221))
% 0.19/0.67 [25]~P1(x251)+E(x251,a1)
% 0.19/0.67 [28]~E(x281,x282)+P2(x281,x282)
% 0.19/0.67 [29]~P1(x291)+~P3(x292,x291)
% 0.19/0.67 [30]~P3(x302,x301)+~P3(x301,x302)
% 0.19/0.67 [32]P1(x321)+~P1(f8(x322,x321))
% 0.19/0.67 [33]P1(x331)+~P1(f8(x331,x332))
% 0.19/0.67 [34]P2(x341,x342)+P3(f3(x341,x342),x341)
% 0.19/0.67 [39]P2(x391,x392)+~P3(f3(x391,x392),x392)
% 0.19/0.67 [26]~P1(x262)+~P1(x261)+E(x261,x262)
% 0.19/0.67 [31]~P2(x312,x311)+~P2(x311,x312)+E(x311,x312)
% 0.19/0.67 [35]~P2(x353,x352)+P3(x351,x352)+~P3(x351,x353)
% 0.19/0.67 [41]~P3(f4(x412,x413,x411),x411)+~P3(f4(x412,x413,x411),x413)+E(x411,f8(x412,x413))
% 0.19/0.67 [42]~P3(f4(x422,x423,x421),x421)+~P3(f4(x422,x423,x421),x422)+E(x421,f8(x422,x423))
% 0.19/0.67 [36]~P3(x361,x364)+P3(x361,x362)+~E(x362,f8(x363,x364))
% 0.19/0.67 [37]~P3(x371,x373)+P3(x371,x372)+~E(x372,f8(x373,x374))
% 0.19/0.67 [40]P3(f4(x402,x403,x401),x401)+P3(f4(x402,x403,x401),x403)+P3(f4(x402,x403,x401),x402)+E(x401,f8(x402,x403))
% 0.19/0.67 [38]~P3(x381,x384)+P3(x381,x382)+P3(x381,x383)+~E(x384,f8(x383,x382))
% 0.19/0.67 %EqnAxiom
% 0.19/0.67 [1]E(x11,x11)
% 0.19/0.67 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.67 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.67 [4]~E(x41,x42)+E(f8(x41,x43),f8(x42,x43))
% 0.19/0.67 [5]~E(x51,x52)+E(f8(x53,x51),f8(x53,x52))
% 0.19/0.67 [6]~E(x61,x62)+E(f4(x61,x63,x64),f4(x62,x63,x64))
% 0.19/0.67 [7]~E(x71,x72)+E(f4(x73,x71,x74),f4(x73,x72,x74))
% 0.19/0.67 [8]~E(x81,x82)+E(f4(x83,x84,x81),f4(x83,x84,x82))
% 0.19/0.67 [9]~E(x91,x92)+E(f3(x91,x93),f3(x92,x93))
% 0.19/0.67 [10]~E(x101,x102)+E(f3(x103,x101),f3(x103,x102))
% 0.19/0.67 [11]~P1(x111)+P1(x112)+~E(x111,x112)
% 0.19/0.67 [12]P3(x122,x123)+~E(x121,x122)+~P3(x121,x123)
% 0.19/0.67 [13]P3(x133,x132)+~E(x131,x132)+~P3(x133,x131)
% 0.19/0.67 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143)
% 0.19/0.67 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151)
% 0.19/0.67
% 0.19/0.67 %-------------------------------------------
% 0.19/0.67 cnf(43,plain,
% 0.19/0.67 (E(x431,f8(x431,x431))),
% 0.19/0.67 inference(scs_inference,[],[21,2])).
% 0.19/0.67 cnf(44,plain,
% 0.19/0.67 (~P3(x441,a1)),
% 0.19/0.67 inference(scs_inference,[],[16,21,2,29])).
% 0.19/0.67 cnf(51,plain,
% 0.19/0.67 (E(f8(x511,x511),x511)),
% 0.19/0.67 inference(rename_variables,[],[21])).
% 0.19/0.67 cnf(53,plain,
% 0.19/0.67 (E(f8(x531,x531),x531)),
% 0.19/0.67 inference(rename_variables,[],[21])).
% 0.19/0.67 cnf(54,plain,
% 0.19/0.67 (~E(f8(a5,a7),f8(a7,a7))),
% 0.19/0.67 inference(scs_inference,[],[18,20,16,23,24,21,51,53,2,29,34,15,14,11,3])).
% 0.19/0.67 cnf(55,plain,
% 0.19/0.67 (E(f8(x551,x551),x551)),
% 0.19/0.67 inference(rename_variables,[],[21])).
% 0.19/0.67 cnf(57,plain,
% 0.19/0.67 (E(f8(x571,x571),x571)),
% 0.19/0.67 inference(rename_variables,[],[21])).
% 0.19/0.67 cnf(61,plain,
% 0.19/0.67 (E(a2,a1)),
% 0.19/0.67 inference(scs_inference,[],[18,20,16,17,23,24,21,51,53,55,57,2,29,34,15,14,11,3,38,28,25])).
% 0.19/0.67 cnf(68,plain,
% 0.19/0.67 (E(f3(f8(x681,x681),x682),f3(x681,x682))),
% 0.19/0.67 inference(scs_inference,[],[18,20,16,17,23,24,21,51,53,55,57,2,29,34,15,14,11,3,38,28,25,33,32,10,9])).
% 0.19/0.67 cnf(74,plain,
% 0.19/0.67 (~P3(f3(a1,x741),f8(a1,a1))),
% 0.19/0.67 inference(scs_inference,[],[18,20,16,17,23,24,21,51,53,55,57,2,29,34,15,14,11,3,38,28,25,33,32,10,9,8,7,6,5,4,13])).
% 0.19/0.67 cnf(75,plain,
% 0.19/0.67 (E(f8(x751,x751),x751)),
% 0.19/0.67 inference(rename_variables,[],[21])).
% 0.19/0.67 cnf(78,plain,
% 0.19/0.67 (~P3(x781,a5)+P3(x781,a7)),
% 0.19/0.67 inference(scs_inference,[],[18,20,16,17,23,24,21,51,53,55,57,75,2,29,34,15,14,11,3,38,28,25,33,32,10,9,8,7,6,5,4,13,12,35])).
% 0.19/0.67 cnf(90,plain,
% 0.19/0.67 (~E(a7,f8(a5,a7))),
% 0.19/0.67 inference(scs_inference,[],[24,2])).
% 0.19/0.67 cnf(91,plain,
% 0.19/0.67 (~E(a5,a7)),
% 0.19/0.67 inference(scs_inference,[],[24,54,2,4])).
% 0.19/0.67 cnf(93,plain,
% 0.19/0.67 (~P3(x931,a2)),
% 0.19/0.67 inference(scs_inference,[],[17,24,23,54,44,61,2,4,11,13])).
% 0.19/0.67 cnf(96,plain,
% 0.19/0.67 (~P3(f3(f8(a1,a1),x961),f8(a1,a1))),
% 0.19/0.67 inference(scs_inference,[],[22,17,24,23,68,74,54,44,61,2,4,11,13,3,12])).
% 0.19/0.67 cnf(123,plain,
% 0.19/0.67 (~P3(f4(a5,a7,a7),a7)),
% 0.19/0.67 inference(scs_inference,[],[90,41])).
% 0.19/0.67 cnf(142,plain,
% 0.19/0.67 (~P3(f4(a5,a7,a7),a5)),
% 0.19/0.67 inference(scs_inference,[],[43,20,19,96,93,90,91,44,18,41,40,31,28,2,4,34,15,3,78])).
% 0.19/0.67 cnf(149,plain,
% 0.19/0.67 ($false),
% 0.19/0.67 inference(scs_inference,[],[123,142,90,40]),
% 0.19/0.67 ['proof']).
% 0.19/0.67 % SZS output end Proof
% 0.19/0.67 % Total time :0.020000s
%------------------------------------------------------------------------------