TSTP Solution File: SET906+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET906+1 : TPTP v8.1.2. Released v3.2.0.
% 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 14:31:38 EDT 2023
% Result : Theorem 0.21s 0.66s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET906+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n002.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 : Sat Aug 26 14:31:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.57 start to proof:theBenchmark
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 % File :CSE---1.6
% 0.21/0.65 % Problem :theBenchmark
% 0.21/0.65 % Transform :cnf
% 0.21/0.65 % Format :tptp:raw
% 0.21/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.65
% 0.21/0.65 % Result :Theorem 0.030000s
% 0.21/0.65 % Output :CNFRefutation 0.030000s
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 %------------------------------------------------------------------------------
% 0.21/0.65 % File : SET906+1 : TPTP v8.1.2. Released v3.2.0.
% 0.21/0.65 % Domain : Set theory
% 0.21/0.65 % Problem : subset(set_union2(unordered_pair(A,B),C),C) => in(A,C)
% 0.21/0.65 % Version : [Urb06] axioms : Especial.
% 0.21/0.65 % English :
% 0.21/0.65
% 0.21/0.65 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.21/0.65 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.21/0.65 % Source : [Urb06]
% 0.21/0.65 % Names : zfmisc_1__t47_zfmisc_1 [Urb06]
% 0.21/0.65
% 0.21/0.65 % Status : Theorem
% 0.21/0.65 % Rating : 0.19 v7.5.0, 0.22 v7.4.0, 0.10 v7.3.0, 0.14 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.17 v6.2.0, 0.32 v6.1.0, 0.33 v6.0.0, 0.35 v5.5.0, 0.26 v5.4.0, 0.29 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.25 v4.1.0, 0.26 v4.0.1, 0.30 v4.0.0, 0.29 v3.7.0, 0.20 v3.5.0, 0.21 v3.4.0, 0.32 v3.3.0, 0.14 v3.2.0
% 0.21/0.65 % Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% 0.21/0.65 % Number of atoms : 25 ( 7 equ)
% 0.21/0.65 % Maximal formula atoms : 4 ( 1 avg)
% 0.21/0.65 % Number of connectives : 18 ( 6 ~; 2 |; 0 &)
% 0.21/0.65 % ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% 0.21/0.65 % Maximal formula depth : 8 ( 5 avg)
% 0.21/0.65 % Maximal term depth : 3 ( 1 avg)
% 0.21/0.65 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.21/0.65 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.21/0.65 % Number of variables : 30 ( 28 !; 2 ?)
% 0.21/0.65 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.65
% 0.21/0.65 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.21/0.65 % library, www.mizar.org
% 0.21/0.65 %------------------------------------------------------------------------------
% 0.21/0.65 fof(antisymmetry_r2_hidden,axiom,
% 0.21/0.65 ! [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_k2_tarski,axiom,
% 0.21/0.65 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 0.21/0.65
% 0.21/0.65 fof(commutativity_k2_xboole_0,axiom,
% 0.21/0.65 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.21/0.65
% 0.21/0.65 fof(d2_tarski,axiom,
% 0.21/0.65 ! [A,B,C] :
% 0.21/0.65 ( C = unordered_pair(A,B)
% 0.21/0.65 <=> ! [D] :
% 0.21/0.65 ( in(D,C)
% 0.21/0.65 <=> ( D = A
% 0.21/0.65 | D = B ) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(d2_xboole_0,axiom,
% 0.21/0.65 ! [A,B,C] :
% 0.21/0.65 ( C = set_union2(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(d3_tarski,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( subset(A,B)
% 0.21/0.66 <=> ! [C] :
% 0.21/0.66 ( in(C,A)
% 0.21/0.66 => in(C,B) ) ) ).
% 0.21/0.66
% 0.21/0.66 fof(fc2_xboole_0,axiom,
% 0.21/0.66 ! [A,B] :
% 0.21/0.66 ( ~ empty(A)
% 0.21/0.66 => ~ empty(set_union2(A,B)) ) ).
% 0.21/0.66
% 0.21/0.66 fof(fc3_xboole_0,axiom,
% 0.21/0.66 ! [A,B] :
% 0.21/0.66 ( ~ empty(A)
% 0.21/0.66 => ~ empty(set_union2(B,A)) ) ).
% 0.21/0.66
% 0.21/0.66 fof(idempotence_k2_xboole_0,axiom,
% 0.21/0.66 ! [A,B] : set_union2(A,A) = A ).
% 0.21/0.66
% 0.21/0.66 fof(rc1_xboole_0,axiom,
% 0.21/0.66 ? [A] : empty(A) ).
% 0.21/0.66
% 0.21/0.66 fof(rc2_xboole_0,axiom,
% 0.21/0.66 ? [A] : ~ empty(A) ).
% 0.21/0.66
% 0.21/0.66 fof(reflexivity_r1_tarski,axiom,
% 0.21/0.66 ! [A,B] : subset(A,A) ).
% 0.21/0.66
% 0.21/0.66 fof(t47_zfmisc_1,conjecture,
% 0.21/0.66 ! [A,B,C] :
% 0.21/0.66 ( subset(set_union2(unordered_pair(A,B),C),C)
% 0.21/0.66 => in(A,C) ) ).
% 0.21/0.66
% 0.21/0.66 %------------------------------------------------------------------------------
% 0.21/0.66 %-------------------------------------------
% 0.21/0.66 % Proof found
% 0.21/0.66 % SZS status Theorem for theBenchmark
% 0.21/0.66 % SZS output start Proof
% 0.21/0.66 %ClaNum:46(EqnAxiom:20)
% 0.21/0.66 %VarNum:159(SingletonVarNum:61)
% 0.21/0.66 %MaxLitNum:4
% 0.21/0.66 %MaxfuncDepth:2
% 0.21/0.66 %SharedTerms:11
% 0.21/0.66 %goalClause: 26 28
% 0.21/0.66 %singleGoalClaCount:2
% 0.21/0.66 [21]P1(a1)
% 0.21/0.66 [27]~P1(a7)
% 0.21/0.66 [28]~P3(a6,a9)
% 0.21/0.66 [26]P2(f5(f10(a6,a8),a9),a9)
% 0.21/0.66 [22]P2(x221,x221)
% 0.21/0.66 [23]E(f5(x231,x231),x231)
% 0.21/0.66 [24]E(f10(x241,x242),f10(x242,x241))
% 0.21/0.66 [25]E(f5(x251,x252),f5(x252,x251))
% 0.21/0.66 [31]~P3(x312,x311)+~P3(x311,x312)
% 0.21/0.66 [33]P1(x331)+~P1(f5(x332,x331))
% 0.21/0.66 [34]P1(x341)+~P1(f5(x341,x342))
% 0.21/0.66 [35]P2(x351,x352)+P3(f2(x351,x352),x351)
% 0.21/0.66 [40]P2(x401,x402)+~P3(f2(x401,x402),x402)
% 0.21/0.66 [36]~P2(x363,x362)+P3(x361,x362)+~P3(x361,x363)
% 0.21/0.66 [42]~E(f3(x422,x423,x421),x423)+~P3(f3(x422,x423,x421),x421)+E(x421,f10(x422,x423))
% 0.21/0.66 [43]~E(f3(x432,x433,x431),x432)+~P3(f3(x432,x433,x431),x431)+E(x431,f10(x432,x433))
% 0.21/0.66 [45]~P3(f4(x452,x453,x451),x451)+~P3(f4(x452,x453,x451),x453)+E(x451,f5(x452,x453))
% 0.21/0.66 [46]~P3(f4(x462,x463,x461),x461)+~P3(f4(x462,x463,x461),x462)+E(x461,f5(x462,x463))
% 0.21/0.66 [29]P3(x291,x292)+~E(x291,x293)+~E(x292,f10(x294,x293))
% 0.21/0.66 [30]P3(x301,x302)+~E(x301,x303)+~E(x302,f10(x303,x304))
% 0.21/0.66 [37]~P3(x371,x374)+P3(x371,x372)+~E(x372,f5(x373,x374))
% 0.21/0.66 [38]~P3(x381,x383)+P3(x381,x382)+~E(x382,f5(x383,x384))
% 0.21/0.66 [41]E(f3(x412,x413,x411),x413)+E(f3(x412,x413,x411),x412)+P3(f3(x412,x413,x411),x411)+E(x411,f10(x412,x413))
% 0.21/0.66 [44]P3(f4(x442,x443,x441),x441)+P3(f4(x442,x443,x441),x443)+P3(f4(x442,x443,x441),x442)+E(x441,f5(x442,x443))
% 0.21/0.66 [32]~P3(x321,x324)+E(x321,x322)+E(x321,x323)+~E(x324,f10(x323,x322))
% 0.21/0.66 [39]~P3(x391,x394)+P3(x391,x392)+P3(x391,x393)+~E(x394,f5(x393,x392))
% 0.21/0.66 %EqnAxiom
% 0.21/0.66 [1]E(x11,x11)
% 0.21/0.66 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.66 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43))
% 0.21/0.66 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52))
% 0.21/0.66 [6]~E(x61,x62)+E(f10(x61,x63),f10(x62,x63))
% 0.21/0.66 [7]~E(x71,x72)+E(f10(x73,x71),f10(x73,x72))
% 0.21/0.66 [8]~E(x81,x82)+E(f3(x81,x83,x84),f3(x82,x83,x84))
% 0.21/0.66 [9]~E(x91,x92)+E(f3(x93,x91,x94),f3(x93,x92,x94))
% 0.21/0.66 [10]~E(x101,x102)+E(f3(x103,x104,x101),f3(x103,x104,x102))
% 0.21/0.66 [11]~E(x111,x112)+E(f4(x111,x113,x114),f4(x112,x113,x114))
% 0.21/0.66 [12]~E(x121,x122)+E(f4(x123,x121,x124),f4(x123,x122,x124))
% 0.21/0.66 [13]~E(x131,x132)+E(f4(x133,x134,x131),f4(x133,x134,x132))
% 0.21/0.66 [14]~E(x141,x142)+E(f2(x141,x143),f2(x142,x143))
% 0.21/0.66 [15]~E(x151,x152)+E(f2(x153,x151),f2(x153,x152))
% 0.21/0.66 [16]~P1(x161)+P1(x162)+~E(x161,x162)
% 0.21/0.66 [17]P2(x172,x173)+~E(x171,x172)+~P2(x171,x173)
% 0.21/0.66 [18]P2(x183,x182)+~E(x181,x182)+~P2(x183,x181)
% 0.21/0.66 [19]P3(x192,x193)+~E(x191,x192)+~P3(x191,x193)
% 0.21/0.66 [20]P3(x203,x202)+~E(x201,x202)+~P3(x203,x201)
% 0.21/0.66
% 0.21/0.66 %-------------------------------------------
% 0.21/0.66 cnf(47,plain,
% 0.21/0.66 (E(x471,f5(x471,x471))),
% 0.21/0.66 inference(scs_inference,[],[23,2])).
% 0.21/0.66 cnf(50,plain,
% 0.21/0.66 (E(f5(x501,x502),f5(x502,x501))),
% 0.21/0.66 inference(rename_variables,[],[25])).
% 0.21/0.66 cnf(52,plain,
% 0.21/0.66 (E(f10(x521,x522),f10(x522,x521))),
% 0.21/0.66 inference(rename_variables,[],[24])).
% 0.21/0.66 cnf(53,plain,
% 0.21/0.66 (E(f5(x531,x531),x531)),
% 0.21/0.66 inference(rename_variables,[],[23])).
% 0.21/0.66 cnf(55,plain,
% 0.21/0.66 (P3(f5(x551,x551),f10(x551,x552))),
% 0.21/0.66 inference(scs_inference,[],[26,23,53,24,52,25,2,18,17,30,29])).
% 0.21/0.66 cnf(59,plain,
% 0.21/0.66 (E(f5(x591,x591),x591)),
% 0.21/0.66 inference(rename_variables,[],[23])).
% 0.21/0.66 cnf(80,plain,
% 0.21/0.66 (E(f5(x801,x801),x801)),
% 0.21/0.66 inference(rename_variables,[],[23])).
% 0.21/0.66 cnf(81,plain,
% 0.21/0.66 (~P3(f5(a6,a6),a9)),
% 0.21/0.66 inference(scs_inference,[],[26,28,27,23,53,59,80,24,52,25,2,18,17,30,29,39,31,34,33,15,14,13,12,11,10,9,8,7,6,5,4,20,19])).
% 0.21/0.66 cnf(82,plain,
% 0.21/0.66 (E(f5(x821,x821),x821)),
% 0.21/0.66 inference(rename_variables,[],[23])).
% 0.21/0.66 cnf(84,plain,
% 0.21/0.66 (~E(a1,f5(a7,a7))),
% 0.21/0.66 inference(scs_inference,[],[26,28,21,27,23,53,59,80,82,24,52,25,2,18,17,30,29,39,31,34,33,15,14,13,12,11,10,9,8,7,6,5,4,20,19,16,3])).
% 0.21/0.66 cnf(88,plain,
% 0.21/0.66 (~P3(f10(x881,a9),a9)),
% 0.21/0.66 inference(scs_inference,[],[26,28,21,27,23,53,59,80,82,24,52,25,50,2,18,17,30,29,39,31,34,33,15,14,13,12,11,10,9,8,7,6,5,4,20,19,16,3,36,38])).
% 0.21/0.66 cnf(89,plain,
% 0.21/0.66 (E(f5(x891,x892),f5(x892,x891))),
% 0.21/0.66 inference(rename_variables,[],[25])).
% 0.21/0.66 cnf(91,plain,
% 0.21/0.66 (~P3(a6,f10(a6,a8))),
% 0.21/0.66 inference(scs_inference,[],[26,28,21,27,23,53,59,80,82,24,52,25,50,89,2,18,17,30,29,39,31,34,33,15,14,13,12,11,10,9,8,7,6,5,4,20,19,16,3,36,38,37])).
% 0.21/0.66 cnf(100,plain,
% 0.21/0.66 (P3(f5(x1001,x1001),f10(x1001,x1002))),
% 0.21/0.66 inference(rename_variables,[],[55])).
% 0.21/0.66 cnf(103,plain,
% 0.21/0.66 (E(f10(x1031,x1032),f10(x1032,x1031))),
% 0.21/0.66 inference(rename_variables,[],[24])).
% 0.21/0.66 cnf(106,plain,
% 0.21/0.66 (E(x1061,f5(x1061,x1061))),
% 0.21/0.66 inference(rename_variables,[],[47])).
% 0.21/0.66 cnf(109,plain,
% 0.21/0.66 (E(f5(x1091,x1092),f5(x1092,x1091))),
% 0.21/0.66 inference(rename_variables,[],[25])).
% 0.21/0.66 cnf(118,plain,
% 0.21/0.66 (E(f5(x1181,x1181),x1181)),
% 0.21/0.66 inference(rename_variables,[],[23])).
% 0.21/0.66 cnf(124,plain,
% 0.21/0.66 ($false),
% 0.21/0.66 inference(scs_inference,[],[26,24,103,25,109,23,118,28,47,106,55,100,88,81,84,91,36,39,32,30,38,37,2,31,3,29,20,19]),
% 0.21/0.66 ['proof']).
% 0.21/0.66 % SZS output end Proof
% 0.21/0.66 % Total time :0.030000s
%------------------------------------------------------------------------------