TSTP Solution File: SET907+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET907+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 : 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 14:31:38 EDT 2023
% Result : Theorem 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET907+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
% 0.13/0.35 % Computer : n018.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 : Sat Aug 26 09:30:44 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % File :CSE---1.6
% 0.20/0.62 % Problem :theBenchmark
% 0.20/0.62 % Transform :cnf
% 0.20/0.62 % Format :tptp:raw
% 0.20/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.62
% 0.20/0.62 % Result :Theorem 0.000000s
% 0.20/0.62 % Output :CNFRefutation 0.000000s
% 0.20/0.62 %-------------------------------------------
% 0.20/0.63 %------------------------------------------------------------------------------
% 0.20/0.63 % File : SET907+1 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.63 % Domain : Set theory
% 0.20/0.63 % Problem : ( in(A,B) & in(C,B) ) => set_union2(unordered_pair(A,C),B) = B
% 0.20/0.63 % Version : [Urb06] axioms : Especial.
% 0.20/0.63 % English :
% 0.20/0.63
% 0.20/0.63 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.20/0.63 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.20/0.63 % Source : [Urb06]
% 0.20/0.63 % Names : zfmisc_1__t48_zfmisc_1 [Urb06]
% 0.20/0.63
% 0.20/0.63 % Status : Theorem
% 0.20/0.63 % Rating : 0.03 v7.4.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.00 v6.2.0, 0.04 v6.1.0, 0.07 v6.0.0, 0.09 v5.5.0, 0.07 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.07 v3.2.0
% 0.20/0.63 % Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% 0.20/0.63 % Number of atoms : 20 ( 5 equ)
% 0.20/0.63 % Maximal formula atoms : 3 ( 1 avg)
% 0.20/0.63 % Number of connectives : 14 ( 6 ~; 0 |; 2 &)
% 0.20/0.63 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.20/0.63 % Maximal formula depth : 6 ( 4 avg)
% 0.20/0.63 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.63 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.20/0.63 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.20/0.63 % Number of variables : 24 ( 22 !; 2 ?)
% 0.20/0.63 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.63
% 0.20/0.63 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.20/0.63 % library, www.mizar.org
% 0.20/0.63 %------------------------------------------------------------------------------
% 0.20/0.63 fof(antisymmetry_r2_hidden,axiom,
% 0.20/0.63 ! [A,B] :
% 0.20/0.63 ( in(A,B)
% 0.20/0.63 => ~ in(B,A) ) ).
% 0.20/0.63
% 0.20/0.63 fof(commutativity_k2_tarski,axiom,
% 0.20/0.63 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 0.20/0.63
% 0.20/0.63 fof(commutativity_k2_xboole_0,axiom,
% 0.20/0.63 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.20/0.63
% 0.20/0.63 fof(fc2_xboole_0,axiom,
% 0.20/0.63 ! [A,B] :
% 0.20/0.63 ( ~ empty(A)
% 0.20/0.63 => ~ empty(set_union2(A,B)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(fc3_xboole_0,axiom,
% 0.20/0.63 ! [A,B] :
% 0.20/0.63 ( ~ empty(A)
% 0.20/0.63 => ~ empty(set_union2(B,A)) ) ).
% 0.20/0.63
% 0.20/0.63 fof(idempotence_k2_xboole_0,axiom,
% 0.20/0.63 ! [A,B] : set_union2(A,A) = A ).
% 0.20/0.63
% 0.20/0.63 fof(rc1_xboole_0,axiom,
% 0.20/0.63 ? [A] : empty(A) ).
% 0.20/0.63
% 0.20/0.63 fof(rc2_xboole_0,axiom,
% 0.20/0.63 ? [A] : ~ empty(A) ).
% 0.20/0.63
% 0.20/0.63 fof(reflexivity_r1_tarski,axiom,
% 0.20/0.63 ! [A,B] : subset(A,A) ).
% 0.20/0.63
% 0.20/0.63 fof(t12_xboole_1,axiom,
% 0.20/0.63 ! [A,B] :
% 0.20/0.63 ( subset(A,B)
% 0.20/0.63 => set_union2(A,B) = B ) ).
% 0.20/0.63
% 0.20/0.63 fof(t38_zfmisc_1,axiom,
% 0.20/0.63 ! [A,B,C] :
% 0.20/0.63 ( subset(unordered_pair(A,B),C)
% 0.20/0.63 <=> ( in(A,C)
% 0.20/0.63 & in(B,C) ) ) ).
% 0.20/0.63
% 0.20/0.63 fof(t48_zfmisc_1,conjecture,
% 0.20/0.63 ! [A,B,C] :
% 0.20/0.63 ( ( in(A,B)
% 0.20/0.63 & in(C,B) )
% 0.20/0.63 => set_union2(unordered_pair(A,C),B) = B ) ).
% 0.20/0.63
% 0.20/0.63 %------------------------------------------------------------------------------
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark
% 0.20/0.63 % SZS output start Proof
% 0.20/0.63 %ClaNum:28(EqnAxiom:12)
% 0.20/0.63 %VarNum:45(SingletonVarNum:23)
% 0.20/0.63 %MaxLitNum:3
% 0.20/0.63 %MaxfuncDepth:2
% 0.20/0.63 %SharedTerms:12
% 0.20/0.63 %goalClause: 14 15 21
% 0.20/0.63 %singleGoalClaCount:3
% 0.20/0.63 [13]P1(a1)
% 0.20/0.63 [14]P2(a2,a4)
% 0.20/0.63 [15]P2(a5,a4)
% 0.20/0.63 [20]~P1(a3)
% 0.20/0.63 [21]~E(f6(f7(a2,a5),a4),a4)
% 0.20/0.63 [16]P3(x161,x161)
% 0.20/0.63 [17]E(f6(x171,x171),x171)
% 0.20/0.63 [18]E(f7(x181,x182),f7(x182,x181))
% 0.20/0.63 [19]E(f6(x191,x192),f6(x192,x191))
% 0.20/0.63 [23]~P2(x232,x231)+~P2(x231,x232)
% 0.20/0.63 [22]~P3(x221,x222)+E(f6(x221,x222),x222)
% 0.20/0.63 [24]P1(x241)+~P1(f6(x242,x241))
% 0.20/0.63 [25]P1(x251)+~P1(f6(x251,x252))
% 0.20/0.63 [26]P2(x261,x262)+~P3(f7(x263,x261),x262)
% 0.20/0.63 [27]P2(x271,x272)+~P3(f7(x271,x273),x272)
% 0.20/0.63 [28]~P2(x282,x283)+~P2(x281,x283)+P3(f7(x281,x282),x283)
% 0.20/0.63 %EqnAxiom
% 0.20/0.63 [1]E(x11,x11)
% 0.20/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.63 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.20/0.63 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.20/0.63 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63))
% 0.20/0.63 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72))
% 0.20/0.63 [8]~P1(x81)+P1(x82)+~E(x81,x82)
% 0.20/0.63 [9]P2(x92,x93)+~E(x91,x92)+~P2(x91,x93)
% 0.20/0.63 [10]P2(x103,x102)+~E(x101,x102)+~P2(x103,x101)
% 0.20/0.63 [11]P3(x112,x113)+~E(x111,x112)+~P3(x111,x113)
% 0.20/0.63 [12]P3(x123,x122)+~E(x121,x122)+~P3(x123,x121)
% 0.20/0.63
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 cnf(33,plain,
% 0.20/0.63 (P3(x331,x331)),
% 0.20/0.63 inference(rename_variables,[],[16])).
% 0.20/0.63 cnf(36,plain,
% 0.20/0.63 (P3(x361,x361)),
% 0.20/0.63 inference(rename_variables,[],[16])).
% 0.20/0.63 cnf(41,plain,
% 0.20/0.63 (P3(x411,x411)),
% 0.20/0.63 inference(rename_variables,[],[16])).
% 0.20/0.63 cnf(46,plain,
% 0.20/0.63 (E(f6(x461,x461),x461)),
% 0.20/0.63 inference(rename_variables,[],[17])).
% 0.20/0.63 cnf(48,plain,
% 0.20/0.63 (E(f6(x481,x481),x481)),
% 0.20/0.63 inference(rename_variables,[],[17])).
% 0.20/0.63 cnf(51,plain,
% 0.20/0.63 ($false),
% 0.20/0.64 inference(scs_inference,[],[14,16,33,36,41,15,20,21,17,46,48,2,23,27,26,22,12,11,10,9,8,3,28]),
% 0.20/0.64 ['proof']).
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time :0.000000s
%------------------------------------------------------------------------------