TSTP Solution File: SET987+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET987+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 : n032.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 14:31:53 EDT 2023
% Result : Theorem 0.15s 0.53s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET987+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sat Aug 26 12:12:28 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.15/0.48 start to proof:theBenchmark
% 0.15/0.53 %-------------------------------------------
% 0.15/0.53 % File :CSE---1.6
% 0.15/0.53 % Problem :theBenchmark
% 0.15/0.53 % Transform :cnf
% 0.15/0.53 % Format :tptp:raw
% 0.15/0.53 % Command :java -jar mcs_scs.jar %d %s
% 0.15/0.53
% 0.15/0.53 % Result :Theorem 0.010000s
% 0.15/0.53 % Output :CNFRefutation 0.010000s
% 0.15/0.53 %-------------------------------------------
% 0.15/0.53 %------------------------------------------------------------------------------
% 0.15/0.53 % File : SET987+1 : TPTP v8.1.2. Released v3.2.0.
% 0.15/0.53 % Domain : Set theory
% 0.15/0.53 % Problem : ~ in(A,B) => difference(union(B,singleton(A)),singleton(A)) = B
% 0.15/0.53 % Version : [Urb06] axioms : Especial.
% 0.15/0.53 % English :
% 0.15/0.53
% 0.15/0.53 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.15/0.53 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.15/0.53 % Source : [Urb06]
% 0.15/0.53 % Names : zfmisc_1__t141_zfmisc_1 [Urb06]
% 0.15/0.53
% 0.15/0.53 % Status : Theorem
% 0.15/0.53 % Rating : 0.08 v8.1.0, 0.06 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.00 v7.0.0, 0.03 v6.4.0, 0.08 v6.1.0, 0.07 v6.0.0, 0.09 v5.5.0, 0.11 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, 0.05 v3.3.0, 0.14 v3.2.0
% 0.15/0.53 % Syntax : Number of formulae : 10 ( 5 unt; 0 def)
% 0.15/0.53 % Number of atoms : 15 ( 5 equ)
% 0.15/0.53 % Maximal formula atoms : 2 ( 1 avg)
% 0.15/0.53 % Number of connectives : 13 ( 8 ~; 0 |; 0 &)
% 0.15/0.53 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.15/0.53 % Maximal formula depth : 5 ( 4 avg)
% 0.15/0.53 % Maximal term depth : 4 ( 1 avg)
% 0.15/0.53 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.15/0.53 % Number of functors : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.15/0.53 % Number of variables : 18 ( 16 !; 2 ?)
% 0.15/0.53 % SPC : FOF_THM_RFO_SEQ
% 0.15/0.53
% 0.15/0.53 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.15/0.53 % library, www.mizar.org
% 0.15/0.53 %------------------------------------------------------------------------------
% 0.15/0.53 fof(antisymmetry_r2_hidden,axiom,
% 0.15/0.53 ! [A,B] :
% 0.15/0.53 ( in(A,B)
% 0.15/0.53 => ~ in(B,A) ) ).
% 0.15/0.53
% 0.15/0.53 fof(commutativity_k2_xboole_0,axiom,
% 0.15/0.53 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.15/0.53
% 0.15/0.53 fof(fc2_xboole_0,axiom,
% 0.15/0.53 ! [A,B] :
% 0.15/0.53 ( ~ empty(A)
% 0.15/0.53 => ~ empty(set_union2(A,B)) ) ).
% 0.15/0.53
% 0.15/0.53 fof(fc3_xboole_0,axiom,
% 0.15/0.53 ! [A,B] :
% 0.15/0.53 ( ~ empty(A)
% 0.15/0.53 => ~ empty(set_union2(B,A)) ) ).
% 0.15/0.53
% 0.15/0.53 fof(idempotence_k2_xboole_0,axiom,
% 0.15/0.53 ! [A,B] : set_union2(A,A) = A ).
% 0.15/0.53
% 0.15/0.53 fof(rc1_xboole_0,axiom,
% 0.15/0.53 ? [A] : empty(A) ).
% 0.15/0.53
% 0.15/0.53 fof(rc2_xboole_0,axiom,
% 0.15/0.53 ? [A] : ~ empty(A) ).
% 0.15/0.53
% 0.15/0.53 fof(t141_zfmisc_1,conjecture,
% 0.15/0.53 ! [A,B] :
% 0.15/0.53 ( ~ in(A,B)
% 0.15/0.53 => set_difference(set_union2(B,singleton(A)),singleton(A)) = B ) ).
% 0.15/0.53
% 0.15/0.53 fof(t40_xboole_1,axiom,
% 0.15/0.53 ! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) ).
% 0.15/0.53
% 0.15/0.53 fof(t65_zfmisc_1,axiom,
% 0.15/0.53 ! [A,B] :
% 0.15/0.53 ( set_difference(A,singleton(B)) = A
% 0.15/0.53 <=> ~ in(B,A) ) ).
% 0.15/0.53
% 0.15/0.53 %------------------------------------------------------------------------------
% 0.15/0.53 %-------------------------------------------
% 0.15/0.53 % Proof found
% 0.15/0.53 % SZS status Theorem for theBenchmark
% 0.15/0.53 % SZS output start Proof
% 0.15/0.53 %ClaNum:23(EqnAxiom:11)
% 0.15/0.53 %VarNum:32(SingletonVarNum:15)
% 0.15/0.53 %MaxLitNum:2
% 0.15/0.53 %MaxfuncDepth:2
% 0.15/0.53 %SharedTerms:11
% 0.15/0.53 %goalClause: 17 18
% 0.15/0.53 %singleGoalClaCount:2
% 0.15/0.53 [12]P1(a1)
% 0.15/0.53 [16]~P1(a4)
% 0.15/0.53 [17]~P2(a5,a6)
% 0.15/0.53 [18]~E(f3(f2(a6,f7(a5)),f7(a5)),a6)
% 0.15/0.53 [13]E(f2(x131,x131),x131)
% 0.15/0.53 [14]E(f2(x141,x142),f2(x142,x141))
% 0.15/0.53 [15]E(f3(f2(x151,x152),x152),f3(x151,x152))
% 0.15/0.53 [20]~P2(x202,x201)+~P2(x201,x202)
% 0.15/0.53 [21]P1(x211)+~P1(f2(x212,x211))
% 0.15/0.53 [22]P1(x221)+~P1(f2(x221,x222))
% 0.15/0.53 [19]P2(x192,x191)+E(f3(x191,f7(x192)),x191)
% 0.15/0.53 [23]~P2(x232,x231)+~E(f3(x231,f7(x232)),x231)
% 0.15/0.53 %EqnAxiom
% 0.15/0.53 [1]E(x11,x11)
% 0.15/0.53 [2]E(x22,x21)+~E(x21,x22)
% 0.15/0.53 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.15/0.53 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.15/0.53 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.15/0.53 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.15/0.53 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.15/0.53 [8]~E(x81,x82)+E(f7(x81),f7(x82))
% 0.15/0.53 [9]~P1(x91)+P1(x92)+~E(x91,x92)
% 0.15/0.53 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103)
% 0.15/0.53 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111)
% 0.15/0.53
% 0.15/0.53 %-------------------------------------------
% 0.15/0.54 cnf(26,plain,
% 0.15/0.54 (E(f2(x261,x261),x261)),
% 0.15/0.54 inference(rename_variables,[],[13])).
% 0.15/0.54 cnf(28,plain,
% 0.15/0.54 (E(f2(x281,x281),x281)),
% 0.15/0.54 inference(rename_variables,[],[13])).
% 0.15/0.54 cnf(36,plain,
% 0.15/0.54 (E(f2(x361,f2(x362,x362)),f2(x361,x362))),
% 0.15/0.54 inference(scs_inference,[],[16,18,13,26,28,2,9,3,22,21,8,7,6,5])).
% 0.15/0.54 cnf(38,plain,
% 0.15/0.54 (E(f3(a6,f7(a5)),a6)),
% 0.15/0.54 inference(scs_inference,[],[17,16,18,13,26,28,2,9,3,22,21,8,7,6,5,4,19])).
% 0.15/0.54 cnf(40,plain,
% 0.15/0.54 (~P2(a5,f2(a6,a6))),
% 0.15/0.54 inference(scs_inference,[],[17,16,18,13,26,28,2,9,3,22,21,8,7,6,5,4,19,11])).
% 0.15/0.54 cnf(41,plain,
% 0.15/0.54 (~P2(x411,a6)+~E(x411,a5)),
% 0.15/0.54 inference(scs_inference,[],[17,16,18,13,26,28,2,9,3,22,21,8,7,6,5,4,19,11,10])).
% 0.15/0.54 cnf(47,plain,
% 0.15/0.54 (E(f2(x471,f2(x472,x472)),f2(x471,x472))),
% 0.15/0.54 inference(rename_variables,[],[36])).
% 0.15/0.54 cnf(51,plain,
% 0.15/0.54 ($false),
% 0.15/0.54 inference(scs_inference,[],[12,15,18,13,16,36,47,38,40,41,2,11,10,9,3]),
% 0.15/0.54 ['proof']).
% 0.15/0.54 % SZS output end Proof
% 0.15/0.54 % Total time :0.010000s
%------------------------------------------------------------------------------