TSTP Solution File: SET903+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET903+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 : n008.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 14:31:37 EDT 2023
% Result : Theorem 0.19s 0.63s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET903+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
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 08:36:32 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % File :CSE---1.6
% 0.19/0.63 % Problem :theBenchmark
% 0.19/0.63 % Transform :cnf
% 0.19/0.63 % Format :tptp:raw
% 0.19/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.63
% 0.19/0.63 % Result :Theorem 0.010000s
% 0.19/0.63 % Output :CNFRefutation 0.010000s
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 % File : SET903+1 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.63 % Domain : Set theory
% 0.19/0.63 % Problem : ~ ( sgtn(A) = union(B,C) & B != C & B != empty & C != empty )
% 0.19/0.63 % Version : [Urb06] axioms : Especial.
% 0.19/0.63 % English :
% 0.19/0.63
% 0.19/0.63 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.19/0.63 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.19/0.63 % Source : [Urb06]
% 0.19/0.63 % Names : zfmisc_1__t44_zfmisc_1 [Urb06]
% 0.19/0.63
% 0.19/0.63 % Status : Theorem
% 0.19/0.63 % Rating : 0.11 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.04 v6.2.0, 0.12 v6.1.0, 0.13 v6.0.0, 0.04 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.1, 0.17 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.14 v3.2.0
% 0.19/0.63 % Syntax : Number of formulae : 9 ( 5 unt; 0 def)
% 0.19/0.63 % Number of atoms : 20 ( 13 equ)
% 0.19/0.63 % Maximal formula atoms : 7 ( 2 avg)
% 0.19/0.63 % Number of connectives : 24 ( 13 ~; 0 |; 9 &)
% 0.19/0.63 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.63 % Maximal formula depth : 10 ( 5 avg)
% 0.19/0.63 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.63 % Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% 0.19/0.63 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.63 % Number of variables : 16 ( 14 !; 2 ?)
% 0.19/0.63 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.63
% 0.19/0.63 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.63 % library, www.mizar.org
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 fof(commutativity_k2_xboole_0,axiom,
% 0.19/0.63 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.19/0.63
% 0.19/0.63 fof(fc1_xboole_0,axiom,
% 0.19/0.63 empty(empty_set) ).
% 0.19/0.63
% 0.19/0.63 fof(fc2_xboole_0,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ( ~ empty(A)
% 0.19/0.63 => ~ empty(set_union2(A,B)) ) ).
% 0.19/0.63
% 0.19/0.63 fof(fc3_xboole_0,axiom,
% 0.19/0.63 ! [A,B] :
% 0.19/0.63 ( ~ empty(A)
% 0.19/0.63 => ~ empty(set_union2(B,A)) ) ).
% 0.19/0.63
% 0.19/0.63 fof(idempotence_k2_xboole_0,axiom,
% 0.19/0.63 ! [A,B] : set_union2(A,A) = A ).
% 0.19/0.63
% 0.19/0.63 fof(rc1_xboole_0,axiom,
% 0.19/0.63 ? [A] : empty(A) ).
% 0.19/0.63
% 0.19/0.63 fof(rc2_xboole_0,axiom,
% 0.19/0.63 ? [A] : ~ empty(A) ).
% 0.19/0.63
% 0.19/0.63 fof(t43_zfmisc_1,axiom,
% 0.19/0.63 ! [A,B,C] :
% 0.19/0.63 ~ ( singleton(A) = set_union2(B,C)
% 0.19/0.63 & ~ ( B = singleton(A)
% 0.19/0.63 & C = singleton(A) )
% 0.19/0.63 & ~ ( B = empty_set
% 0.19/0.63 & C = singleton(A) )
% 0.19/0.63 & ~ ( B = singleton(A)
% 0.19/0.63 & C = empty_set ) ) ).
% 0.19/0.63
% 0.19/0.63 fof(t44_zfmisc_1,conjecture,
% 0.19/0.63 ! [A,B,C] :
% 0.19/0.63 ~ ( singleton(A) = set_union2(B,C)
% 0.19/0.63 & B != C
% 0.19/0.63 & B != empty_set
% 0.19/0.63 & C != empty_set ) ).
% 0.19/0.63
% 0.19/0.63 %------------------------------------------------------------------------------
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % Proof found
% 0.19/0.63 % SZS status Theorem for theBenchmark
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 %ClaNum:26(EqnAxiom:7)
% 0.19/0.63 %VarNum:32(SingletonVarNum:16)
% 0.19/0.63 %MaxLitNum:3
% 0.19/0.63 %MaxfuncDepth:1
% 0.19/0.63 %SharedTerms:15
% 0.19/0.63 %goalClause: 10 13 14 15
% 0.19/0.63 %singleGoalClaCount:4
% 0.19/0.63 [8]P1(a1)
% 0.19/0.63 [9]P1(a2)
% 0.19/0.63 [13]~E(a3,a1)
% 0.19/0.63 [14]~E(a6,a1)
% 0.19/0.63 [15]~E(a6,a3)
% 0.19/0.63 [16]~P1(a5)
% 0.19/0.63 [10]E(f7(a3,a6),f8(a4))
% 0.19/0.63 [11]E(f7(x111,x111),x111)
% 0.19/0.63 [12]E(f7(x121,x122),f7(x122,x121))
% 0.19/0.63 [25]P1(x251)+~P1(f7(x252,x251))
% 0.19/0.63 [26]P1(x261)+~P1(f7(x261,x262))
% 0.19/0.63 [17]E(x171,a1)+E(x171,f8(x172))+~E(f8(x172),f7(x173,x171))
% 0.19/0.63 [18]E(x181,a1)+E(x181,f8(x182))+~E(f8(x182),f7(x181,x183))
% 0.19/0.63 [22]~E(f8(x222),f7(x223,x221))+E(x221,f8(x222))+E(x223,f8(x222))
% 0.19/0.63 %EqnAxiom
% 0.19/0.63 [1]E(x11,x11)
% 0.19/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.63 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43))
% 0.19/0.63 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52))
% 0.19/0.63 [6]~E(x61,x62)+E(f8(x61),f8(x62))
% 0.19/0.63 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.19/0.63
% 0.19/0.63 %-------------------------------------------
% 0.19/0.64 cnf(29,plain,
% 0.19/0.64 (E(f7(x291,x291),x291)),
% 0.19/0.64 inference(rename_variables,[],[11])).
% 0.19/0.64 cnf(32,plain,
% 0.19/0.64 (E(a3,f8(a4))),
% 0.19/0.64 inference(scs_inference,[],[10,13,16,11,29,2,7,3,18])).
% 0.19/0.64 cnf(34,plain,
% 0.19/0.64 (E(a6,f8(a4))),
% 0.19/0.64 inference(scs_inference,[],[10,13,14,16,11,29,2,7,3,18,17])).
% 0.19/0.64 cnf(44,plain,
% 0.19/0.64 (~E(f8(a4),a3)),
% 0.19/0.64 inference(scs_inference,[],[15,8,16,34,7,3])).
% 0.19/0.64 cnf(73,plain,
% 0.19/0.64 ($false),
% 0.19/0.64 inference(scs_inference,[],[32,9,11,16,44,7,3,2]),
% 0.19/0.64 ['proof']).
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64 % Total time :0.010000s
%------------------------------------------------------------------------------