TSTP Solution File: SET930+1 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET930+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 : n011.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 14:31:45 EDT 2023
% Result : Theorem 1.63s 1.83s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n011.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 09:18:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 start to proof:theBenchmark
% 1.63/1.82 %-------------------------------------------
% 1.63/1.82 % File :CSE---1.6
% 1.63/1.82 % Problem :theBenchmark
% 1.63/1.82 % Transform :cnf
% 1.63/1.82 % Format :tptp:raw
% 1.63/1.82 % Command :java -jar mcs_scs.jar %d %s
% 1.63/1.82
% 1.63/1.82 % Result :Theorem 1.180000s
% 1.63/1.82 % Output :CNFRefutation 1.180000s
% 1.63/1.82 %-------------------------------------------
% 1.63/1.82 %------------------------------------------------------------------------------
% 1.63/1.82 % File : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 1.63/1.82 % Domain : Set theory
% 1.63/1.82 % Problem : Basic properties of sets, theorem 74
% 1.63/1.82 % Version : [Urb06] axioms : Especial.
% 1.63/1.82 % English : ~ ( difference(unordered_pair(A,B),C) != empty_set
% 1.63/1.82 % & difference(unordered_pair(A,B),C) != singleton(A)
% 1.63/1.82 % & difference(unordered_pair(A,B),C) != singleton(B)
% 1.63/1.82 % & difference(unordered_pair(A,B),C) != unordered_pair(A,B) )
% 1.63/1.82
% 1.63/1.82 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 1.63/1.82 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 1.63/1.82 % Source : [Urb06]
% 1.63/1.82 % Names : zfmisc_1__t74_zfmisc_1 [Urb06]
% 1.63/1.82
% 1.63/1.82 % Status : Theorem
% 1.63/1.82 % Rating : 0.14 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.10 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.13 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.17 v6.0.0, 0.09 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0, 0.26 v5.2.0, 0.10 v5.0.0, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.14 v3.2.0
% 1.63/1.82 % Syntax : Number of formulae : 9 ( 4 unt; 0 def)
% 1.63/1.82 % Number of atoms : 20 ( 9 equ)
% 1.63/1.82 % Maximal formula atoms : 4 ( 2 avg)
% 1.63/1.82 % Number of connectives : 21 ( 10 ~; 1 |; 6 &)
% 1.63/1.82 % ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% 1.63/1.82 % Maximal formula depth : 9 ( 5 avg)
% 1.63/1.82 % Maximal term depth : 3 ( 1 avg)
% 1.63/1.82 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 1.63/1.82 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% 1.63/1.82 % Number of variables : 18 ( 16 !; 2 ?)
% 1.63/1.82 % SPC : FOF_THM_RFO_SEQ
% 1.63/1.82
% 1.63/1.82 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 1.63/1.82 % library, www.mizar.org
% 1.63/1.82 %------------------------------------------------------------------------------
% 1.63/1.82 fof(antisymmetry_r2_hidden,axiom,
% 1.63/1.82 ! [A,B] :
% 1.63/1.82 ( in(A,B)
% 1.63/1.82 => ~ in(B,A) ) ).
% 1.63/1.83
% 1.63/1.83 fof(commutativity_k2_tarski,axiom,
% 1.63/1.83 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 1.63/1.83
% 1.63/1.83 fof(fc1_xboole_0,axiom,
% 1.63/1.83 empty(empty_set) ).
% 1.63/1.83
% 1.63/1.83 fof(l39_zfmisc_1,axiom,
% 1.63/1.83 ! [A,B,C] :
% 1.63/1.83 ( set_difference(unordered_pair(A,B),C) = singleton(A)
% 1.63/1.83 <=> ( ~ in(A,C)
% 1.63/1.83 & ( in(B,C)
% 1.63/1.83 | A = B ) ) ) ).
% 1.63/1.83
% 1.63/1.83 fof(rc1_xboole_0,axiom,
% 1.63/1.83 ? [A] : empty(A) ).
% 1.63/1.83
% 1.63/1.83 fof(rc2_xboole_0,axiom,
% 1.63/1.83 ? [A] : ~ empty(A) ).
% 1.63/1.83
% 1.63/1.83 fof(t72_zfmisc_1,axiom,
% 1.63/1.83 ! [A,B,C] :
% 1.63/1.83 ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
% 1.63/1.83 <=> ( ~ in(A,C)
% 1.63/1.83 & ~ in(B,C) ) ) ).
% 1.63/1.83
% 1.63/1.83 fof(t73_zfmisc_1,axiom,
% 1.63/1.83 ! [A,B,C] :
% 1.63/1.83 ( set_difference(unordered_pair(A,B),C) = empty_set
% 1.63/1.83 <=> ( in(A,C)
% 1.63/1.83 & in(B,C) ) ) ).
% 1.63/1.83
% 1.63/1.83 fof(t74_zfmisc_1,conjecture,
% 1.63/1.83 ! [A,B,C] :
% 1.63/1.83 ~ ( set_difference(unordered_pair(A,B),C) != empty_set
% 1.63/1.83 & set_difference(unordered_pair(A,B),C) != singleton(A)
% 1.63/1.83 & set_difference(unordered_pair(A,B),C) != singleton(B)
% 1.63/1.83 & set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) ).
% 1.63/1.83
% 1.63/1.83 %------------------------------------------------------------------------------
% 1.63/1.83 %-------------------------------------------
% 1.63/1.83 % Proof found
% 1.63/1.83 % SZS status Theorem for theBenchmark
% 1.63/1.83 % SZS output start Proof
% 1.63/1.83 %ClaNum:30(EqnAxiom:11)
% 1.63/1.83 %VarNum:78(SingletonVarNum:34)
% 1.63/1.83 %MaxLitNum:3
% 1.63/1.83 %MaxfuncDepth:2
% 1.63/1.83 %SharedTerms:17
% 1.63/1.83 %goalClause: 16 17 18 19
% 1.63/1.83 %singleGoalClaCount:4
% 1.63/1.83 [12]P1(a1)
% 1.63/1.83 [13]P1(a2)
% 1.63/1.83 [15]~P1(a4)
% 1.63/1.83 [16]~E(f8(f3(a5,a6),a7),a1)
% 1.63/1.83 [17]~E(f8(f3(a5,a6),a7),f9(a5))
% 1.63/1.83 [18]~E(f8(f3(a5,a6),a7),f9(a6))
% 1.63/1.83 [19]~E(f8(f3(a5,a6),a7),f3(a5,a6))
% 1.63/1.83 [14]E(f3(x141,x142),f3(x142,x141))
% 1.63/1.83 [20]~P2(x202,x201)+~P2(x201,x202)
% 1.63/1.83 [22]P2(x221,x222)+~E(f8(f3(x223,x221),x222),a1)
% 1.63/1.83 [23]P2(x231,x232)+~E(f8(f3(x231,x233),x232),a1)
% 1.63/1.83 [28]~P2(x281,x283)+~E(f8(f3(x281,x282),x283),f9(x281))
% 1.63/1.83 [29]~P2(x292,x293)+~E(f8(f3(x291,x292),x293),f3(x291,x292))
% 1.63/1.83 [30]~P2(x301,x303)+~E(f8(f3(x301,x302),x303),f3(x301,x302))
% 1.63/1.83 [21]P2(x211,x213)+~E(x211,x212)+E(f8(f3(x211,x212),x213),f9(x211))
% 1.63/1.83 [24]P2(x241,x243)+~P2(x242,x243)+E(f8(f3(x241,x242),x243),f9(x241))
% 1.63/1.83 [25]P2(x252,x253)+P2(x251,x253)+E(f8(f3(x251,x252),x253),f3(x251,x252))
% 1.63/1.83 [26]~P2(x262,x263)+~P2(x261,x263)+E(f8(f3(x261,x262),x263),a1)
% 1.63/1.83 [27]E(x271,x272)+P2(x271,x273)+~E(f8(f3(x272,x271),x273),f9(x272))
% 1.63/1.83 %EqnAxiom
% 1.63/1.83 [1]E(x11,x11)
% 1.63/1.83 [2]E(x22,x21)+~E(x21,x22)
% 1.63/1.83 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 1.63/1.83 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 1.63/1.83 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 1.63/1.83 [6]~E(x61,x62)+E(f8(x61,x63),f8(x62,x63))
% 1.63/1.83 [7]~E(x71,x72)+E(f8(x73,x71),f8(x73,x72))
% 1.63/1.83 [8]~E(x81,x82)+E(f9(x81),f9(x82))
% 1.63/1.83 [9]~P1(x91)+P1(x92)+~E(x91,x92)
% 1.63/1.83 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103)
% 1.63/1.83 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111)
% 1.63/1.83
% 1.63/1.83 %-------------------------------------------
% 1.63/1.83 cnf(31,plain,
% 1.63/1.83 (~E(f8(f3(a5,a6),a7),f3(a6,a5))),
% 1.63/1.83 inference(scs_inference,[],[19,14,3])).
% 1.63/1.83 cnf(32,plain,
% 1.63/1.83 (E(f3(x321,x322),f3(x322,x321))),
% 1.63/1.83 inference(rename_variables,[],[14])).
% 1.63/1.83 cnf(36,plain,
% 1.63/1.83 (E(f8(f3(x361,x362),x363),f8(f3(x362,x361),x363))),
% 1.63/1.83 inference(scs_inference,[],[16,19,14,32,3,2,8,7,6])).
% 1.63/1.83 cnf(50,plain,
% 1.63/1.83 (~E(f8(f3(a6,a5),a7),a1)),
% 1.63/1.83 inference(scs_inference,[],[16,13,15,36,9,3])).
% 1.63/1.83 cnf(63,plain,
% 1.63/1.83 (~E(f9(a6),f8(f3(a5,a6),a7))),
% 1.63/1.83 inference(scs_inference,[],[18,2])).
% 1.63/1.83 cnf(78,plain,
% 1.63/1.83 (~E(f8(f3(a6,a5),a7),f3(a6,a5))),
% 1.63/1.83 inference(scs_inference,[],[31,36,3])).
% 1.63/1.83 cnf(145,plain,
% 1.63/1.83 (~E(f8(f3(a6,a5),a7),f9(a6))),
% 1.63/1.83 inference(scs_inference,[],[63,36,3,2])).
% 1.63/1.83 cnf(257,plain,
% 1.63/1.83 (~P2(a5,a7)),
% 1.63/1.83 inference(scs_inference,[],[50,145,24,26])).
% 1.63/1.83 cnf(264,plain,
% 1.63/1.83 ($false),
% 1.63/1.83 inference(scs_inference,[],[257,78,17,25,24]),
% 1.63/1.83 ['proof']).
% 1.63/1.83 % SZS output end Proof
% 1.63/1.83 % Total time :1.180000s
%------------------------------------------------------------------------------