TSTP Solution File: SET950+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n007.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 : Wed Aug 31 18:22:50 EDT 2022
% Result : Theorem 0.21s 0.57s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 6 unt; 0 def)
% Number of atoms : 202 ( 47 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 243 ( 89 ~; 77 |; 61 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 148 ( 113 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f88,plain,
$false,
inference(avatar_sat_refutation,[],[f78,f82,f87]) ).
fof(f87,plain,
spl9_2,
inference(avatar_contradiction_clause,[],[f86]) ).
fof(f86,plain,
( $false
| spl9_2 ),
inference(subsumption_resolution,[],[f85,f41]) ).
fof(f41,plain,
in(sK7,sK6),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( ! [X4,X5] :
( ~ in(X5,sK8)
| sK7 != ordered_pair(X5,X4)
| ~ in(X4,sK5) )
& in(sK7,sK6)
& subset(sK6,cartesian_product2(sK8,sK5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f26,f27]) ).
fof(f27,plain,
( ? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ~ in(X5,X3)
| ordered_pair(X5,X4) != X2
| ~ in(X4,X0) )
& in(X2,X1)
& subset(X1,cartesian_product2(X3,X0)) )
=> ( ! [X5,X4] :
( ~ in(X5,sK8)
| sK7 != ordered_pair(X5,X4)
| ~ in(X4,sK5) )
& in(sK7,sK6)
& subset(sK6,cartesian_product2(sK8,sK5)) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ~ in(X5,X3)
| ordered_pair(X5,X4) != X2
| ~ in(X4,X0) )
& in(X2,X1)
& subset(X1,cartesian_product2(X3,X0)) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
? [X2,X3,X1,X0] :
( ! [X5,X4] :
( ~ in(X4,X0)
| ordered_pair(X4,X5) != X1
| ~ in(X5,X2) )
& in(X1,X3)
& subset(X3,cartesian_product2(X0,X2)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
~ ! [X0,X3,X1,X2] :
~ ( subset(X3,cartesian_product2(X0,X2))
& ! [X5,X4] :
~ ( in(X4,X0)
& ordered_pair(X4,X5) = X1
& in(X5,X2) )
& in(X1,X3) ),
inference(rectify,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X1,X3,X2,X0] :
~ ( in(X3,X0)
& ! [X4,X5] :
~ ( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
& subset(X0,cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X1,X3,X2,X0] :
~ ( in(X3,X0)
& ! [X4,X5] :
~ ( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
& subset(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f85,plain,
( ~ in(sK7,sK6)
| spl9_2 ),
inference(resolution,[],[f84,f51]) ).
fof(f51,plain,
! [X0] :
( in(X0,cartesian_product2(sK8,sK5))
| ~ in(X0,sK6) ),
inference(resolution,[],[f31,f40]) ).
fof(f40,plain,
subset(sK6,cartesian_product2(sK8,sK5)),
inference(cnf_transformation,[],[f28]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ subset(X1,X0)
| ~ in(X2,X1)
| in(X2,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X1,X0)
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
=> in(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f84,plain,
( ~ in(sK7,cartesian_product2(sK8,sK5))
| spl9_2 ),
inference(resolution,[],[f77,f45]) ).
fof(f45,plain,
! [X0,X1,X8] :
( in(sK3(X0,X1,X8),X1)
| ~ in(X8,cartesian_product2(X1,X0)) ),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X2,X0,X1,X8] :
( in(sK3(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X1,X0) = X2
| ( ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4,X5] :
( ~ in(X4,X1)
| ~ in(X5,X0)
| ordered_pair(X4,X5) != sK0(X0,X1,X2) ) )
& ( in(sK0(X0,X1,X2),X2)
| ( in(sK1(X0,X1,X2),X1)
& in(sK2(X0,X1,X2),X0)
& ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2)) = sK0(X0,X1,X2) ) ) ) )
& ( ! [X8] :
( ( ( in(sK3(X0,X1,X8),X1)
& in(sK4(X0,X1,X8),X0)
& ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8 )
| ~ in(X8,X2) )
& ( in(X8,X2)
| ! [X11,X12] :
( ~ in(X11,X1)
| ~ in(X12,X0)
| ordered_pair(X11,X12) != X8 ) ) )
| cartesian_product2(X1,X0) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f21,f24,f23,f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X2)
| ! [X4,X5] :
( ~ in(X4,X1)
| ~ in(X5,X0)
| ordered_pair(X4,X5) != X3 ) )
& ( in(X3,X2)
| ? [X6,X7] :
( in(X6,X1)
& in(X7,X0)
& ordered_pair(X6,X7) = X3 ) ) )
=> ( ( ~ in(sK0(X0,X1,X2),X2)
| ! [X5,X4] :
( ~ in(X4,X1)
| ~ in(X5,X0)
| ordered_pair(X4,X5) != sK0(X0,X1,X2) ) )
& ( in(sK0(X0,X1,X2),X2)
| ? [X7,X6] :
( in(X6,X1)
& in(X7,X0)
& sK0(X0,X1,X2) = ordered_pair(X6,X7) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( in(X6,X1)
& in(X7,X0)
& sK0(X0,X1,X2) = ordered_pair(X6,X7) )
=> ( in(sK1(X0,X1,X2),X1)
& in(sK2(X0,X1,X2),X0)
& ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2)) = sK0(X0,X1,X2) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1,X8] :
( ? [X9,X10] :
( in(X9,X1)
& in(X10,X0)
& ordered_pair(X9,X10) = X8 )
=> ( in(sK3(X0,X1,X8),X1)
& in(sK4(X0,X1,X8),X0)
& ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8 ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X1,X0) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ! [X4,X5] :
( ~ in(X4,X1)
| ~ in(X5,X0)
| ordered_pair(X4,X5) != X3 ) )
& ( in(X3,X2)
| ? [X6,X7] :
( in(X6,X1)
& in(X7,X0)
& ordered_pair(X6,X7) = X3 ) ) ) )
& ( ! [X8] :
( ( ? [X9,X10] :
( in(X9,X1)
& in(X10,X0)
& ordered_pair(X9,X10) = X8 )
| ~ in(X8,X2) )
& ( in(X8,X2)
| ! [X11,X12] :
( ~ in(X11,X1)
| ~ in(X12,X0)
| ordered_pair(X11,X12) != X8 ) ) )
| cartesian_product2(X1,X0) != X2 ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X1,X0,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ! [X5,X4] :
( ~ in(X5,X0)
| ~ in(X4,X1)
| ordered_pair(X5,X4) != X3 ) )
& ( in(X3,X2)
| ? [X5,X4] :
( in(X5,X0)
& in(X4,X1)
& ordered_pair(X5,X4) = X3 ) ) ) )
& ( ! [X3] :
( ( ? [X5,X4] :
( in(X5,X0)
& in(X4,X1)
& ordered_pair(X5,X4) = X3 )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X5,X4] :
( ~ in(X5,X0)
| ~ in(X4,X1)
| ordered_pair(X5,X4) != X3 ) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X1,X0,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( ? [X5,X4] :
( in(X5,X0)
& in(X4,X1)
& ordered_pair(X5,X4) = X3 )
<=> in(X3,X2) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( ? [X5,X4] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& in(X5,X1) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f77,plain,
( ~ in(sK3(sK5,sK8,sK7),sK8)
| spl9_2 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f75,plain,
( spl9_2
<=> in(sK3(sK5,sK8,sK7),sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f82,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f81]) ).
fof(f81,plain,
( $false
| spl9_1 ),
inference(subsumption_resolution,[],[f80,f41]) ).
fof(f80,plain,
( ~ in(sK7,sK6)
| spl9_1 ),
inference(resolution,[],[f79,f51]) ).
fof(f79,plain,
( ~ in(sK7,cartesian_product2(sK8,sK5))
| spl9_1 ),
inference(resolution,[],[f73,f46]) ).
fof(f46,plain,
! [X0,X1,X8] :
( in(sK4(X0,X1,X8),X0)
| ~ in(X8,cartesian_product2(X1,X0)) ),
inference(equality_resolution,[],[f34]) ).
fof(f34,plain,
! [X2,X0,X1,X8] :
( in(sK4(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f73,plain,
( ~ in(sK4(sK5,sK8,sK7),sK5)
| spl9_1 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f71,plain,
( spl9_1
<=> in(sK4(sK5,sK8,sK7),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f78,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f69,f75,f71]) ).
fof(f69,plain,
( ~ in(sK3(sK5,sK8,sK7),sK8)
| ~ in(sK4(sK5,sK8,sK7),sK5) ),
inference(trivial_inequality_removal,[],[f68]) ).
fof(f68,plain,
( sK7 != sK7
| ~ in(sK4(sK5,sK8,sK7),sK5)
| ~ in(sK3(sK5,sK8,sK7),sK8) ),
inference(superposition,[],[f42,f65]) ).
fof(f65,plain,
sK7 = ordered_pair(sK3(sK5,sK8,sK7),sK4(sK5,sK8,sK7)),
inference(resolution,[],[f59,f41]) ).
fof(f59,plain,
! [X0] :
( ~ in(X0,sK6)
| ordered_pair(sK3(sK5,sK8,X0),sK4(sK5,sK8,X0)) = X0 ),
inference(resolution,[],[f47,f51]) ).
fof(f47,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X1,X0))
| ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8 ),
inference(equality_resolution,[],[f33]) ).
fof(f33,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X4,X5] :
( sK7 != ordered_pair(X5,X4)
| ~ in(X5,sK8)
| ~ in(X4,sK5) ),
inference(cnf_transformation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 14:17:01 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.55 % (8470)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.21/0.56 % (8466)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.56 % (8479)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.56 % (8482)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.21/0.57 % (8466)First to succeed.
% 0.21/0.57 % (8487)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.21/0.57 % (8466)Refutation found. Thanks to Tanya!
% 0.21/0.57 % SZS status Theorem for theBenchmark
% 0.21/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.57 % (8466)------------------------------
% 0.21/0.57 % (8466)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.57 % (8466)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.57 % (8466)Termination reason: Refutation
% 0.21/0.57
% 0.21/0.57 % (8466)Memory used [KB]: 6012
% 0.21/0.57 % (8466)Time elapsed: 0.139 s
% 0.21/0.57 % (8466)Instructions burned: 4 (million)
% 0.21/0.57 % (8466)------------------------------
% 0.21/0.57 % (8466)------------------------------
% 0.21/0.57 % (8461)Success in time 0.217 s
%------------------------------------------------------------------------------