TSTP Solution File: SET961+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n019.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 : Sat Sep 2 00:05:54 EDT 2023
% Result : Theorem 0.16s 0.41s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 156 ( 70 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 179 ( 72 ~; 70 |; 27 &)
% ( 3 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 86 (; 74 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f868,plain,
$false,
inference(trivial_inequality_removal,[],[f867]) ).
fof(f867,plain,
empty_set != empty_set,
inference(superposition,[],[f33,f723]) ).
fof(f723,plain,
empty_set = sK0,
inference(trivial_inequality_removal,[],[f667]) ).
fof(f667,plain,
( empty_set != empty_set
| empty_set = sK0 ),
inference(superposition,[],[f34,f665]) ).
fof(f665,plain,
( empty_set = sK1
| empty_set = sK0 ),
inference(trivial_inequality_removal,[],[f602]) ).
fof(f602,plain,
( sK0 != sK0
| empty_set = sK0
| empty_set = sK1 ),
inference(superposition,[],[f35,f559]) ).
fof(f559,plain,
( sK0 = sK1
| empty_set = sK0
| empty_set = sK1 ),
inference(resolution,[],[f529,f38]) ).
fof(f38,plain,
! [X0] :
( in(sK2(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( ( empty_set = X0
| in(sK2(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f20,f21]) ).
fof(f21,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.4HLULQcqRV/Vampire---4.8_28184',d1_xboole_0) ).
fof(f529,plain,
! [X3] :
( ~ in(X3,sK1)
| sK0 = sK1
| empty_set = sK0 ),
inference(resolution,[],[f527,f38]) ).
fof(f527,plain,
! [X0,X1] :
( ~ in(X1,sK0)
| ~ in(X0,sK1)
| sK0 = sK1 ),
inference(duplicate_literal_removal,[],[f510]) ).
fof(f510,plain,
! [X0,X1] :
( sK0 = sK1
| ~ in(X0,sK1)
| ~ in(X1,sK0)
| sK0 = sK1 ),
inference(resolution,[],[f509,f415]) ).
fof(f415,plain,
! [X0] :
( ~ in(sK3(sK1,sK0),sK1)
| ~ in(X0,sK0)
| sK0 = sK1 ),
inference(factoring,[],[f118]) ).
fof(f118,plain,
! [X6,X5] :
( ~ in(sK3(X6,sK0),sK1)
| ~ in(sK3(X6,sK0),X6)
| ~ in(X5,sK0)
| sK0 = X6 ),
inference(resolution,[],[f104,f44]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| ~ in(sK3(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK3(X0,X1),X1)
| ~ in(sK3(X0,X1),X0) )
& ( in(sK3(X0,X1),X1)
| in(sK3(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK3(X0,X1),X1)
| ~ in(sK3(X0,X1),X0) )
& ( in(sK3(X0,X1),X1)
| in(sK3(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.4HLULQcqRV/Vampire---4.8_28184',t2_tarski) ).
fof(f104,plain,
! [X8,X9] :
( in(X8,sK0)
| ~ in(X9,sK0)
| ~ in(X8,sK1) ),
inference(resolution,[],[f47,f63]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
| in(X1,sK0) ),
inference(superposition,[],[f46,f32]) ).
fof(f32,plain,
cartesian_product2(sK0,sK1) = cartesian_product2(sK1,sK0),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( sK0 != sK1
& empty_set != sK1
& empty_set != sK0
& cartesian_product2(sK0,sK1) = cartesian_product2(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f17]) ).
fof(f17,plain,
( ? [X0,X1] :
( X0 != X1
& empty_set != X1
& empty_set != X0
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) )
=> ( sK0 != sK1
& empty_set != sK1
& empty_set != sK0
& cartesian_product2(sK0,sK1) = cartesian_product2(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0,X1] :
( X0 != X1
& empty_set != X1
& empty_set != X0
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
? [X0,X1] :
( X0 != X1
& empty_set != X1
& empty_set != X0
& cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = X1
| empty_set = X1
| empty_set = X0 ) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = X1
| empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.4HLULQcqRV/Vampire---4.8_28184',t114_zfmisc_1) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4HLULQcqRV/Vampire---4.8_28184',l55_zfmisc_1) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f509,plain,
! [X0] :
( in(sK3(sK1,sK0),sK1)
| sK0 = sK1
| ~ in(X0,sK1) ),
inference(duplicate_literal_removal,[],[f493]) ).
fof(f493,plain,
! [X0] :
( ~ in(X0,sK1)
| sK0 = sK1
| sK0 = sK1
| in(sK3(sK1,sK0),sK1) ),
inference(resolution,[],[f488,f43]) ).
fof(f43,plain,
! [X0,X1] :
( in(sK3(X0,X1),X1)
| X0 = X1
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f488,plain,
! [X0] :
( ~ in(sK3(sK1,sK0),sK0)
| ~ in(X0,sK1)
| sK0 = sK1 ),
inference(factoring,[],[f425]) ).
fof(f425,plain,
! [X6,X5] :
( ~ in(sK3(sK1,sK0),sK0)
| ~ in(X6,sK1)
| ~ in(X5,sK0)
| sK0 = sK1 ),
inference(resolution,[],[f415,f105]) ).
fof(f105,plain,
! [X10,X11] :
( in(X11,sK1)
| ~ in(X11,sK0)
| ~ in(X10,sK1) ),
inference(resolution,[],[f47,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
| in(X0,sK1) ),
inference(superposition,[],[f45,f32]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f35,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.09/0.13 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 30 15:48:42 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % (28291)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.39 % (28295)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.12/0.39 % (28296)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.12/0.39 % (28293)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.12/0.39 % (28294)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.12/0.39 % (28298)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.12/0.39 % (28292)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.12/0.39 % (28297)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.12/0.39 Detected minimum model sizes of [3]
% 0.12/0.39 Detected maximum model sizes of [max]
% 0.12/0.39 TRYING [3]
% 0.12/0.39 Detected minimum model sizes of [3]
% 0.12/0.39 Detected maximum model sizes of [max]
% 0.12/0.39 TRYING [3]
% 0.12/0.40 TRYING [4]
% 0.12/0.40 TRYING [5]
% 0.12/0.40 TRYING [4]
% 0.16/0.41 % (28297)First to succeed.
% 0.16/0.41 % (28297)Refutation found. Thanks to Tanya!
% 0.16/0.41 % SZS status Theorem for Vampire---4
% 0.16/0.41 % SZS output start Proof for Vampire---4
% See solution above
% 0.16/0.41 % (28297)------------------------------
% 0.16/0.41 % (28297)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.16/0.41 % (28297)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.16/0.41 % (28297)Termination reason: Refutation
% 0.16/0.41
% 0.16/0.41 % (28297)Memory used [KB]: 1279
% 0.16/0.41 % (28297)Time elapsed: 0.022 s
% 0.16/0.41 % (28297)------------------------------
% 0.16/0.41 % (28297)------------------------------
% 0.16/0.41 % (28291)Success in time 0.081 s
% 0.16/0.41 28294 Aborted by signal SIGHUP on /export/starexec/sandbox2/tmp/tmp.4HLULQcqRV/Vampire---4.8_28184
% 0.16/0.41 % (28294)------------------------------
% 0.16/0.41 % (28294)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.16/0.41 % (28294)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.16/0.41 % (28294)Termination reason: Unknown
% 0.16/0.41 % (28294)Termination phase: Saturation
% 0.16/0.41
% 0.16/0.41 % (28294)Memory used [KB]: 5373
% 0.16/0.41 % (28294)Time elapsed: 0.024 s
% 0.16/0.41 % (28294)------------------------------
% 0.16/0.41 % (28294)------------------------------
% 0.16/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------