%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU186+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:47:38 PM UTC 2026
% Result : Theorem 2.90s 1.37s
% Output : Refutation 2.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 69 ( 28 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 78 ( 34 ~; 21 |; 16 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 44 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : X1 != ordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f11,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f147,conjecture,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f148,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f147]) ).
fof(f180,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f276,plain,
? [X0] :
( empty_set != X0
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& relation(X0) ),
inference(ennf_transformation,[],[f148]) ).
fof(f277,plain,
? [X0] :
( empty_set != X0
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& relation(X0) ),
inference(flattening,[],[f276]) ).
fof(f295,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 ) )
& ( ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f180]) ).
fof(f296,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( in(X1,X0)
& ! [X2,X3] : ordered_pair(X2,X3) != X1 ) )
& ( ! [X4] :
( ~ in(X4,X0)
| ? [X5,X6] : ordered_pair(X5,X6) = X4 )
| ~ relation(X0) ) ),
inference(rectify,[],[f295]) ).
fof(f297,plain,
! [X0] :
( ( relation(X0)
| ( in(sK0(X0),X0)
& ! [X2,X3] : ordered_pair(X2,X3) != sK0(X0) ) )
& ( ! [X4] :
( ~ in(X4,X0)
| ordered_pair(sK1(X4),sK2(X4)) = X4 )
| ~ relation(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0(X0)),skolemize(X5,sK1(X4)),skolemize(X6,sK2(X4))],[f296]) ).
fof(f304,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f305,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f304]) ).
fof(f306,plain,
! [X0] :
( ( X0 = empty_set
| in(sK7(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f305]) ).
fof(f382,plain,
( empty_set != sK47
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),sK47)
& relation(sK47) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(X0,sK47)],[f277]) ).
fof(f395,plain,
! [X0,X4] :
( ~ relation(X0)
| ordered_pair(sK1(X4),sK2(X4)) = X4
| ~ in(X4,X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f411,plain,
! [X0] :
( in(sK7(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f306]) ).
fof(f625,plain,
relation(sK47),
inference(cnf_transformation,[],[f382]) ).
fof(f626,plain,
! [X2,X1] : ~ in(ordered_pair(X1,X2),sK47),
inference(cnf_transformation,[],[f382]) ).
fof(f627,plain,
empty_set != sK47,
inference(cnf_transformation,[],[f382]) ).
fof(f1377,plain,
! [X0] :
( ~ in(X0,sK47)
| ordered_pair(sK1(X0),sK2(X0)) = X0 ),
inference(resolution,[],[f395,f625]) ).
fof(f1379,plain,
( sK7(sK47) = ordered_pair(sK1(sK7(sK47)),sK2(sK7(sK47)))
| empty_set = sK47 ),
inference(resolution,[],[f1377,f411]) ).
fof(f1381,plain,
sK7(sK47) = ordered_pair(sK1(sK7(sK47)),sK2(sK7(sK47))),
inference(forward_subsumption_resolution,[],[f1379,f627]) ).
fof(f1394,plain,
~ in(sK7(sK47),sK47),
inference(superposition,[],[f626,f1381]) ).
fof(f1422,plain,
empty_set = sK47,
inference(resolution,[],[f1394,f411]) ).
fof(f1423,plain,
$false,
inference(forward_subsumption_resolution,[],[f1422,f627]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU186+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 03:59:12 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.90/1.37 % (1170939)Detected formulas, will run a generic FOF schedule.
% 2.90/1.37 % (1170948)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3737691777:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.90/1.37 % (1170948)Instruction limit reached!
% 2.90/1.37 % (1170948)------------------------------
% 2.90/1.37 % (1170948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.37 % (1170948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.37 % (1170948)CaDiCaL version: 2.1.3
% 2.90/1.37 % (1170948)Termination reason: Instruction limit
% 2.90/1.37 % (1170948)Termination phase: Saturation
% 2.90/1.37 % (1170948)Time elapsed: 0.043 s
% 2.90/1.37 % (1170948)Peak memory usage: 89 MB
% 2.90/1.37 % (1170948)Instructions burned: 120 (million)
% 2.90/1.37 % (1170947)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1104738257:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.90/1.37 % (1170945)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3518812295:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.90/1.37 % (1170946)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1053426873:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.90/1.37 % (1170944)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=576019402:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.90/1.37 % (1170949)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3976803364:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.90/1.37 % (1170950)dis-21_1_sil=8000:lcm=predicate:random_seed=531428614:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.90/1.37 % (1170949)First to succeed.
% 2.90/1.37 % (1170949)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1170939"
% 2.90/1.37 % (1170947)Instruction limit reached!
% 2.90/1.37 % (1170947)------------------------------
% 2.90/1.37 % (1170947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.37 % (1170947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.37 % (1170947)CaDiCaL version: 2.1.3
% 2.90/1.37 % (1170947)Termination reason: Instruction limit
% 2.90/1.37 % (1170947)Termination phase: Saturation
% 2.90/1.37 % (1170947)Time elapsed: 0.073 s
% 2.90/1.37 % (1170947)Peak memory usage: 90 MB
% 2.90/1.37 % (1170947)Instructions burned: 110 (million)
% 2.90/1.37 % (1170950)Instruction limit reached!
% 2.90/1.37 % (1170950)------------------------------
% 2.90/1.37 % (1170950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.37 % (1170950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.37 % (1170950)CaDiCaL version: 2.1.3
% 2.90/1.37 % (1170950)Termination reason: Instruction limit
% 2.90/1.37 % (1170950)Termination phase: Saturation
% 2.90/1.37 % (1170950)Time elapsed: 0.081 s
% 2.90/1.37 % (1170950)Peak memory usage: 90 MB
% 2.90/1.37 % (1170950)Instructions burned: 129 (million)
% 2.90/1.37 % (1170956)lrs+10_1_sil=8000:sp=occurrence:random_seed=3558052252:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.90/1.37 % (1170949)Refutation found. Thanks to Tanya!
% 2.90/1.37 % SZS status Theorem for theBenchmark
% 2.90/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.90/1.37 % (1170949)------------------------------
% 2.90/1.37 % (1170949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.37 % (1170949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.37 % (1170949)CaDiCaL version: 2.1.3
% 2.90/1.37 % (1170949)Termination reason: Refutation
% 2.90/1.37 % (1170949)Time elapsed: 0.017 s
% 2.90/1.37 % (1170949)Peak memory usage: 89 MB
% 2.90/1.37 % (1170949)Instructions burned: 41 (million)
% 2.90/1.37 % (1170949)------------------------------
% 2.90/1.37 % (1170949)------------------------------
% 2.90/1.37 % (1170939)Success in time 0.332 s
% 2.90/1.37 % Vampire exiting
%------------------------------------------------------------------------------