%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU177+1 : 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 : n009.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 12:47:35 PM UTC 2026
% Result : Theorem 2.65s 1.35s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 6 unt; 0 def)
% Number of atoms : 128 ( 18 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 160 ( 60 ~; 60 |; 26 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 62 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f25,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f26,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f27,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f28,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| ~ in(X1,relation_rng(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| ~ in(X1,relation_rng(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f28]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f35,plain,
( ( ~ in(sK0,relation_dom(sK2))
| ~ in(sK1,relation_rng(sK2)) )
& in(ordered_pair(sK0,sK1),sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f29]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f32]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK4(X0,X1),X3),X0)
| ~ in(sK4(X0,X1),X1) )
& ( in(ordered_pair(sK4(X0,X1),sK5(X0,X1)),X0)
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK6(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X4,sK5(X0,X1)),skolemize(X7,sK6(X0,X5))],[f38]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f33]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK7(X0,X1)),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK9(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f41]) ).
fof(f45,plain,
relation(sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f46,plain,
in(ordered_pair(sK0,sK1),sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f47,plain,
( ~ in(sK1,relation_rng(sK2))
| ~ in(sK0,relation_dom(sK2)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f64,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f54]) ).
fof(f66,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X6,X5),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f58]) ).
fof(f71,plain,
( in(sK0,relation_dom(sK2))
| ~ relation(sK2) ),
inference(resolution,[],[f64,f46]) ).
fof(f72,plain,
in(sK0,relation_dom(sK2)),
inference(forward_subsumption_resolution,[],[f71,f45]) ).
fof(f75,plain,
( in(sK1,relation_rng(sK2))
| ~ relation(sK2) ),
inference(resolution,[],[f66,f46]) ).
fof(f76,plain,
in(sK1,relation_rng(sK2)),
inference(forward_subsumption_resolution,[],[f75,f45]) ).
fof(f77,plain,
~ in(sK0,relation_dom(sK2)),
inference(resolution,[],[f76,f47]) ).
fof(f80,plain,
$false,
inference(forward_subsumption_resolution,[],[f77,f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU177+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:54:00 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.65/1.35 % (2645180)Detected formulas, will run a generic FOF schedule.
% 2.65/1.35 % (2645189)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=825760304:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/1.35 % (2645189)First to succeed.
% 2.65/1.35 % (2645189)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2645180"
% 2.65/1.35 % (2645185)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=2549070049:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/1.35 % (2645188)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4020242036:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/1.35 % (2645187)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=1756242230:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/1.35 % (2645190)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3245297670:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/1.35 % (2645186)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=1042463626:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/1.35 % (2645191)dis-21_1_sil=8000:lcm=predicate:random_seed=3106375030: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)
% 2.65/1.35 % (2645188)Also succeeded, but the first one will report.
% 2.65/1.35 % (2645191)Also succeeded, but the first one will report.
% 2.65/1.35 % (2645190)Also succeeded, but the first one will report.
% 2.65/1.35 % (2645189)Refutation found. Thanks to Tanya!
% 2.65/1.35 % SZS status Theorem for theBenchmark
% 2.65/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/1.35 % (2645189)------------------------------
% 2.65/1.35 % (2645189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/1.35 % (2645189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/1.35 % (2645189)CaDiCaL version: 2.1.3
% 2.65/1.35 % (2645189)Termination reason: Refutation
% 2.65/1.35 % (2645189)Time elapsed: 0.002 s
% 2.65/1.35 % (2645189)Peak memory usage: 88 MB
% 2.65/1.35 % (2645189)Instructions burned: 2 (million)
% 2.65/1.35 % (2645189)------------------------------
% 2.65/1.35 % (2645189)------------------------------
% 2.65/1.35 % (2645180)Success in time 0.291 s
% 2.65/1.35 % Vampire exiting
%------------------------------------------------------------------------------