%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU208+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:47:44 PM UTC 2026
% Result : Theorem 1.78s 1.13s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 6 unt; 0 def)
% Number of atoms : 221 ( 20 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 297 ( 119 ~; 114 |; 49 &)
% ( 10 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 132 ( 98 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f33,plain,
? [X0,X1,X2] :
( ( in(X0,relation_inverse_image(X2,X1))
<~> ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) ) )
& relation(X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f36,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f43,plain,
? [X0,X1,X2] :
( ( ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) )
& ( ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) )
| in(X0,relation_inverse_image(X2,X1)) )
& relation(X2) ),
inference(nnf_transformation,[],[f33]) ).
fof(f44,plain,
? [X0,X1,X2] :
( ( ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) )
& ( ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) )
| in(X0,relation_inverse_image(X2,X1)) )
& relation(X2) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
? [X0,X1,X2] :
( ( ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) )
& ( ? [X4] :
( in(X4,relation_rng(X2))
& in(ordered_pair(X0,X4),X2)
& in(X4,X1) )
| in(X0,relation_inverse_image(X2,X1)) )
& relation(X2) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
( ( ! [X3] :
( ~ in(X3,relation_rng(sK2))
| ~ in(ordered_pair(sK0,X3),sK2)
| ~ in(X3,sK1) )
| ~ in(sK0,relation_inverse_image(sK2,sK1)) )
& ( ( in(sK3,relation_rng(sK2))
& in(ordered_pair(sK0,sK3),sK2)
& in(sK3,sK1) )
| in(sK0,relation_inverse_image(sK2,sK1)) )
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X4,sK3)],[f45]) ).
fof(f47,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) ) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f36]) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(X5,X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ? [X8] :
( in(ordered_pair(X6,X8),X0)
& in(X8,X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(sK4(X0,X1,X2),X4),X0)
| ~ in(X4,X1) )
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2)),X0)
& in(sK5(X0,X1,X2),X1) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(X6,sK6(X0,X1,X6)),X0)
& in(sK6(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4(X0,X1,X2)),skolemize(X5,sK5(X0,X1,X2)),skolemize(X8,sK6(X0,X1,X6))],[f48]) ).
fof(f52,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,[],[f41]) ).
fof(f53,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,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK9(X0,X1)),X0)
| ~ in(sK9(X0,X1),X1) )
& ( in(ordered_pair(sK10(X0,X1),sK9(X0,X1)),X0)
| in(sK9(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK11(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X2,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X7,sK11(X0,X5))],[f53]) ).
fof(f57,plain,
relation(sK2),
inference(cnf_transformation,[],[f46]) ).
fof(f58,plain,
( in(sK0,relation_inverse_image(sK2,sK1))
| in(sK3,sK1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
( in(sK0,relation_inverse_image(sK2,sK1))
| in(ordered_pair(sK0,sK3),sK2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f61,plain,
! [X3] :
( ~ in(sK0,relation_inverse_image(sK2,sK1))
| ~ in(ordered_pair(sK0,X3),sK2)
| ~ in(X3,sK1)
| ~ in(X3,relation_rng(sK2)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f64,plain,
! [X2,X0,X1,X6] :
( in(sK6(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f65,plain,
! [X2,X0,X1,X6] :
( in(ordered_pair(X6,sK6(X0,X1,X6)),X0)
| ~ in(X6,X2)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f66,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f80,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f86,plain,
! [X0,X1,X6,X7] :
( in(X6,relation_inverse_image(X0,X1))
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f66]) ).
fof(f87,plain,
! [X0,X1,X6] :
( in(ordered_pair(X6,sK6(X0,X1,X6)),X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f65]) ).
fof(f88,plain,
! [X0,X1,X6] :
( in(sK6(X0,X1,X6),X1)
| ~ in(X6,relation_inverse_image(X0,X1))
| ~ relation(X0) ),
inference(equality_resolution,[],[f64]) ).
fof(f89,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X6,X5),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f80]) ).
fof(f129,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0,X0),sK2)
| ~ in(X0,sK1)
| ~ relation(sK2)
| ~ in(ordered_pair(sK0,X1),sK2)
| ~ in(X1,sK1)
| ~ in(X1,relation_rng(sK2)) ),
inference(resolution,[],[f86,f61]) ).
fof(f130,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0,X0),sK2)
| ~ in(X0,sK1)
| ~ relation(sK2)
| ~ in(ordered_pair(sK0,X1),sK2)
| ~ in(X1,sK1) ),
inference(forward_subsumption_resolution,[],[f129,f89]) ).
fof(f131,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0,X1),sK2)
| ~ in(X0,sK1)
| ~ in(ordered_pair(sK0,X0),sK2)
| ~ in(X1,sK1) ),
inference(forward_subsumption_resolution,[],[f130,f57]) ).
fof(f135,plain,
! [X0] :
( ~ in(ordered_pair(sK0,X0),sK2)
| ~ in(X0,sK1)
| ~ in(X0,sK1) ),
inference(factoring,[],[f131]) ).
fof(f136,plain,
! [X0] :
( ~ in(ordered_pair(sK0,X0),sK2)
| ~ in(X0,sK1) ),
inference(duplicate_literal_removal,[],[f135]) ).
fof(f144,plain,
! [X0] :
( ~ in(sK0,relation_inverse_image(sK2,X0))
| ~ relation(sK2)
| ~ in(sK6(sK2,X0,sK0),sK1) ),
inference(resolution,[],[f87,f136]) ).
fof(f155,plain,
! [X0] :
( ~ in(sK6(sK2,X0,sK0),sK1)
| ~ in(sK0,relation_inverse_image(sK2,X0)) ),
inference(forward_subsumption_resolution,[],[f144,f57]) ).
fof(f159,plain,
( ~ in(sK0,relation_inverse_image(sK2,sK1))
| ~ in(sK0,relation_inverse_image(sK2,sK1))
| ~ relation(sK2) ),
inference(resolution,[],[f155,f88]) ).
fof(f160,plain,
( ~ in(sK0,relation_inverse_image(sK2,sK1))
| ~ relation(sK2) ),
inference(duplicate_literal_removal,[],[f159]) ).
fof(f161,plain,
~ in(sK0,relation_inverse_image(sK2,sK1)),
inference(forward_subsumption_resolution,[],[f160,f57]) ).
fof(f164,plain,
in(ordered_pair(sK0,sK3),sK2),
inference(resolution,[],[f161,f59]) ).
fof(f166,plain,
in(sK3,sK1),
inference(resolution,[],[f161,f58]) ).
fof(f203,plain,
~ in(sK3,sK1),
inference(resolution,[],[f164,f136]) ).
fof(f210,plain,
$false,
inference(forward_subsumption_resolution,[],[f203,f166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU208+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 04:06:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.78/1.13 % (2246846)Detected formulas, will run a generic FOF schedule.
% 1.78/1.13 % (2246855)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=454186754:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.78/1.13 % (2246855)First to succeed.
% 1.78/1.13 % (2246855)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2246846"
% 1.78/1.13 % (2246856)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1505266331:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.78/1.13 % (2246851)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=4146787853:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.78/1.13 % (2246852)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=2645553604:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.78/1.13 % (2246853)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=2443330929:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.78/1.13 % (2246854)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1886726802:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.78/1.13 % (2246854)Refutation not found, incomplete strategy
% 1.78/1.13 % (2246854)------------------------------
% 1.78/1.13 % (2246854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.78/1.13 % (2246854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/1.13 % (2246854)CaDiCaL version: 2.1.3
% 1.78/1.13 % (2246854)Termination reason: Refutation not found, incomplete strategy
% 1.78/1.13 % (2246854)Time elapsed: 0.003 s
% 1.78/1.13 % (2246854)Peak memory usage: 88 MB
% 1.78/1.13 % (2246854)Instructions burned: 2 (million)
% 1.78/1.13 % (2246857)dis-21_1_sil=8000:lcm=predicate:random_seed=4265231151: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)
% 1.78/1.13 % (2246856)Also succeeded, but the first one will report.
% 1.78/1.13 % (2246857)Also succeeded, but the first one will report.
% 1.78/1.13 % (2246855)Refutation found. Thanks to Tanya!
% 1.78/1.13 % SZS status Theorem for theBenchmark
% 1.78/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.22 % (2246855)------------------------------
% 2.57/1.22 % (2246855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.22 % (2246855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.22 % (2246855)CaDiCaL version: 2.1.3
% 2.57/1.22 % (2246855)Termination reason: Refutation
% 2.57/1.22 % (2246855)Time elapsed: 0.003 s
% 2.57/1.22 % (2246855)Peak memory usage: 88 MB
% 2.57/1.22 % (2246855)Instructions burned: 8 (million)
% 2.57/1.22 % (2246855)------------------------------
% 2.57/1.22 % (2246855)------------------------------
% 2.57/1.22 % (2246846)Success in time 0.288 s
% 2.57/1.22 % Vampire exiting
%------------------------------------------------------------------------------