%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU241+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 : n012.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 12:47:58 PM UTC 2026
% Result : Theorem 0.29s 0.84s
% Output : Refutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 4 unt; 0 def)
% Number of atoms : 241 ( 29 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 315 ( 127 ~; 128 |; 42 &)
% ( 7 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 80 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_2) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( ( in(X2,X1)
& in(X3,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X2),X0) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
fof(f25,conjecture,
! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( antisymmetric(X0)
<=> ! [X1,X2] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) )
=> X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f35,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f39,plain,
? [X0] :
( ( antisymmetric(X0)
<~> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X1),X0) ) )
& relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f40,plain,
? [X0] :
( ( antisymmetric(X0)
<~> ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X1),X0) ) )
& relation(X0) ),
inference(flattening,[],[f39]) ).
fof(f44,plain,
! [X0] :
( ( antisymmetric(X0)
<=> is_antisymmetric_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( is_antisymmetric_in(X0,X1)
<=> ! [X2,X3] :
( X2 = X3
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
? [X0] :
( ( ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) )
| ~ antisymmetric(X0) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X1),X0) )
| antisymmetric(X0) )
& relation(X0) ),
inference(nnf_transformation,[],[f40]) ).
fof(f50,plain,
? [X0] :
( ( ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) )
| ~ antisymmetric(X0) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X1),X0) )
| antisymmetric(X0) )
& relation(X0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
? [X0] :
( ( ? [X1,X2] :
( X1 != X2
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X1),X0) )
| ~ antisymmetric(X0) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X4,X3),X0) )
| antisymmetric(X0) )
& relation(X0) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
( ( ( sK1 != sK2
& in(ordered_pair(sK1,sK2),sK0)
& in(ordered_pair(sK2,sK1),sK0) )
| ~ antisymmetric(sK0) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(ordered_pair(X3,X4),sK0)
| ~ in(ordered_pair(X4,X3),sK0) )
| antisymmetric(sK0) )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f51]) ).
fof(f53,plain,
! [X0] :
( ( ( antisymmetric(X0)
| ~ is_antisymmetric_in(X0,relation_field(X0)) )
& ( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(X2,X1)
& in(X3,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X2),X0) ) )
& ( ! [X2,X3] :
( X2 = X3
| ~ in(X2,X1)
| ~ in(X3,X1)
| ~ in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X3,X2),X0) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f48]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ? [X2,X3] :
( X2 != X3
& in(X2,X1)
& in(X3,X1)
& in(ordered_pair(X2,X3),X0)
& in(ordered_pair(X3,X2),X0) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X4),X0) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( is_antisymmetric_in(X0,X1)
| ( sK5(X0,X1) != sK6(X0,X1)
& in(sK5(X0,X1),X1)
& in(sK6(X0,X1),X1)
& in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
& in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0) ) )
& ( ! [X4,X5] :
( X4 = X5
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X4),X0) )
| ~ is_antisymmetric_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1))],[f57]) ).
fof(f59,plain,
relation(sK0),
inference(cnf_transformation,[],[f52]) ).
fof(f60,plain,
! [X3,X4] :
( ~ in(ordered_pair(X4,X3),sK0)
| ~ in(ordered_pair(X3,X4),sK0)
| X3 = X4
| antisymmetric(sK0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f61,plain,
( in(ordered_pair(sK2,sK1),sK0)
| ~ antisymmetric(sK0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f62,plain,
( in(ordered_pair(sK1,sK2),sK0)
| ~ antisymmetric(sK0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f63,plain,
( sK1 != sK2
| ~ antisymmetric(sK0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f68,plain,
! [X0] :
( is_antisymmetric_in(X0,relation_field(X0))
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f69,plain,
! [X0] :
( ~ is_antisymmetric_in(X0,relation_field(X0))
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X0,X1),X2)
| in(X1,relation_field(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f74,plain,
! [X0,X1,X4,X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(X4,X1)
| ~ in(X5,X1)
| ~ in(ordered_pair(X4,X5),X0)
| X4 = X5
| ~ is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f75,plain,
! [X0,X1] :
( in(ordered_pair(sK6(X0,X1),sK5(X0,X1)),X0)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f76,plain,
! [X0,X1] :
( in(ordered_pair(sK5(X0,X1),sK6(X0,X1)),X0)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f79,plain,
! [X0,X1] :
( sK5(X0,X1) != sK6(X0,X1)
| is_antisymmetric_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f96,plain,
( in(sK1,relation_field(sK0))
| ~ relation(sK0)
| ~ antisymmetric(sK0) ),
inference(resolution,[],[f72,f61]) ).
fof(f97,plain,
( in(sK2,relation_field(sK0))
| ~ relation(sK0)
| ~ antisymmetric(sK0) ),
inference(resolution,[],[f72,f62]) ).
fof(f98,plain,
( in(sK2,relation_field(sK0))
| ~ antisymmetric(sK0) ),
inference(forward_subsumption_resolution,[],[f97,f59]) ).
fof(f99,plain,
( in(sK1,relation_field(sK0))
| ~ antisymmetric(sK0) ),
inference(forward_subsumption_resolution,[],[f96,f59]) ).
fof(f116,plain,
! [X0] :
( is_antisymmetric_in(sK0,X0)
| ~ relation(sK0)
| ~ in(ordered_pair(sK6(sK0,X0),sK5(sK0,X0)),sK0)
| sK5(sK0,X0) = sK6(sK0,X0)
| antisymmetric(sK0) ),
inference(resolution,[],[f76,f60]) ).
fof(f123,plain,
! [X0] :
( is_antisymmetric_in(sK0,X0)
| ~ relation(sK0)
| sK5(sK0,X0) = sK6(sK0,X0)
| antisymmetric(sK0) ),
inference(forward_subsumption_resolution,[],[f116,f75]) ).
fof(f124,plain,
! [X0] :
( is_antisymmetric_in(sK0,X0)
| ~ relation(sK0)
| antisymmetric(sK0) ),
inference(forward_subsumption_resolution,[],[f123,f79]) ).
fof(f125,plain,
! [X0] :
( is_antisymmetric_in(sK0,X0)
| antisymmetric(sK0) ),
inference(forward_subsumption_resolution,[],[f124,f59]) ).
fof(f126,plain,
( antisymmetric(sK0)
| antisymmetric(sK0)
| ~ relation(sK0) ),
inference(resolution,[],[f125,f69]) ).
fof(f127,plain,
( antisymmetric(sK0)
| ~ relation(sK0) ),
inference(duplicate_literal_removal,[],[f126]) ).
fof(f128,plain,
antisymmetric(sK0),
inference(forward_subsumption_resolution,[],[f127,f59]) ).
fof(f131,plain,
! [X0] :
( ~ in(sK2,X0)
| ~ in(sK1,X0)
| ~ in(ordered_pair(sK2,sK1),sK0)
| sK1 = sK2
| ~ is_antisymmetric_in(sK0,X0)
| ~ relation(sK0)
| ~ antisymmetric(sK0) ),
inference(resolution,[],[f74,f62]) ).
fof(f140,plain,
! [X0] :
( ~ in(sK2,X0)
| ~ in(sK1,X0)
| sK1 = sK2
| ~ is_antisymmetric_in(sK0,X0)
| ~ relation(sK0)
| ~ antisymmetric(sK0) ),
inference(forward_subsumption_resolution,[],[f131,f61]) ).
fof(f144,plain,
! [X0] :
( ~ in(sK2,X0)
| ~ in(sK1,X0)
| ~ is_antisymmetric_in(sK0,X0)
| ~ relation(sK0)
| ~ antisymmetric(sK0) ),
inference(forward_subsumption_resolution,[],[f140,f63]) ).
fof(f146,plain,
! [X0] :
( ~ in(sK2,X0)
| ~ in(sK1,X0)
| ~ is_antisymmetric_in(sK0,X0)
| ~ antisymmetric(sK0) ),
inference(forward_subsumption_resolution,[],[f144,f59]) ).
fof(f148,plain,
! [X0] :
( ~ is_antisymmetric_in(sK0,X0)
| ~ in(sK1,X0)
| ~ in(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f146,f128]) ).
fof(f151,plain,
( ~ in(sK1,relation_field(sK0))
| ~ in(sK2,relation_field(sK0))
| ~ antisymmetric(sK0)
| ~ relation(sK0) ),
inference(resolution,[],[f148,f68]) ).
fof(f153,plain,
( ~ in(sK2,relation_field(sK0))
| ~ antisymmetric(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f151,f99]) ).
fof(f154,plain,
( ~ antisymmetric(sK0)
| ~ relation(sK0) ),
inference(forward_subsumption_resolution,[],[f153,f98]) ).
fof(f155,plain,
~ relation(sK0),
inference(forward_subsumption_resolution,[],[f154,f128]) ).
fof(f156,plain,
$false,
inference(forward_subsumption_resolution,[],[f155,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU241+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.32 % Computer : n012.cluster.edu
% 0.05/0.32 % Model : x86_64 x86_64
% 0.05/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.32 % Memory : 8046.5625MB
% 0.05/0.32 % OS : Linux 6.8.0-71-generic
% 0.05/0.32 % CPULimit : 300
% 0.05/0.32 % WCLimit : 300
% 0.05/0.32 % DateTime : Mon Sep 28 04:15:49 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 Running first-order theorem proving
% 0.08/0.34 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
% 0.29/0.84 % (3008587)Detected formulas, will run a generic FOF schedule.
% 0.29/0.84 % (3008594)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=2895844732:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.29/0.84 % (3008596)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3101921478:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.29/0.84 % (3008598)dis-21_1_sil=8000:lcm=predicate:random_seed=2319044350: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)
% 0.29/0.84 % (3008597)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1291486985:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.29/0.84 % (3008593)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=353393815:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.29/0.84 % (3008595)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3292644686:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.29/0.84 % (3008592)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=1775135022:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.29/0.84 % (3008595)Refutation not found, incomplete strategy
% 0.29/0.84 % (3008595)------------------------------
% 0.29/0.84 % (3008595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/0.84 % (3008595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.84 % (3008595)CaDiCaL version: 2.1.3
% 0.29/0.84 % (3008595)Termination reason: Refutation not found, incomplete strategy
% 0.29/0.84 % (3008595)Time elapsed: 0.001 s
% 0.29/0.84 % (3008595)Peak memory usage: 87 MB
% 0.29/0.84 % (3008596)First to succeed.
% 0.29/0.84 % (3008598)Also succeeded, but the first one will report.
% 0.29/0.84 % (3008596)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3008587"
% 0.29/0.84 % (3008597)Also succeeded, but the first one will report.
% 0.29/0.84 % (3008595)------------------------------
% 0.29/0.84 % (3008595)------------------------------
% 0.29/0.84 % (3008596)Refutation found. Thanks to Tanya!
% 0.29/0.84 % SZS status Theorem for theBenchmark
% 0.29/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 2.35/0.94 % (3008596)------------------------------
% 2.35/0.94 % (3008596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.94 % (3008596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.94 % (3008596)CaDiCaL version: 2.1.3
% 2.35/0.94 % (3008596)Termination reason: Refutation
% 2.35/0.94 % (3008596)Time elapsed: 0.002 s
% 2.35/0.94 % (3008596)Peak memory usage: 88 MB
% 2.35/0.94 % (3008596)Instructions burned: 5 (million)
% 2.35/0.94 % (3008596)------------------------------
% 2.35/0.94 % (3008596)------------------------------
% 2.35/0.94 % (3008587)Success in time 0.301 s
% 2.35/0.94 % Vampire exiting
%------------------------------------------------------------------------------