%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU180+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 : n008.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 12:47:36 PM UTC 2026
% Result : Theorem 2.19s 1.14s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 7 unt; 0 def)
% Number of atoms : 218 ( 32 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 280 ( 108 ~; 109 |; 46 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 128 ( 103 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f6,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(f8,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f33,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f39,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,[],[f34]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_field(X2))
| ~ in(X1,relation_field(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f39]) ).
fof(f45,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f51,plain,
( ( ~ in(sK0,relation_field(sK2))
| ~ in(sK1,relation_field(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)],[f40]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( X2 = set_union2(X0,X1)
| ( ( ( ~ in(sK3(X0,X1,X2),X0)
& ~ in(sK3(X0,X1,X2),X1) )
| ~ in(sK3(X0,X1,X2),X2) )
& ( in(sK3(X0,X1,X2),X0)
| in(sK3(X0,X1,X2),X1)
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f54]) ).
fof(f59,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,[],[f49]) ).
fof(f60,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,[],[f59]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(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))],[f60]) ).
fof(f62,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,[],[f50]) ).
fof(f63,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,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK10(X0,X1)),X0)
| ~ in(sK10(X0,X1),X1) )
& ( in(ordered_pair(sK11(X0,X1),sK10(X0,X1)),X0)
| in(sK10(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK12(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X2,sK10(X0,X1)),skolemize(X4,sK11(X0,X1)),skolemize(X7,sK12(X0,X5))],[f63]) ).
fof(f65,plain,
relation(sK2),
inference(cnf_transformation,[],[f51]) ).
fof(f66,plain,
in(ordered_pair(sK0,sK1),sK2),
inference(cnf_transformation,[],[f51]) ).
fof(f67,plain,
( ~ in(sK1,relation_field(sK2))
| ~ in(sK0,relation_field(sK2)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f70,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f55]) ).
fof(f71,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f55]) ).
fof(f80,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f89,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f93,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f96,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f71]) ).
fof(f97,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f70]) ).
fof(f99,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f89]) ).
fof(f101,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X6,X5),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f93]) ).
fof(f141,plain,
! [X0,X1] :
( in(X1,relation_field(X0))
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(superposition,[],[f96,f80]) ).
fof(f142,plain,
! [X0,X1] :
( in(X1,relation_field(X0))
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(superposition,[],[f97,f80]) ).
fof(f156,plain,
( in(sK0,relation_dom(sK2))
| ~ relation(sK2) ),
inference(resolution,[],[f99,f66]) ).
fof(f159,plain,
in(sK0,relation_dom(sK2)),
inference(forward_subsumption_resolution,[],[f156,f65]) ).
fof(f162,plain,
( in(sK1,relation_rng(sK2))
| ~ relation(sK2) ),
inference(resolution,[],[f101,f66]) ).
fof(f165,plain,
in(sK1,relation_rng(sK2)),
inference(forward_subsumption_resolution,[],[f162,f65]) ).
fof(f322,plain,
( ~ in(sK1,relation_rng(sK2))
| ~ relation(sK2)
| ~ in(sK0,relation_field(sK2)) ),
inference(resolution,[],[f142,f67]) ).
fof(f325,plain,
( ~ relation(sK2)
| ~ in(sK0,relation_field(sK2)) ),
inference(forward_subsumption_resolution,[],[f322,f165]) ).
fof(f326,plain,
~ in(sK0,relation_field(sK2)),
inference(forward_subsumption_resolution,[],[f325,f65]) ).
fof(f328,plain,
( ~ in(sK0,relation_dom(sK2))
| ~ relation(sK2) ),
inference(resolution,[],[f326,f141]) ).
fof(f329,plain,
~ relation(sK2),
inference(forward_subsumption_resolution,[],[f328,f159]) ).
fof(f331,plain,
$false,
inference(forward_subsumption_resolution,[],[f329,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU180+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n008.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 28 03:55:54 UTC 2026
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.39 Running first-order theorem proving
% 0.15/0.39 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
% 2.19/1.14 % (1851952)Detected formulas, will run a generic FOF schedule.
% 2.19/1.14 % (1852038)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=529515153:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.19/1.14 % (1852038)First to succeed.
% 2.19/1.14 % (1852038)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1851952"
% 2.19/1.14 % (1852037)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1469301338:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.19/1.14 % (1852035)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=1623043705:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.19/1.14 % (1852036)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=4238882513:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.19/1.14 % (1852034)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=2780339812:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.19/1.14 % (1852037)Refutation not found, incomplete strategy
% 2.19/1.14 % (1852037)------------------------------
% 2.19/1.14 % (1852037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.19/1.14 % (1852037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/1.14 % (1852037)CaDiCaL version: 2.1.3
% 2.19/1.14 % (1852037)Termination reason: Refutation not found, incomplete strategy
% 2.19/1.14 % (1852037)Time elapsed: 0.002 s
% 2.19/1.14 % (1852037)Peak memory usage: 88 MB
% 2.19/1.14 % (1852037)Instructions burned: 1 (million)
% 2.19/1.14 % (1852040)dis-21_1_sil=8000:lcm=predicate:random_seed=2221065564: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)
% 2.19/1.14 % (1852039)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2996272224:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.19/1.14 % (1852039)Also succeeded, but the first one will report.
% 2.19/1.14 % (1852040)Instruction limit reached!
% 2.19/1.14 % (1852040)------------------------------
% 2.19/1.14 % (1852040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.19/1.14 % (1852040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.19/1.14 % (1852040)CaDiCaL version: 2.1.3
% 2.19/1.14 % (1852040)Termination reason: Instruction limit
% 2.19/1.14 % (1852040)Termination phase: Saturation
% 2.19/1.14 % (1852040)Time elapsed: 0.082 s
% 2.19/1.14 % (1852040)Peak memory usage: 90 MB
% 2.19/1.14 % (1852040)Instructions burned: 129 (million)
% 2.19/1.14 % (1852038)Refutation found. Thanks to Tanya!
% 2.19/1.14 % SZS status Theorem for theBenchmark
% 2.19/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.35 % (1852038)------------------------------
% 2.78/1.35 % (1852038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.35 % (1852038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.35 % (1852038)CaDiCaL version: 2.1.3
% 2.78/1.35 % (1852038)Termination reason: Refutation
% 2.78/1.35 % (1852038)Time elapsed: 0.005 s
% 2.78/1.35 % (1852038)Peak memory usage: 88 MB
% 2.78/1.35 % (1852038)Instructions burned: 11 (million)
% 2.78/1.35 % (1852038)------------------------------
% 2.78/1.35 % (1852038)------------------------------
% 2.78/1.35 % (1851952)Success in time 0.307 s
% 2.78/1.35 % Vampire exiting
%------------------------------------------------------------------------------