%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU037+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:47:06 PM UTC 2026
% Result : Theorem 0.39s 0.80s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 62 ( 13 unt; 4 def)
% Number of atoms : 231 ( 45 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 305 ( 136 ~; 123 |; 32 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 56 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0) )
=> ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f35,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f37,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f42,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f43,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f42]) ).
fof(f52,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f53,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f52]) ).
fof(f60,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f61,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
( apply(relation_dom_restriction(sK2,sK0),sK1) != apply(sK2,sK1)
& in(sK1,set_intersection2(relation_dom(sK2),sK0))
& relation(sK2)
& function(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f43]) ).
fof(f67,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(nnf_transformation,[],[f61]) ).
fof(f68,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ( apply(X1,sK7(X1,X2)) != apply(X2,sK7(X1,X2))
& in(sK7(X1,X2),relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X1,X2))],[f69]) ).
fof(f71,plain,
function(sK2),
inference(cnf_transformation,[],[f62]) ).
fof(f72,plain,
relation(sK2),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
in(sK1,set_intersection2(relation_dom(sK2),sK0)),
inference(cnf_transformation,[],[f62]) ).
fof(f74,plain,
apply(relation_dom_restriction(sK2,sK0),sK1) != apply(sK2,sK1),
inference(cnf_transformation,[],[f62]) ).
fof(f83,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f84,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f100,plain,
! [X2,X0,X1,X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1))
| relation_dom_restriction(X2,X0) != X1
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f101,plain,
! [X2,X0,X1] :
( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) != X1
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f104,definition,
~ sP8(apply(relation_dom_restriction(sK2,sK0),sK1)),
introduced(definition,[new_symbols(definition,[sP8])],[inequality_splitting_name_introduction]) ).
fof(f105,plain,
sP8(apply(sK2,sK1)),
inference(inequality_splitting,[],[f74,f104]) ).
fof(f106,plain,
! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f101]) ).
fof(f107,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f100]) ).
fof(f110,plain,
( in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
| ~ relation(sK2)
| ~ function(sK2)
| ~ relation(relation_dom_restriction(sK2,sK0))
| ~ function(relation_dom_restriction(sK2,sK0)) ),
inference(superposition,[],[f73,f106]) ).
fof(f111,plain,
( in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
| ~ function(sK2)
| ~ relation(relation_dom_restriction(sK2,sK0))
| ~ function(relation_dom_restriction(sK2,sK0)) ),
inference(forward_subsumption_resolution,[],[f110,f72]) ).
fof(f112,plain,
( in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
| ~ relation(relation_dom_restriction(sK2,sK0))
| ~ function(relation_dom_restriction(sK2,sK0)) ),
inference(forward_subsumption_resolution,[],[f111,f71]) ).
fof(f114,definition,
( spl9_1
<=> function(relation_dom_restriction(sK2,sK0)) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f115,plain,
( function(relation_dom_restriction(sK2,sK0))
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f116,plain,
( ~ function(relation_dom_restriction(sK2,sK0))
| spl9_1 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f118,definition,
( spl9_2
<=> relation(relation_dom_restriction(sK2,sK0)) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f119,plain,
( relation(relation_dom_restriction(sK2,sK0))
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f120,plain,
( ~ relation(relation_dom_restriction(sK2,sK0))
| spl9_2 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f122,definition,
( spl9_3
<=> in(sK1,relation_dom(relation_dom_restriction(sK2,sK0))) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f124,plain,
( in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( ~ spl9_1
| ~ spl9_2
| spl9_3 ),
inference(avatar_split_clause,[],[f112,f122,f118,f114]) ).
fof(f126,plain,
( ~ relation(sK2)
| ~ function(sK2)
| spl9_1 ),
inference(resolution,[],[f116,f83]) ).
fof(f127,plain,
( ~ function(sK2)
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f126,f72]) ).
fof(f128,plain,
( $false
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f127,f71]) ).
fof(f129,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f128]) ).
fof(f130,plain,
( ~ sP8(apply(sK2,sK1))
| ~ in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
| ~ relation(sK2)
| ~ function(sK2)
| ~ relation(relation_dom_restriction(sK2,sK0))
| ~ function(relation_dom_restriction(sK2,sK0)) ),
inference(superposition,[],[f104,f107]) ).
fof(f132,plain,
( ~ relation(sK2)
| ~ function(sK2)
| spl9_2 ),
inference(resolution,[],[f120,f84]) ).
fof(f133,plain,
( ~ function(sK2)
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f132,f72]) ).
fof(f136,plain,
( $false
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f133,f71]) ).
fof(f137,plain,
spl9_2,
inference(avatar_contradiction_clause,[],[f136]) ).
fof(f138,plain,
( ~ in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
| ~ relation(sK2)
| ~ function(sK2)
| ~ relation(relation_dom_restriction(sK2,sK0))
| ~ function(relation_dom_restriction(sK2,sK0)) ),
inference(forward_subsumption_resolution,[],[f130,f105]) ).
fof(f139,plain,
( ~ relation(sK2)
| ~ function(sK2)
| ~ relation(relation_dom_restriction(sK2,sK0))
| ~ function(relation_dom_restriction(sK2,sK0))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f138,f124]) ).
fof(f140,plain,
( ~ function(sK2)
| ~ relation(relation_dom_restriction(sK2,sK0))
| ~ function(relation_dom_restriction(sK2,sK0))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f139,f72]) ).
fof(f141,plain,
( ~ relation(relation_dom_restriction(sK2,sK0))
| ~ function(relation_dom_restriction(sK2,sK0))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f140,f71]) ).
fof(f142,plain,
( ~ function(relation_dom_restriction(sK2,sK0))
| ~ spl9_2
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f141,f119]) ).
fof(f143,plain,
( $false
| ~ spl9_1
| ~ spl9_2
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f142,f115]) ).
fof(f144,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3 ),
inference(avatar_contradiction_clause,[],[f143]) ).
cnf(s1,plain,
( ~ spl9_1
| ~ spl9_2
| spl9_3 ),
inference(sat_conversion,[],[f125]) ).
cnf(s2,plain,
spl9_1,
inference(sat_conversion,[],[f129]) ).
cnf(s4,plain,
spl9_2,
inference(sat_conversion,[],[f137]) ).
cnf(s5,plain,
( ~ spl9_1
| ~ spl9_2
| ~ spl9_3 ),
inference(sat_conversion,[],[f144]) ).
cnf(s6,plain,
~ spl9_3,
inference(rat,[],[s5,s4,s2]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s4,s2]) ).
fof(f145,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU037+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 28 03:24:34 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.39/0.80 % (2987821)Detected formulas, will run a generic FOF schedule.
% 0.39/0.80 % (2987832)dis-21_1_sil=8000:lcm=predicate:random_seed=4061099800: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)
% 0.39/0.80 % (2987828)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=2702950247:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.39/0.80 % (2987826)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=883514109:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.39/0.80 % (2987827)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=1491866716:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.39/0.80 % (2987830)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1682123880:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.39/0.80 % (2987831)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=930743356:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.39/0.80 % (2987829)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4232374406:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.39/0.80 % (2987829)First to succeed.
% 0.39/0.80 % (2987830)Also succeeded, but the first one will report.
% 0.39/0.80 % (2987829)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2987821"
% 0.39/0.80 % (2987831)Also succeeded, but the first one will report.
% 0.39/0.80 % (2987832)Instruction limit reached!
% 0.39/0.80 % (2987832)------------------------------
% 0.39/0.80 % (2987832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.39/0.80 % (2987832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.80 % (2987832)CaDiCaL version: 2.1.3
% 0.39/0.80 % (2987832)Termination reason: Instruction limit
% 0.39/0.80 % (2987832)Termination phase: Saturation
% 0.39/0.80 % (2987832)Time elapsed: 0.044 s
% 0.39/0.80 % (2987832)Peak memory usage: 90 MB
% 0.39/0.80 % (2987832)Instructions burned: 129 (million)
% 0.39/0.80 % (2987840)lrs+10_1_sil=8000:sp=occurrence:random_seed=361006747:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.39/0.80 % (2987840)Also succeeded, but the first one will report.
% 0.39/0.80 % (2987829)Refutation found. Thanks to Tanya!
% 0.39/0.80 % SZS status Theorem for theBenchmark
% 0.39/0.80 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.90 % (2987829)------------------------------
% 0.07/0.90 % (2987829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.07/0.90 % (2987829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.90 % (2987829)CaDiCaL version: 2.1.3
% 0.07/0.90 % (2987829)Termination reason: Refutation
% 0.07/0.90 % (2987829)Time elapsed: 0.002 s
% 0.07/0.90 % (2987829)Peak memory usage: 89 MB
% 0.07/0.90 % (2987829)Instructions burned: 4 (million)
% 0.07/0.90 % (2987829)------------------------------
% 0.07/0.90 % (2987829)------------------------------
% 0.07/0.90 % (2987821)Success in time 0.275 s
% 0.07/0.90 % Vampire exiting
%------------------------------------------------------------------------------