%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU045+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 : n001.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 12:47:07 PM UTC 2026
% Result : Theorem 2.67s 1.30s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 8 unt; 2 def)
% Number of atoms : 217 ( 32 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 275 ( 102 ~; 91 |; 59 &)
% ( 11 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 106 ( 94 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f20,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f33,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
=> apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t87_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
=> apply(relation_rng_restriction(X0,X2),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f36,plain,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( in(X4,relation_dom(X1))
=> apply(X2,X4) = apply(X1,X4) ) ) ) ) ),
inference(rectify,[],[f35]) ).
fof(f37,plain,
? [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_rng_restriction(X0,X2)))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f38,plain,
? [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X2),X1) != apply(X2,X1)
& in(X1,relation_dom(relation_rng_restriction(X0,X2)))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f37]) ).
fof(f45,plain,
! [X0,X1] :
( ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0,X1] :
( ( relation(relation_rng_restriction(X0,X1))
& function(relation_rng_restriction(X0,X1)) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f48,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f49,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f48]) ).
fof(f56,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f57,definition,
! [X1,X0,X2] :
( ( X1 = relation_rng_restriction(X0,X2)
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0,X2) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f58,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X1,X0,X2)
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(definition_folding,[],[f49,f57,f56]) ).
fof(f59,plain,
( apply(relation_rng_restriction(sK2,sK4),sK3) != apply(sK4,sK3)
& in(sK3,relation_dom(relation_rng_restriction(sK2,sK4)))
& relation(sK4)
& function(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f38]) ).
fof(f62,plain,
! [X1,X0,X2] :
( ( ( X1 = relation_rng_restriction(X0,X2)
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ sP1(X1,X0,X2) ),
inference(nnf_transformation,[],[f57]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( ( relation_rng_restriction(X1,X2) = X0
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X1)) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| in(X3,relation_dom(X1)) ) )
| ? [X4] :
( apply(X2,X4) != apply(X1,X4)
& in(X4,relation_dom(X1)) ) )
& ( ( ! [X3] :
( ( in(X3,relation_dom(X1))
| ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| ~ in(X3,relation_dom(X1)) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ? [X3] :
( ( ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0)
| ~ in(X3,relation_dom(X1)) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| in(X3,relation_dom(X1)) ) )
| ? [X4] :
( apply(X2,X4) != apply(X1,X4)
& in(X4,relation_dom(X1)) ) )
& ( ( ! [X3] :
( ( in(X3,relation_dom(X1))
| ~ in(X3,relation_dom(X2))
| ~ in(apply(X2,X3),X0) )
& ( ( in(X3,relation_dom(X2))
& in(apply(X2,X3),X0) )
| ~ in(X3,relation_dom(X1)) ) )
& ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,relation_dom(X0))
| ~ in(apply(X0,X3),X1)
| ~ in(X3,relation_dom(X2)) )
& ( ( in(X3,relation_dom(X0))
& in(apply(X0,X3),X1) )
| in(X3,relation_dom(X2)) ) )
| ? [X4] :
( apply(X2,X4) != apply(X0,X4)
& in(X4,relation_dom(X2)) ) )
& ( ( ! [X5] :
( ( in(X5,relation_dom(X2))
| ~ in(X5,relation_dom(X0))
| ~ in(apply(X0,X5),X1) )
& ( ( in(X5,relation_dom(X0))
& in(apply(X0,X5),X1) )
| ~ in(X5,relation_dom(X2)) ) )
& ! [X6] :
( apply(X0,X6) = apply(X2,X6)
| ~ in(X6,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ in(sK7(X0,X1,X2),relation_dom(X0))
| ~ in(apply(X0,sK7(X0,X1,X2)),X1)
| ~ in(sK7(X0,X1,X2),relation_dom(X2)) )
& ( ( in(sK7(X0,X1,X2),relation_dom(X0))
& in(apply(X0,sK7(X0,X1,X2)),X1) )
| in(sK7(X0,X1,X2),relation_dom(X2)) ) )
| ( apply(X2,sK8(X0,X2)) != apply(X0,sK8(X0,X2))
& in(sK8(X0,X2),relation_dom(X2)) ) )
& ( ( ! [X5] :
( ( in(X5,relation_dom(X2))
| ~ in(X5,relation_dom(X0))
| ~ in(apply(X0,X5),X1) )
& ( ( in(X5,relation_dom(X0))
& in(apply(X0,X5),X1) )
| ~ in(X5,relation_dom(X2)) ) )
& ! [X6] :
( apply(X0,X6) = apply(X2,X6)
| ~ in(X6,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X4,sK8(X0,X2))],[f66]) ).
fof(f73,plain,
function(sK4),
inference(cnf_transformation,[],[f59]) ).
fof(f74,plain,
relation(sK4),
inference(cnf_transformation,[],[f59]) ).
fof(f75,plain,
in(sK3,relation_dom(relation_rng_restriction(sK2,sK4))),
inference(cnf_transformation,[],[f59]) ).
fof(f76,plain,
apply(relation_rng_restriction(sK2,sK4),sK3) != apply(sK4,sK3),
inference(cnf_transformation,[],[f59]) ).
fof(f87,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f89,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f90,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| relation_rng_restriction(X1,X2) != X0
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f92,plain,
! [X2,X0,X1,X6] :
( apply(X0,X6) = apply(X2,X6)
| ~ in(X6,relation_dom(X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f102,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f119,plain,
! [X2,X1] :
( sP0(X2,X1,relation_rng_restriction(X1,X2))
| ~ sP1(relation_rng_restriction(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f90]) ).
fof(f176,plain,
! [X0,X1] :
( apply(sK4,sK3) != apply(X0,sK3)
| ~ in(sK3,relation_dom(relation_rng_restriction(sK2,sK4)))
| ~ sP0(X0,X1,relation_rng_restriction(sK2,sK4)) ),
inference(superposition,[],[f76,f92]) ).
fof(f180,plain,
! [X0,X1] :
( apply(sK4,sK3) != apply(X0,sK3)
| ~ sP0(X0,X1,relation_rng_restriction(sK2,sK4)) ),
inference(forward_subsumption_resolution,[],[f176,f75]) ).
fof(f215,plain,
! [X0] : ~ sP0(sK4,X0,relation_rng_restriction(sK2,sK4)),
inference(equality_resolution,[],[f180]) ).
fof(f223,plain,
~ sP1(relation_rng_restriction(sK2,sK4),sK2,sK4),
inference(resolution,[],[f215,f119]) ).
fof(f231,plain,
( ~ relation(sK4)
| ~ function(sK4)
| ~ relation(relation_rng_restriction(sK2,sK4))
| ~ function(relation_rng_restriction(sK2,sK4)) ),
inference(resolution,[],[f223,f102]) ).
fof(f234,plain,
( ~ function(sK4)
| ~ relation(relation_rng_restriction(sK2,sK4))
| ~ function(relation_rng_restriction(sK2,sK4)) ),
inference(forward_subsumption_resolution,[],[f231,f74]) ).
fof(f235,plain,
( ~ function(relation_rng_restriction(sK2,sK4))
| ~ relation(relation_rng_restriction(sK2,sK4)) ),
inference(forward_subsumption_resolution,[],[f234,f73]) ).
fof(f249,plain,
( ~ relation(relation_rng_restriction(sK2,sK4))
| ~ relation(sK4)
| ~ function(sK4) ),
inference(resolution,[],[f235,f87]) ).
fof(f252,plain,
( ~ relation(sK4)
| ~ function(sK4) ),
inference(forward_subsumption_resolution,[],[f249,f89]) ).
fof(f253,plain,
~ function(sK4),
inference(forward_subsumption_resolution,[],[f252,f74]) ).
fof(f254,plain,
$false,
inference(forward_subsumption_resolution,[],[f253,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU045+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:33:26 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.67/1.30 % (4180588)Detected formulas, will run a generic FOF schedule.
% 2.67/1.30 % (4180665)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=3143810018:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.30 % (4180667)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3151843864:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.30 % (4180664)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=1795824966:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.30 % (4180666)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=306148418:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.30 % (4180669)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3162425732:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.30 % (4180666)Refutation not found, incomplete strategy
% 2.67/1.30 % (4180666)------------------------------
% 2.67/1.30 % (4180666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.30 % (4180666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.30 % (4180666)CaDiCaL version: 2.1.3
% 2.67/1.30 % (4180666)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.30 % (4180666)Time elapsed: 0.004 s
% 2.67/1.30 % (4180666)Peak memory usage: 88 MB
% 2.67/1.30 % (4180666)Instructions burned: 5 (million)
% 2.67/1.30 % (4180667)First to succeed.
% 2.67/1.30 % (4180667)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4180588"
% 2.67/1.30 % (4180663)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=2640648485:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.30 % (4180670)dis-21_1_sil=8000:lcm=predicate:random_seed=990483337: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)
% 2.67/1.30 % (4180670)Also succeeded, but the first one will report.
% 2.67/1.30 % (4180669)Instruction limit reached!
% 2.67/1.30 % (4180669)------------------------------
% 2.67/1.30 % (4180669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.30 % (4180669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.30 % (4180669)CaDiCaL version: 2.1.3
% 2.67/1.30 % (4180669)Termination reason: Instruction limit
% 2.67/1.30 % (4180669)Termination phase: Saturation
% 2.67/1.30 % (4180669)Time elapsed: 0.083 s
% 2.67/1.30 % (4180669)Peak memory usage: 89 MB
% 2.67/1.30 % (4180669)Instructions burned: 140 (million)
% 2.67/1.30 % (4180666)------------------------------
% 2.67/1.30 % (4180666)------------------------------
% 2.67/1.30 % (4180690)lrs+10_1_sil=8000:sp=occurrence:random_seed=1626132982:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.67/1.30 % (4180667)Refutation found. Thanks to Tanya!
% 2.67/1.30 % SZS status Theorem for theBenchmark
% 2.67/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.41 % (4180667)------------------------------
% 3.57/1.41 % (4180667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.41 % (4180667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.41 % (4180667)CaDiCaL version: 2.1.3
% 3.57/1.41 % (4180667)Termination reason: Refutation
% 3.57/1.41 % (4180667)Time elapsed: 0.008 s
% 3.57/1.41 % (4180667)Peak memory usage: 88 MB
% 3.57/1.41 % (4180667)Instructions burned: 10 (million)
% 3.57/1.41 % (4180667)------------------------------
% 3.57/1.41 % (4180667)------------------------------
% 3.57/1.41 % (4180588)Success in time 0.434 s
% 3.57/1.41 % Vampire exiting
%------------------------------------------------------------------------------