%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU019+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 : n019.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 12:47:05 PM UTC 2026
% Result : Theorem 2.07s 1.30s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 217 ( 71 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 278 ( 112 ~; 124 |; 32 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 87 ( 79 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f10,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f25,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f28,conjecture,
! [X0] : one_to_one(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
fof(f29,negated_conjecture,
~ ! [X0] : one_to_one(identity_relation(X0)),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f34,plain,
? [X0] : ~ one_to_one(identity_relation(X0)),
inference(ennf_transformation,[],[f29]) ).
fof(f35,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f35]) ).
fof(f49,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f50,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
~ one_to_one(identity_relation(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f34]) ).
fof(f52,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f36]) ).
fof(f53,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK1(X0) != sK2(X0)
& in(sK1(X0),relation_dom(X0))
& in(sK2(X0),relation_dom(X0))
& apply(X0,sK1(X0)) = apply(X0,sK2(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f53]) ).
fof(f58,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(nnf_transformation,[],[f50]) ).
fof(f59,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(rectify,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ( sK6(X0,X1) != apply(X1,sK6(X0,X1))
& in(sK6(X0,X1),X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f60]) ).
fof(f65,plain,
~ one_to_one(identity_relation(sK0)),
inference(cnf_transformation,[],[f51]) ).
fof(f66,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f67,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f70,plain,
! [X0] :
( apply(X0,sK1(X0)) = apply(X0,sK2(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f71,plain,
! [X0] :
( in(sK2(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f72,plain,
! [X0] :
( in(sK1(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f73,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f91,plain,
! [X3,X0,X1] :
( apply(X1,X3) = X3
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f92,plain,
! [X0,X1] :
( relation_dom(X1) = X0
| identity_relation(X0) != X1
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f103,plain,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(equality_resolution,[],[f92]) ).
fof(f104,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(equality_resolution,[],[f91]) ).
fof(f125,plain,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f103,f67]) ).
fof(f126,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(forward_subsumption_resolution,[],[f125,f66]) ).
fof(f128,plain,
! [X0] :
( in(sK1(identity_relation(X0)),X0)
| one_to_one(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(superposition,[],[f72,f126]) ).
fof(f129,plain,
! [X0] :
( in(sK2(identity_relation(X0)),X0)
| one_to_one(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(superposition,[],[f71,f126]) ).
fof(f134,plain,
! [X0] :
( in(sK2(identity_relation(X0)),X0)
| one_to_one(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f129,f67]) ).
fof(f135,plain,
! [X0] :
( in(sK1(identity_relation(X0)),X0)
| one_to_one(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f128,f67]) ).
fof(f137,plain,
! [X0] :
( in(sK2(identity_relation(X0)),X0)
| one_to_one(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f134,f66]) ).
fof(f138,plain,
! [X0] :
( in(sK1(identity_relation(X0)),X0)
| one_to_one(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f135,f66]) ).
fof(f140,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f104,f67]) ).
fof(f141,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0) ),
inference(forward_subsumption_resolution,[],[f140,f66]) ).
fof(f146,plain,
! [X0] :
( sK2(identity_relation(X0)) = apply(identity_relation(X0),sK1(identity_relation(X0)))
| one_to_one(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| ~ in(sK2(identity_relation(X0)),X0) ),
inference(superposition,[],[f70,f141]) ).
fof(f147,plain,
! [X0] :
( sK2(identity_relation(X0)) = apply(identity_relation(X0),sK1(identity_relation(X0)))
| one_to_one(identity_relation(X0))
| ~ function(identity_relation(X0))
| ~ in(sK2(identity_relation(X0)),X0) ),
inference(forward_subsumption_resolution,[],[f146,f67]) ).
fof(f149,plain,
! [X0] :
( sK2(identity_relation(X0)) = apply(identity_relation(X0),sK1(identity_relation(X0)))
| one_to_one(identity_relation(X0))
| ~ in(sK2(identity_relation(X0)),X0) ),
inference(forward_subsumption_resolution,[],[f147,f66]) ).
fof(f205,plain,
! [X0] :
( sK2(identity_relation(X0)) = apply(identity_relation(X0),sK1(identity_relation(X0)))
| one_to_one(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f149,f137]) ).
fof(f208,plain,
! [X0] :
( sK1(identity_relation(X0)) = sK2(identity_relation(X0))
| ~ in(sK1(identity_relation(X0)),X0)
| one_to_one(identity_relation(X0)) ),
inference(superposition,[],[f141,f205]) ).
fof(f211,plain,
! [X0] :
( sK1(identity_relation(X0)) = sK2(identity_relation(X0))
| one_to_one(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f208,f138]) ).
fof(f218,plain,
! [X0] :
( sK1(identity_relation(X0)) != sK1(identity_relation(X0))
| one_to_one(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| one_to_one(identity_relation(X0)) ),
inference(superposition,[],[f73,f211]) ).
fof(f221,plain,
! [X0] :
( sK1(identity_relation(X0)) != sK1(identity_relation(X0))
| one_to_one(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(duplicate_literal_removal,[],[f218]) ).
fof(f222,plain,
! [X0] :
( one_to_one(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(trivial_inequality_removal,[],[f221]) ).
fof(f227,plain,
! [X0] :
( one_to_one(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f222,f67]) ).
fof(f228,plain,
! [X0] : one_to_one(identity_relation(X0)),
inference(forward_subsumption_resolution,[],[f227,f66]) ).
fof(f229,plain,
$false,
inference(resolution,[],[f228,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU019+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 : n019.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 03:22:33 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
% 2.07/1.30 % (3632155)Detected formulas, will run a generic FOF schedule.
% 2.07/1.30 % (3632160)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=734942682:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.07/1.30 % (3632161)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=3090917108:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.07/1.30 % (3632165)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1999404879:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.07/1.30 % (3632166)dis-21_1_sil=8000:lcm=predicate:random_seed=2724411774: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)
% 2.07/1.30 % (3632164)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1754226463:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.07/1.30 % (3632163)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1262399262:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.07/1.30 % (3632162)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=3630185240:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.07/1.30 % (3632163)Refutation not found, incomplete strategy
% 2.07/1.30 % (3632163)------------------------------
% 2.07/1.30 % (3632163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.07/1.30 % (3632163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/1.30 % (3632163)CaDiCaL version: 2.1.3
% 2.07/1.30 % (3632163)Termination reason: Refutation not found, incomplete strategy
% 2.07/1.30 % (3632163)Time elapsed: 0.001 s
% 2.07/1.30 % (3632163)Peak memory usage: 88 MB
% 2.07/1.30 % (3632164)First to succeed.
% 2.07/1.30 % (3632165)Also succeeded, but the first one will report.
% 2.07/1.30 % (3632164)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3632155"
% 2.07/1.30 % (3632166)Instruction limit reached!
% 2.07/1.30 % (3632166)------------------------------
% 2.07/1.30 % (3632166)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.07/1.30 % (3632166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.07/1.30 % (3632166)CaDiCaL version: 2.1.3
% 2.07/1.30 % (3632166)Termination reason: Instruction limit
% 2.07/1.30 % (3632166)Termination phase: Saturation
% 2.07/1.30 % (3632166)Time elapsed: 0.078 s
% 2.07/1.30 % (3632166)Peak memory usage: 89 MB
% 2.07/1.30 % (3632166)Instructions burned: 129 (million)
% 2.07/1.30 % (3632174)lrs+10_1_sil=8000:sp=occurrence:random_seed=3086122142:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.07/1.30 % (3632163)------------------------------
% 2.07/1.30 % (3632163)------------------------------
% 2.07/1.30 % (3632164)Refutation found. Thanks to Tanya!
% 2.07/1.30 % SZS status Theorem for theBenchmark
% 2.07/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.50 % (3632164)------------------------------
% 0.16/1.50 % (3632164)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (3632164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (3632164)CaDiCaL version: 2.1.3
% 0.16/1.50 % (3632164)Termination reason: Refutation
% 0.16/1.50 % (3632164)Time elapsed: 0.006 s
% 0.16/1.50 % (3632164)Peak memory usage: 88 MB
% 0.16/1.50 % (3632164)Instructions burned: 8 (million)
% 0.16/1.50 % (3632164)------------------------------
% 0.16/1.50 % (3632164)------------------------------
% 0.16/1.50 % (3632155)Success in time 0.433 s
% 0.16/1.50 % Vampire exiting
%------------------------------------------------------------------------------