%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU187+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 : n016.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 12:47:38 PM UTC 2026
% Result : Theorem 2.80s 1.34s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 4 unt; 0 def)
% Number of atoms : 188 ( 42 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 236 ( 100 ~; 95 |; 26 &)
% ( 9 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 118 ( 99 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f4,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(f5,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(f19,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f22,axiom,
? [X0] :
( empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f28,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f29,conjecture,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f30,negated_conjecture,
~ ( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f32,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f34,plain,
( empty_set != relation_dom(empty_set)
| empty_set != relation_rng(empty_set) ),
inference(ennf_transformation,[],[f30]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f42,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f43,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f45,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f47,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,[],[f38]) ).
fof(f48,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,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f48]) ).
fof(f50,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,[],[f41]) ).
fof(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK3(X0,X1)),X0)
| ~ in(sK3(X0,X1),X1) )
& ( in(ordered_pair(sK4(X0,X1),sK3(X0,X1)),X0)
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK5(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f51]) ).
fof(f56,plain,
( empty(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f22]) ).
fof(f57,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f58,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK10(X0,X1),X1)
| ~ in(sK10(X0,X1),X0) )
& ( in(sK10(X0,X1),X1)
| in(sK10(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f57]) ).
fof(f59,plain,
( empty_set != relation_rng(empty_set)
| empty_set != relation_dom(empty_set) ),
inference(cnf_transformation,[],[f34]) ).
fof(f62,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f67,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK5(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f71,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f73,plain,
empty(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f80,plain,
empty(sK9),
inference(cnf_transformation,[],[f56]) ).
fof(f81,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f82,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f83,plain,
! [X0,X1] :
( in(sK10(X0,X1),X1)
| X0 = X1
| in(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f88,plain,
! [X0,X5] :
( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f62]) ).
fof(f90,plain,
! [X0,X5] :
( in(ordered_pair(sK5(X0,X5),X5),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f67]) ).
fof(f97,plain,
! [X0,X1] :
( in(sK10(X0,X1),X0)
| X0 = X1
| ~ empty(X1) ),
inference(resolution,[],[f83,f82]) ).
fof(f108,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ empty(X1) ),
inference(resolution,[],[f88,f82]) ).
fof(f111,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X1) ),
inference(forward_subsumption_resolution,[],[f108,f81]) ).
fof(f115,plain,
! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) ),
inference(resolution,[],[f90,f82]) ).
fof(f118,plain,
! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ empty(X1) ),
inference(forward_subsumption_resolution,[],[f115,f81]) ).
fof(f120,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| ~ empty(X0)
| ~ empty(X1) ),
inference(resolution,[],[f111,f97]) ).
fof(f124,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| ~ empty(X0)
| ~ empty(X1) ),
inference(resolution,[],[f118,f97]) ).
fof(f138,plain,
! [X0] :
( empty_set != X0
| empty_set != relation_dom(empty_set)
| ~ empty(empty_set)
| ~ empty(X0) ),
inference(superposition,[],[f59,f124]) ).
fof(f147,plain,
! [X0] :
( empty_set != relation_dom(empty_set)
| ~ empty(empty_set)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f138,f71]) ).
fof(f148,plain,
! [X0] :
( empty_set != relation_dom(empty_set)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f147,f73]) ).
fof(f150,plain,
! [X0,X1] :
( empty_set != X0
| ~ empty(X1)
| ~ empty(empty_set)
| ~ empty(X0) ),
inference(superposition,[],[f148,f120]) ).
fof(f151,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ empty(empty_set)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f150,f71]) ).
fof(f152,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[],[f151,f73]) ).
fof(f164,plain,
! [X0] : ~ empty(X0),
inference(resolution,[],[f152,f73]) ).
fof(f181,plain,
$false,
inference(resolution,[],[f164,f80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU187+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 04:02:02 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.80/1.34 % (3243691)Detected formulas, will run a generic FOF schedule.
% 2.80/1.34 % (3243700)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1730163940:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.80/1.34 % (3243700)First to succeed.
% 2.80/1.34 % (3243700)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3243691"
% 2.80/1.34 % (3243699)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2123433141:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.80/1.34 % (3243702)dis-21_1_sil=8000:lcm=predicate:random_seed=3411106553: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)
% 2.80/1.34 % (3243698)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=3985880124:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.80/1.34 % (3243696)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=2969829803:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.80/1.34 % (3243697)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=2543713138:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.80/1.34 % (3243699)Refutation not found, incomplete strategy
% 2.80/1.34 % (3243699)------------------------------
% 2.80/1.34 % (3243699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.34 % (3243699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.34 % (3243699)CaDiCaL version: 2.1.3
% 2.80/1.34 % (3243699)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.34 % (3243699)Time elapsed: 0.002 s
% 2.80/1.34 % (3243699)Peak memory usage: 88 MB
% 2.80/1.34 % (3243699)Instructions burned: 1 (million)
% 2.80/1.34 % (3243701)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2435249045:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.80/1.34 % (3243702)Also succeeded, but the first one will report.
% 2.80/1.34 % (3243701)Also succeeded, but the first one will report.
% 2.80/1.34 % (3243700)Refutation found. Thanks to Tanya!
% 2.80/1.34 % SZS status Theorem for theBenchmark
% 2.80/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.34 % (3243700)------------------------------
% 2.80/1.34 % (3243700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.34 % (3243700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.34 % (3243700)CaDiCaL version: 2.1.3
% 2.80/1.34 % (3243700)Termination reason: Refutation
% 2.80/1.34 % (3243700)Time elapsed: 0.003 s
% 2.80/1.34 % (3243700)Peak memory usage: 88 MB
% 2.80/1.34 % (3243700)Instructions burned: 6 (million)
% 2.80/1.34 % (3243700)------------------------------
% 2.80/1.34 % (3243700)------------------------------
% 2.80/1.34 % (3243691)Success in time 0.311 s
% 2.80/1.34 % Vampire exiting
%------------------------------------------------------------------------------