%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU177+2 : 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 : n026.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 12:47:35 PM UTC 2026
% Result : Theorem 3.49s 1.39s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 10 unt; 2 def)
% Number of atoms : 144 ( 18 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 170 ( 64 ~; 64 |; 26 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 66 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,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(f21,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(f94,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f95,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f160,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f161,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f202,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| ~ in(X1,relation_rng(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f95]) ).
fof(f203,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| ~ in(X1,relation_rng(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f202]) ).
fof(f277,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,[],[f160]) ).
fof(f278,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,[],[f277]) ).
fof(f279,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK15(X0,X1),X3),X0)
| ~ in(sK15(X0,X1),X1) )
& ( in(ordered_pair(sK15(X0,X1),sK16(X0,X1)),X0)
| in(sK15(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK17(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X2,sK15(X0,X1)),skolemize(X4,sK16(X0,X1)),skolemize(X7,sK17(X0,X5))],[f278]) ).
fof(f287,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,[],[f161]) ).
fof(f288,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,[],[f287]) ).
fof(f289,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK22(X0,X1)),X0)
| ~ in(sK22(X0,X1),X1) )
& ( in(ordered_pair(sK23(X0,X1),sK22(X0,X1)),X0)
| in(sK22(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK24(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23,sK24]),skolemize(X2,sK22(X0,X1)),skolemize(X4,sK23(X0,X1)),skolemize(X7,sK24(X0,X5))],[f288]) ).
fof(f311,plain,
( ( ~ in(sK34,relation_dom(sK36))
| ~ in(sK35,relation_rng(sK36)) )
& in(ordered_pair(sK34,sK35),sK36)
& relation(sK36) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34,sK35,sK36]),skolemize(X0,sK34),skolemize(X1,sK35),skolemize(X2,sK36)],[f203]) ).
fof(f387,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f404,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f485,plain,
relation(sK36),
inference(cnf_transformation,[],[f311]) ).
fof(f486,plain,
in(ordered_pair(sK34,sK35),sK36),
inference(cnf_transformation,[],[f311]) ).
fof(f487,plain,
( ~ in(sK34,relation_dom(sK36))
| ~ in(sK35,relation_rng(sK36)) ),
inference(cnf_transformation,[],[f311]) ).
fof(f585,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0)) ),
inference(equality_resolution,[],[f387]) ).
fof(f593,plain,
! [X0,X6,X5] :
( ~ relation(X0)
| ~ in(ordered_pair(X6,X5),X0)
| in(X5,relation_rng(X0)) ),
inference(equality_resolution,[],[f404]) ).
fof(f602,definition,
( spl42_1
<=> in(sK35,relation_rng(sK36)) ),
introduced(definition,[new_symbols(definition,[spl42_1])],[avatar_definition]) ).
fof(f604,plain,
( ~ in(sK35,relation_rng(sK36))
| spl42_1 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f606,definition,
( spl42_2
<=> in(sK34,relation_dom(sK36)) ),
introduced(definition,[new_symbols(definition,[spl42_2])],[avatar_definition]) ).
fof(f609,plain,
( ~ spl42_1
| ~ spl42_2 ),
inference(avatar_split_clause,[],[f487,f606,f602]) ).
fof(f944,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK36)
| in(X0,relation_dom(sK36)) ),
inference(resolution,[],[f585,f485]) ).
fof(f974,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK36)
| in(X1,relation_rng(sK36)) ),
inference(resolution,[],[f593,f485]) ).
fof(f977,plain,
in(sK34,relation_dom(sK36)),
inference(resolution,[],[f944,f486]) ).
fof(f978,plain,
spl42_2,
inference(avatar_split_clause,[],[f977,f606]) ).
fof(f991,plain,
in(sK35,relation_rng(sK36)),
inference(resolution,[],[f974,f486]) ).
fof(f992,plain,
( $false
| spl42_1 ),
inference(forward_subsumption_resolution,[],[f991,f604]) ).
fof(f993,plain,
spl42_1,
inference(avatar_contradiction_clause,[],[f992]) ).
cnf(s1,plain,
( ~ spl42_1
| ~ spl42_2 ),
inference(sat_conversion,[],[f609]) ).
cnf(s2,plain,
spl42_2,
inference(sat_conversion,[],[f978]) ).
cnf(s3,plain,
spl42_1,
inference(sat_conversion,[],[f993]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f994,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU177+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n026.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:56:27 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.49/1.39 % (3445552)Detected formulas, will run a generic FOF schedule.
% 3.49/1.39 % (3445560)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=69463004:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.49/1.39 % (3445557)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=3163638344:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.49/1.39 % (3445558)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=3109102908:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.49/1.39 % (3445559)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=2484665115:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.49/1.39 % (3445560)Instruction limit reached!
% 3.49/1.39 % (3445560)------------------------------
% 3.49/1.39 % (3445560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.39 % (3445560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.39 % (3445560)CaDiCaL version: 2.1.3
% 3.49/1.39 % (3445560)Termination reason: Instruction limit
% 3.49/1.39 % (3445560)Termination phase: Saturation
% 3.49/1.39 % (3445560)Time elapsed: 0.039 s
% 3.49/1.39 % (3445560)Peak memory usage: 90 MB
% 3.49/1.39 % (3445560)Instructions burned: 110 (million)
% 3.49/1.39 % (3445562)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3571764136:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.49/1.39 % (3445561)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3729949003:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.49/1.39 % (3445563)dis-21_1_sil=8000:lcm=predicate:random_seed=2626648330: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)
% 3.49/1.39 % (3445562)First to succeed.
% 3.49/1.39 % (3445562)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3445552"
% 3.49/1.39 % (3445561)Also succeeded, but the first one will report.
% 3.49/1.39 % (3445563)Instruction limit reached!
% 3.49/1.39 % (3445563)------------------------------
% 3.49/1.39 % (3445563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.39 % (3445563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.39 % (3445563)CaDiCaL version: 2.1.3
% 3.49/1.39 % (3445563)Termination reason: Instruction limit
% 3.49/1.39 % (3445563)Termination phase: Saturation
% 3.49/1.39 % (3445563)Time elapsed: 0.083 s
% 3.49/1.39 % (3445563)Peak memory usage: 90 MB
% 3.49/1.39 % (3445563)Instructions burned: 130 (million)
% 3.49/1.39 % (3445571)lrs+10_1_sil=8000:sp=occurrence:random_seed=955572716:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.49/1.39 % (3445571)Instruction limit reached!
% 3.49/1.39 % (3445571)------------------------------
% 3.49/1.39 % (3445571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.39 % (3445571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.39 % (3445571)CaDiCaL version: 2.1.3
% 3.49/1.39 % (3445571)Termination reason: Instruction limit
% 3.49/1.39 % (3445571)Termination phase: Saturation
% 3.49/1.39 % (3445571)Time elapsed: 0.103 s
% 3.49/1.39 % (3445571)Peak memory usage: 92 MB
% 3.49/1.39 % (3445571)Instructions burned: 288 (million)
% 3.49/1.39 % (3445573)lrs+10_1_sil=32000:urr=on:br=off:random_seed=847092854:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.49/1.39 % (3445573)Also succeeded, but the first one will report.
% 3.49/1.39 % (3445562)Refutation found. Thanks to Tanya!
% 3.49/1.39 % SZS status Theorem for theBenchmark
% 3.49/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.39 % (3445562)------------------------------
% 3.49/1.39 % (3445562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.39 % (3445562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.39 % (3445562)CaDiCaL version: 2.1.3
% 3.49/1.39 % (3445562)Termination reason: Refutation
% 3.49/1.39 % (3445562)Time elapsed: 0.020 s
% 3.49/1.39 % (3445562)Peak memory usage: 90 MB
% 3.49/1.39 % (3445562)Instructions burned: 26 (million)
% 3.49/1.39 % (3445562)------------------------------
% 3.49/1.39 % (3445562)------------------------------
% 3.49/1.39 % (3445552)Success in time 0.431 s
% 3.49/1.39 % Vampire exiting
%------------------------------------------------------------------------------