%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU187+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 3.57s 1.44s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 12 unt; 2 def)
% Number of atoms : 152 ( 40 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 181 ( 74 ~; 70 |; 24 &)
% ( 11 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 68 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f19,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f23,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f64,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f151,conjecture,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f152,negated_conjecture,
~ ( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(negated_conjecture,[status(cth)],[f151]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f286,plain,
( empty_set != relation_dom(empty_set)
| empty_set != relation_rng(empty_set) ),
inference(ennf_transformation,[],[f152]) ).
fof(f312,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f313,plain,
! [X0] :
( ( X0 = empty_set
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f312]) ).
fof(f314,plain,
! [X0] :
( ( X0 = empty_set
| in(sK7(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f313]) ).
fof(f337,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,[],[f187]) ).
fof(f338,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,[],[f337]) ).
fof(f339,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK18(X0,X1),X3),X0)
| ~ in(sK18(X0,X1),X1) )
& ( in(ordered_pair(sK18(X0,X1),sK19(X0,X1)),X0)
| in(sK18(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK20(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20]),skolemize(X2,sK18(X0,X1)),skolemize(X4,sK19(X0,X1)),skolemize(X7,sK20(X0,X5))],[f338]) ).
fof(f347,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,[],[f188]) ).
fof(f348,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,[],[f347]) ).
fof(f349,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK25(X0,X1)),X0)
| ~ in(sK25(X0,X1),X1) )
& ( in(ordered_pair(sK26(X0,X1),sK25(X0,X1)),X0)
| in(sK25(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK27(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X2,sK25(X0,X1)),skolemize(X4,sK26(X0,X1)),skolemize(X7,sK27(X0,X5))],[f348]) ).
fof(f418,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f314]) ).
fof(f419,plain,
! [X0] :
( in(sK7(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f314]) ).
fof(f457,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK20(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f339]) ).
fof(f474,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK27(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f516,plain,
relation(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f637,plain,
( empty_set != relation_dom(empty_set)
| empty_set != relation_rng(empty_set) ),
inference(cnf_transformation,[],[f286]) ).
fof(f671,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f418]) ).
fof(f691,plain,
! [X0,X5] :
( in(ordered_pair(X5,sK20(X0,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f457]) ).
fof(f699,plain,
! [X0,X5] :
( in(ordered_pair(sK27(X0,X5),X5),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f474]) ).
fof(f712,definition,
( spl51_1
<=> empty_set = relation_rng(empty_set) ),
introduced(definition,[new_symbols(definition,[spl51_1])],[avatar_definition]) ).
fof(f714,plain,
( empty_set != relation_rng(empty_set)
| spl51_1 ),
inference(avatar_component_clause,[],[f712]) ).
fof(f716,definition,
( spl51_2
<=> empty_set = relation_dom(empty_set) ),
introduced(definition,[new_symbols(definition,[spl51_2])],[avatar_definition]) ).
fof(f719,plain,
( ~ spl51_1
| ~ spl51_2 ),
inference(avatar_split_clause,[],[f637,f716,f712]) ).
fof(f805,plain,
! [X0] :
( ~ in(X0,relation_dom(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[],[f691,f671]) ).
fof(f806,plain,
! [X0] : ~ in(X0,relation_dom(empty_set)),
inference(forward_subsumption_resolution,[],[f805,f516]) ).
fof(f808,plain,
! [X0] :
( ~ in(X0,relation_rng(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[],[f699,f671]) ).
fof(f809,plain,
! [X0] : ~ in(X0,relation_rng(empty_set)),
inference(forward_subsumption_resolution,[],[f808,f516]) ).
fof(f816,plain,
empty_set = relation_dom(empty_set),
inference(resolution,[],[f806,f419]) ).
fof(f817,plain,
spl51_2,
inference(avatar_split_clause,[],[f816,f716]) ).
fof(f1067,plain,
empty_set = relation_rng(empty_set),
inference(resolution,[],[f809,f419]) ).
fof(f1071,plain,
( $false
| spl51_1 ),
inference(forward_subsumption_resolution,[],[f1067,f714]) ).
fof(f1072,plain,
spl51_1,
inference(avatar_contradiction_clause,[],[f1071]) ).
cnf(s1,plain,
( ~ spl51_1
| ~ spl51_2 ),
inference(sat_conversion,[],[f719]) ).
cnf(s2,plain,
spl51_2,
inference(sat_conversion,[],[f817]) ).
cnf(s27,plain,
spl51_1,
inference(sat_conversion,[],[f1072]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s1,s2,s27]) ).
fof(f1097,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU187+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 28 04:00:22 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.57/1.44 % (4134021)Detected formulas, will run a generic FOF schedule.
% 3.57/1.44 % (4134029)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1102908745:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.57/1.44 % (4134030)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=978414695:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.57/1.44 % (4134029)Instruction limit reached!
% 3.57/1.44 % (4134029)------------------------------
% 3.57/1.44 % (4134029)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.44 % (4134029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.44 % (4134029)CaDiCaL version: 2.1.3
% 3.57/1.44 % (4134029)Termination reason: Instruction limit
% 3.57/1.44 % (4134029)Termination phase: Saturation
% 3.57/1.44 % (4134029)Time elapsed: 0.042 s
% 3.57/1.44 % (4134029)Peak memory usage: 90 MB
% 3.57/1.44 % (4134029)Instructions burned: 111 (million)
% 3.57/1.44 % (4134031)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3420920513:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.57/1.44 % (4134026)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=1683139768:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.57/1.44 % (4134028)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=2215645306:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.57/1.44 % (4134027)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=2674020546:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.57/1.44 % (4134032)dis-21_1_sil=8000:lcm=predicate:random_seed=3780838581: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)
% 3.57/1.44 % (4134031)First to succeed.
% 3.57/1.44 % (4134031)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4134021"
% 3.57/1.44 % (4134030)Instruction limit reached!
% 3.57/1.44 % (4134030)------------------------------
% 3.57/1.44 % (4134030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.44 % (4134030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.44 % (4134030)CaDiCaL version: 2.1.3
% 3.57/1.44 % (4134030)Termination reason: Instruction limit
% 3.57/1.44 % (4134030)Termination phase: Saturation
% 3.57/1.44 % (4134030)Time elapsed: 0.078 s
% 3.57/1.44 % (4134030)Peak memory usage: 89 MB
% 3.57/1.44 % (4134030)Instructions burned: 120 (million)
% 3.57/1.44 % (4134032)Instruction limit reached!
% 3.57/1.44 % (4134032)------------------------------
% 3.57/1.44 % (4134032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.44 % (4134032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.44 % (4134032)CaDiCaL version: 2.1.3
% 3.57/1.44 % (4134032)Termination reason: Instruction limit
% 3.57/1.44 % (4134032)Termination phase: Saturation
% 3.57/1.44 % (4134032)Time elapsed: 0.078 s
% 3.57/1.44 % (4134032)Peak memory usage: 89 MB
% 3.57/1.44 % (4134032)Instructions burned: 130 (million)
% 3.57/1.44 % (4134039)lrs+10_1_sil=8000:sp=occurrence:random_seed=3796632124:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.57/1.44 % (4134039)Also succeeded, but the first one will report.
% 3.57/1.44 % (4134041)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2908063914:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.57/1.44 % (4134041)Also succeeded, but the first one will report.
% 3.57/1.44 % (4134043)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1303074658:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.57/1.44 % (4134031)Refutation found. Thanks to Tanya!
% 3.57/1.44 % SZS status Theorem for theBenchmark
% 3.57/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.45 % (4134031)------------------------------
% 3.57/1.45 % (4134031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.45 % (4134031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.45 % (4134031)CaDiCaL version: 2.1.3
% 3.57/1.45 % (4134031)Termination reason: Refutation
% 3.57/1.45 % (4134031)Time elapsed: 0.019 s
% 3.57/1.45 % (4134031)Peak memory usage: 90 MB
% 3.57/1.45 % (4134031)Instructions burned: 25 (million)
% 3.57/1.45 % (4134031)------------------------------
% 3.57/1.45 % (4134031)------------------------------
% 3.57/1.45 % (4134021)Success in time 0.424 s
% 3.57/1.45 % Vampire exiting
%------------------------------------------------------------------------------