%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU186+1 : 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 : n003.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 0.15s 1.50s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 11 unt; 2 def)
% Number of atoms : 90 ( 19 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 86 ( 39 ~; 29 |; 8 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 44 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : X1 != ordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f11,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f22,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f23,conjecture,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f28,plain,
! [X0] :
( relation(X0)
=> ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : X1 != ordered_pair(X2,X3) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f33,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f34,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
? [X0] :
( empty_set != X0
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f36,plain,
? [X0] :
( empty_set != X0
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& relation(X0) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ~ in(X1,X0)
| ordered_pair(sK0(X1),sK1(X1)) = X1 )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X1)),skolemize(X3,sK1(X1))],[f31]) ).
fof(f41,plain,
! [X0] : element(sK2(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f11]) ).
fof(f46,plain,
( empty_set != sK7
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f36]) ).
fof(f50,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ordered_pair(sK0(X1),sK1(X1)) = X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f52,plain,
! [X0] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f41]) ).
fof(f66,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f67,plain,
relation(sK7),
inference(cnf_transformation,[],[f46]) ).
fof(f68,plain,
! [X2,X1] : ~ in(ordered_pair(X1,X2),sK7),
inference(cnf_transformation,[],[f46]) ).
fof(f69,plain,
empty_set != sK7,
inference(cnf_transformation,[],[f46]) ).
fof(f70,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f89,plain,
! [X0] :
( in(sK2(X0),X0)
| empty(X0) ),
inference(resolution,[],[f66,f52]) ).
fof(f97,plain,
! [X0] :
( ~ relation(X0)
| sK2(X0) = ordered_pair(sK0(sK2(X0)),sK1(sK2(X0)))
| empty(X0) ),
inference(resolution,[],[f50,f89]) ).
fof(f168,plain,
( sK2(sK7) = ordered_pair(sK0(sK2(sK7)),sK1(sK2(sK7)))
| empty(sK7) ),
inference(resolution,[],[f97,f67]) ).
fof(f170,definition,
( spl8_1
<=> empty(sK7) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f172,plain,
( empty(sK7)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f174,definition,
( spl8_2
<=> sK2(sK7) = ordered_pair(sK0(sK2(sK7)),sK1(sK2(sK7))) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f176,plain,
( sK2(sK7) = ordered_pair(sK0(sK2(sK7)),sK1(sK2(sK7)))
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f168,f174,f170]) ).
fof(f208,plain,
( ~ in(sK2(sK7),sK7)
| ~ spl8_2 ),
inference(superposition,[],[f68,f176]) ).
fof(f269,plain,
( empty(sK7)
| ~ spl8_2 ),
inference(resolution,[],[f208,f89]) ).
fof(f270,plain,
( spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f269,f174,f170]) ).
fof(f301,plain,
( empty_set = sK7
| ~ spl8_1 ),
inference(resolution,[],[f172,f70]) ).
fof(f302,plain,
( $false
| ~ spl8_1 ),
inference(forward_subsumption_resolution,[],[f301,f69]) ).
fof(f303,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f302]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f177]) ).
cnf(s2,plain,
( spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f270]) ).
cnf(s3,plain,
~ spl8_1,
inference(sat_conversion,[],[f303]) ).
cnf(s4,plain,
~ spl8_2,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3]) ).
fof(f304,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU186+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 03:58:57 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.39 Running first-order theorem proving
% 0.04/0.39 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
% 0.15/1.50 % (1170521)Detected formulas, will run a generic FOF schedule.
% 0.15/1.50 % (1170532)dis-21_1_sil=8000:lcm=predicate:random_seed=226070984: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)
% 0.15/1.50 % (1170532)Refutation not found, incomplete strategy
% 0.15/1.50 % (1170532)------------------------------
% 0.15/1.50 % (1170532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (1170532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (1170532)CaDiCaL version: 2.1.3
% 0.15/1.50 % (1170532)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.50 % (1170532)Time elapsed: 0.001 s
% 0.15/1.50 % (1170532)Peak memory usage: 88 MB
% 0.15/1.50 % (1170532)Instructions burned: 1 (million)
% 0.15/1.50 % (1170530)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=87548160:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.15/1.50 % (1170526)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=742299709:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.15/1.50 % (1170527)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=2852739524:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.15/1.50 % (1170529)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2993943216:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.15/1.50 % (1170528)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=967185073:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.15/1.50 % (1170529)Refutation not found, incomplete strategy
% 0.15/1.50 % (1170529)------------------------------
% 0.15/1.50 % (1170529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (1170529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (1170529)CaDiCaL version: 2.1.3
% 0.15/1.50 % (1170529)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.50 % (1170529)Time elapsed: 0.001 s
% 0.15/1.50 % (1170530)Refutation not found, incomplete strategy
% 0.15/1.50 % (1170530)------------------------------
% 0.15/1.50 % (1170530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (1170529)Peak memory usage: 88 MB
% 0.15/1.50 % (1170530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (1170530)CaDiCaL version: 2.1.3
% 0.15/1.50 % (1170530)Termination reason: Refutation not found, incomplete strategy
% 0.15/1.50 % (1170530)Time elapsed: 0.001 s
% 0.15/1.50 % (1170530)Peak memory usage: 88 MB
% 0.15/1.50 % (1170531)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=486153347:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.15/1.50 % (1170531)First to succeed.
% 0.15/1.50 % (1170531)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1170521"
% 0.15/1.50 % (1170532)------------------------------
% 0.15/1.50 % (1170532)------------------------------
% 0.15/1.50 % (1170529)------------------------------
% 0.15/1.50 % (1170529)------------------------------
% 0.15/1.50 % (1170530)------------------------------
% 0.15/1.50 % (1170530)------------------------------
% 0.15/1.50 % (1170540)lrs+10_1_sil=8000:sp=occurrence:random_seed=519760087:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.15/1.50 % (1170540)Also succeeded, but the first one will report.
% 0.15/1.50 % (1170531)Refutation found. Thanks to Tanya!
% 0.15/1.50 % SZS status Theorem for theBenchmark
% 0.15/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.50 % (1170531)------------------------------
% 0.15/1.50 % (1170531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (1170531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (1170531)CaDiCaL version: 2.1.3
% 0.15/1.50 % (1170531)Termination reason: Refutation
% 0.15/1.50 % (1170531)Time elapsed: 0.010 s
% 0.15/1.50 % (1170531)Peak memory usage: 90 MB
% 0.15/1.50 % (1170531)Instructions burned: 11 (million)
% 0.15/1.50 % (1170531)------------------------------
% 0.15/1.50 % (1170531)------------------------------
% 0.15/1.50 % (1170521)Success in time 0.46 s
% 0.15/1.50 % Vampire exiting
%------------------------------------------------------------------------------