%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU209+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:52:23 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 76 ( 12 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 73 ( 29 ~; 26 |; 3 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 74 ( 68 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6,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(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f32,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t167_relat_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_inverse_image(X1,X0),relation_dom(X1)) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f45,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,plain,
? [X0,X1] :
( ~ subset(relation_inverse_image(X1,X0),relation_dom(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f64,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f69,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| in(ordered_pair(X3,sK1(X0,X1,X3)),X0)
| ~ in(X3,X2)
| relation_inverse_image(X0,X1) != X2 ),
inference(cnf_transformation,[],[f45]) ).
fof(f72,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f73,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f74,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| relation_dom(X0) != X1 ),
inference(cnf_transformation,[],[f47]) ).
fof(f78,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f101,plain,
relation(sK15),
inference(cnf_transformation,[],[f52]) ).
fof(f102,plain,
~ subset(relation_inverse_image(sK15,sK14),relation_dom(sK15)),
inference(cnf_transformation,[],[f52]) ).
fof(f113,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(X3,sK1(X0,X1,X3)),singleton(X3)),X0)
| ~ in(X3,X2)
| relation_inverse_image(X0,X1) != X2 ),
inference(definition_unfolding,[],[f69,f78]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| in(X2,X1)
| relation_dom(X0) != X1 ),
inference(definition_unfolding,[],[f74,f78]) ).
fof(f122,plain,
! [X3,X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(X3,sK1(X0,X1,X3)),singleton(X3)),X0)
| ~ in(X3,relation_inverse_image(X0,X1)) ),
inference(equality_resolution,[],[f113]) ).
fof(f125,plain,
! [X2,X3,X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| in(X2,relation_dom(X0)) ),
inference(equality_resolution,[],[f119]) ).
fof(f185,plain,
in(sK3(relation_inverse_image(sK15,sK14),relation_dom(sK15)),relation_inverse_image(sK15,sK14)),
inference(resolution,[],[f72,f102]) ).
fof(f189,plain,
~ in(sK3(relation_inverse_image(sK15,sK14),relation_dom(sK15)),relation_dom(sK15)),
inference(resolution,[],[f73,f102]) ).
fof(f247,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK15)
| in(X0,relation_dom(sK15)) ),
inference(resolution,[],[f125,f101]) ).
fof(f248,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK15)
| in(X0,relation_dom(sK15)) ),
inference(forward_demodulation,[],[f247,f64]) ).
fof(f282,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,sK1(sK15,X1,X0)),singleton(X0)),sK15)
| ~ in(X0,relation_inverse_image(sK15,X1)) ),
inference(resolution,[],[f122,f101]) ).
fof(f283,plain,
! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK1(sK15,X1,X0))),sK15)
| ~ in(X0,relation_inverse_image(sK15,X1)) ),
inference(forward_demodulation,[],[f282,f64]) ).
fof(f374,plain,
! [X0,X1] :
( ~ in(X0,relation_inverse_image(sK15,X1))
| in(X0,relation_dom(sK15)) ),
inference(resolution,[],[f283,f248]) ).
fof(f379,plain,
in(sK3(relation_inverse_image(sK15,sK14),relation_dom(sK15)),relation_dom(sK15)),
inference(resolution,[],[f374,f185]) ).
fof(f380,plain,
$false,
inference(forward_subsumption_resolution,[],[f379,f189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU209+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:03:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.47 % (3648108)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (3648114)% WARNING: option uhcvi not known.
% 0.16/0.47 % (3648114)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2655538784:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (3648113)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=375691284_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (3648116)dis+10_1_sil=32000:sp=arity:random_seed=3133993245:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (3648115)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1919191415:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (3648118)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=392250415:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (3648117)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3606568724:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (3648119)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2077243709:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (3648117) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3648108-3648117"...
% 0.16/0.47 % (3648117)...printing done.
% 0.16/0.47 % (3648117)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3648117)------------------------------
% 0.16/0.47 % (3648117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3648117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3648117)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3648117)Termination reason: Refutation
% 0.16/0.47 % (3648117)Time elapsed: 0.010 s
% 0.16/0.47 % (3648117)Peak memory usage: 12 MB
% 0.16/0.47 % (3648117)Instructions burned: 13 (million)
% 0.16/0.47 % (3648108)Success in time 0.048 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------