%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU055+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:51:51 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 20 unt; 0 def)
% Number of atoms : 195 ( 70 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 222 ( 88 ~; 92 |; 29 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 70 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f26,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f27,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
fof(f28,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ! [X1,X2] : relation_image(X0,set_difference(X1,X2)) = set_difference(relation_image(X0,X1),relation_image(X0,X2))
=> one_to_one(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_funct_1) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ! [X1,X2] : relation_image(X0,set_difference(X1,X2)) = set_difference(relation_image(X0,X1),relation_image(X0,X2))
=> one_to_one(X0) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f31,axiom,
! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
<=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
fof(f33,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f26]) ).
fof(f50,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f51,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f50]) ).
fof(f58,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f59,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1,X2] : relation_image(X0,set_difference(X1,X2)) = set_difference(relation_image(X0,X1),relation_image(X0,X2))
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f61,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1,X2] : relation_image(X0,set_difference(X1,X2)) = set_difference(relation_image(X0,X1),relation_image(X0,X2))
& relation(X0)
& function(X0) ),
inference(flattening,[],[f60]) ).
fof(f74,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f51]) ).
fof(f75,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK1(X0) != sK2(X0)
& in(sK1(X0),relation_dom(X0))
& in(sK2(X0),relation_dom(X0))
& apply(X0,sK1(X0)) = apply(X0,sK2(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f75]) ).
fof(f88,plain,
( ~ one_to_one(sK14)
& ! [X1,X2] : relation_image(sK14,set_difference(X1,X2)) = set_difference(relation_image(sK14,X1),relation_image(sK14,X2))
& relation(sK14)
& function(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f61]) ).
fof(f89,plain,
! [X0,X1] :
( ( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
| X0 = X1 )
& ( X0 != X1
| singleton(X0) != set_difference(singleton(X0),singleton(X1)) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f90,plain,
! [X0,X1] :
( ( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f103,plain,
! [X0] :
( ~ relation(X0)
| apply(X0,sK1(X0)) = apply(X0,sK2(X0))
| one_to_one(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f104,plain,
! [X0] :
( in(sK2(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f105,plain,
! [X0] :
( in(sK1(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f106,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f138,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f42]) ).
fof(f139,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f140,plain,
function(sK14),
inference(cnf_transformation,[],[f88]) ).
fof(f141,plain,
relation(sK14),
inference(cnf_transformation,[],[f88]) ).
fof(f142,plain,
! [X2,X1] : relation_image(sK14,set_difference(X1,X2)) = set_difference(relation_image(sK14,X1),relation_image(sK14,X2)),
inference(cnf_transformation,[],[f88]) ).
fof(f143,plain,
~ one_to_one(sK14),
inference(cnf_transformation,[],[f88]) ).
fof(f145,plain,
! [X0,X1] :
( X0 != X1
| singleton(X0) != set_difference(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f146,plain,
! [X0,X1] :
( singleton(X0) = set_difference(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f149,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f162,plain,
! [X1] : singleton(X1) != set_difference(singleton(X1),singleton(X1)),
inference(equality_resolution,[],[f145]) ).
fof(f259,plain,
! [X0] : empty_set = set_difference(X0,X0),
inference(resolution,[],[f149,f138]) ).
fof(f324,plain,
( apply(sK14,sK1(sK14)) = apply(sK14,sK2(sK14))
| one_to_one(sK14)
| ~ function(sK14) ),
inference(resolution,[],[f103,f141]) ).
fof(f325,plain,
( apply(sK14,sK1(sK14)) = apply(sK14,sK2(sK14))
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f324,f143]) ).
fof(f358,plain,
apply(sK14,sK1(sK14)) = apply(sK14,sK2(sK14)),
inference(forward_subsumption_resolution,[],[f325,f140]) ).
fof(f377,plain,
! [X0] :
( relation_image(X0,singleton(sK1(X0))) = singleton(apply(X0,sK1(X0)))
| ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[],[f139,f105]) ).
fof(f378,plain,
! [X0] :
( relation_image(X0,singleton(sK2(X0))) = singleton(apply(X0,sK2(X0)))
| ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[],[f139,f104]) ).
fof(f379,plain,
! [X0] :
( ~ relation(X0)
| relation_image(X0,singleton(sK2(X0))) = singleton(apply(X0,sK2(X0)))
| ~ function(X0)
| one_to_one(X0) ),
inference(duplicate_literal_removal,[],[f378]) ).
fof(f380,plain,
! [X0] :
( ~ relation(X0)
| relation_image(X0,singleton(sK1(X0))) = singleton(apply(X0,sK1(X0)))
| ~ function(X0)
| one_to_one(X0) ),
inference(duplicate_literal_removal,[],[f377]) ).
fof(f413,plain,
! [X0] : singleton(X0) != empty_set,
inference(superposition,[],[f162,f259]) ).
fof(f726,plain,
( relation_image(sK14,singleton(sK2(sK14))) = singleton(apply(sK14,sK2(sK14)))
| ~ function(sK14)
| one_to_one(sK14) ),
inference(resolution,[],[f379,f141]) ).
fof(f727,plain,
( relation_image(sK14,singleton(sK2(sK14))) = singleton(apply(sK14,sK2(sK14)))
| one_to_one(sK14) ),
inference(forward_subsumption_resolution,[],[f726,f140]) ).
fof(f732,plain,
relation_image(sK14,singleton(sK2(sK14))) = singleton(apply(sK14,sK2(sK14))),
inference(forward_subsumption_resolution,[],[f727,f143]) ).
fof(f737,plain,
relation_image(sK14,singleton(sK2(sK14))) = singleton(apply(sK14,sK1(sK14))),
inference(forward_demodulation,[],[f732,f358]) ).
fof(f749,plain,
! [X0] : relation_image(sK14,set_difference(X0,singleton(sK2(sK14)))) = set_difference(relation_image(sK14,X0),singleton(apply(sK14,sK1(sK14)))),
inference(superposition,[],[f142,f737]) ).
fof(f801,plain,
( singleton(apply(sK14,sK1(sK14))) = relation_image(sK14,singleton(sK1(sK14)))
| ~ function(sK14)
| one_to_one(sK14) ),
inference(resolution,[],[f380,f141]) ).
fof(f802,plain,
( singleton(apply(sK14,sK1(sK14))) = relation_image(sK14,singleton(sK1(sK14)))
| one_to_one(sK14) ),
inference(forward_subsumption_resolution,[],[f801,f140]) ).
fof(f807,plain,
singleton(apply(sK14,sK1(sK14))) = relation_image(sK14,singleton(sK1(sK14))),
inference(forward_subsumption_resolution,[],[f802,f143]) ).
fof(f924,plain,
set_difference(singleton(apply(sK14,sK1(sK14))),singleton(apply(sK14,sK1(sK14)))) = relation_image(sK14,set_difference(singleton(sK1(sK14)),singleton(sK2(sK14)))),
inference(superposition,[],[f749,f807]) ).
fof(f1011,plain,
empty_set = relation_image(sK14,set_difference(singleton(sK1(sK14)),singleton(sK2(sK14)))),
inference(forward_demodulation,[],[f924,f259]) ).
fof(f1035,plain,
( empty_set = relation_image(sK14,singleton(sK1(sK14)))
| sK1(sK14) = sK2(sK14) ),
inference(superposition,[],[f1011,f146]) ).
fof(f1073,plain,
( empty_set = singleton(apply(sK14,sK1(sK14)))
| sK1(sK14) = sK2(sK14) ),
inference(forward_demodulation,[],[f1035,f807]) ).
fof(f1085,plain,
sK1(sK14) = sK2(sK14),
inference(forward_subsumption_resolution,[],[f1073,f413]) ).
fof(f1111,plain,
( sK1(sK14) != sK1(sK14)
| one_to_one(sK14)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(superposition,[],[f106,f1085]) ).
fof(f1113,plain,
( one_to_one(sK14)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(trivial_inequality_removal,[],[f1111]) ).
fof(f1114,plain,
( ~ relation(sK14)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f1113,f143]) ).
fof(f1116,plain,
~ function(sK14),
inference(forward_subsumption_resolution,[],[f1114,f141]) ).
fof(f1117,plain,
$false,
inference(forward_subsumption_resolution,[],[f1116,f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU055+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % 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 03:29:42 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
% 0.17/0.46 % (1155293)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (1155301)dis+10_1_sil=32000:sp=arity:random_seed=3290012315:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (1155299)% WARNING: option uhcvi not known.
% 0.17/0.46 % (1155298)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3057872208_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.46 % (1155299)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1435986200:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.46 % (1155300)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=892847690:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.46 % (1155303)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=502437670:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.46 % (1155302)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2018207549:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.46 % (1155304)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2858826592:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.46 % TRYING [1]
% 0.17/0.46 % TRYING [2]
% 0.17/0.46 % TRYING [3]
% 0.17/0.46 % (1155301) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1155293-1155301"...
% 0.17/0.46 % (1155301)...printing done.
% 0.17/0.46 % TRYING [4]
% 0.17/0.46 % (1155301)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1155301)------------------------------
% 0.17/0.47 % (1155301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1155301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1155301)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1155301)Termination reason: Refutation
% 0.17/0.47 % (1155301)Time elapsed: 0.014 s
% 0.17/0.47 % (1155301)Peak memory usage: 12 MB
% 0.17/0.47 % (1155301)Instructions burned: 38 (million)
% 0.17/0.47 % (1155293)Success in time 0.042 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------