%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU151+2 : 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 : n015.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 12:52:07 PM UTC 2026
% Result : Theorem 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 16 unt; 0 def)
% Number of atoms : 152 ( 107 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 183 ( 72 ~; 70 |; 37 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 85 ( 76 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f10,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f39,conjecture,
! [X0,X1,X2,X3] :
~ ( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f40,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f66,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f93,plain,
? [X0,X1,X2,X3] :
( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
inference(ennf_transformation,[],[f40]) ).
fof(f120,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f121,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f121]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f130]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK3(X0,X1,X2) != X0
& sK3(X0,X1,X2) != X1 )
| ~ in(sK3(X0,X1,X2),X2) )
& ( sK3(X0,X1,X2) = X0
| sK3(X0,X1,X2) = X1
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f131]) ).
fof(f155,plain,
( unordered_pair(sK10,sK11) = unordered_pair(sK12,sK13)
& sK10 != sK12
& sK10 != sK13 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f93]) ).
fof(f170,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f122]) ).
fof(f180,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f132]) ).
fof(f181,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f132]) ).
fof(f182,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f132]) ).
fof(f229,plain,
sK10 != sK13,
inference(cnf_transformation,[],[f155]) ).
fof(f230,plain,
sK10 != sK12,
inference(cnf_transformation,[],[f155]) ).
fof(f231,plain,
unordered_pair(sK10,sK11) = unordered_pair(sK12,sK13),
inference(cnf_transformation,[],[f155]) ).
fof(f262,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f66]) ).
fof(f277,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f170,f262]) ).
fof(f309,plain,
! [X3,X0] :
( ~ in(X3,unordered_pair(X0,X0))
| X0 = X3 ),
inference(equality_resolution,[],[f277]) ).
fof(f313,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f182]) ).
fof(f314,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f313]) ).
fof(f315,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f181]) ).
fof(f316,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f315]) ).
fof(f317,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f180]) ).
fof(f338,plain,
in(sK12,unordered_pair(sK10,sK11)),
inference(superposition,[],[f314,f231]) ).
fof(f341,plain,
in(sK13,unordered_pair(sK10,sK11)),
inference(superposition,[],[f316,f231]) ).
fof(f850,plain,
( sK11 = sK12
| sK10 = sK12 ),
inference(resolution,[],[f317,f338]) ).
fof(f851,plain,
( sK11 = sK13
| sK10 = sK13 ),
inference(resolution,[],[f317,f341]) ).
fof(f862,plain,
sK11 = sK13,
inference(forward_subsumption_resolution,[],[f851,f229]) ).
fof(f863,plain,
sK11 = sK12,
inference(forward_subsumption_resolution,[],[f850,f230]) ).
fof(f867,plain,
sK10 != sK11,
inference(superposition,[],[f229,f862]) ).
fof(f884,plain,
unordered_pair(sK10,sK11) = unordered_pair(sK11,sK13),
inference(superposition,[],[f231,f863]) ).
fof(f886,plain,
unordered_pair(sK10,sK11) = unordered_pair(sK11,sK11),
inference(forward_demodulation,[],[f884,f862]) ).
fof(f966,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK10,sK11))
| sK11 = X0 ),
inference(superposition,[],[f309,f886]) ).
fof(f1300,plain,
sK10 = sK11,
inference(resolution,[],[f966,f314]) ).
fof(f1318,plain,
$false,
inference(forward_subsumption_resolution,[],[f1300,f867]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU151+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n015.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:49:16 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.18/0.50 % (2239764)Will run a generic schedule for satisfiability detection.
% 0.18/0.50 % (2239774)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=488417418:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.50 % (2239770)% WARNING: option uhcvi not known.
% 0.18/0.50 % (2239770)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1180112861:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.50 % (2239769)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2373651329_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.50 % (2239771)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1528502164:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.50 % (2239772)dis+10_1_sil=32000:sp=arity:random_seed=2127289863:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.50 % (2239773)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1955053757:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.50 % (2239775)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1671415369:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.50 % TRYING [1]
% 0.18/0.50 % TRYING [2]
% 0.18/0.50 % TRYING [3]
% 0.18/0.50 % TRYING [4]
% 0.18/0.50 % (2239772) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2239764-2239772"...
% 0.18/0.50 % (2239770) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2239764-2239770"...
% 0.18/0.50 % (2239772)...printing done.
% 0.18/0.50 % (2239772)Refutation found. Thanks to Tanya!
% 0.18/0.50 % SZS status Theorem for theBenchmark
% 0.18/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50 % (2239772)------------------------------
% 0.18/0.50 % (2239772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.50 % (2239772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.50 % (2239772)CaDiCaL version: 2.1.3
% 0.18/0.50 % (2239772)Termination reason: Refutation
% 0.18/0.50 % (2239772)Time elapsed: 0.029 s
% 0.18/0.50 % (2239772)Peak memory usage: 12 MB
% 0.18/0.50 % (2239772)Instructions burned: 43 (million)
% 0.18/0.50 % (2239764)Success in time 0.065 s
% 0.18/0.50 % Vampire exiting
%------------------------------------------------------------------------------