%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 12:44:57 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 50 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 44 ( 16 ~; 11 |; 13 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 29 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f10,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X0,X2)
& in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( in(X0,X1)
& in(X2,X1) )
=> set_union2(unordered_pair(X0,X2),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_zfmisc_1) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( in(X0,X1)
& in(X2,X1) )
=> set_union2(unordered_pair(X0,X2),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f20,plain,
? [X0,X1,X2] :
( set_union2(unordered_pair(X0,X2),X1) != X1
& in(X0,X1)
& in(X2,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f21,plain,
? [X0,X1,X2] :
( set_union2(unordered_pair(X0,X2),X1) != X1
& in(X0,X1)
& in(X2,X1) ),
inference(flattening,[],[f20]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X0,X2)
| ~ in(X1,X2) )
& ( ( in(X0,X2)
& in(X1,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
( sK3 != set_union2(unordered_pair(sK2,sK4),sK3)
& in(sK2,sK3)
& in(sK4,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f21]) ).
fof(f28,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ in(X0,X2)
| subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f40,plain,
in(sK4,sK3),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
in(sK2,sK3),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
sK3 != set_union2(unordered_pair(sK2,sK4),sK3),
inference(cnf_transformation,[],[f26]) ).
fof(f63,plain,
! [X0] :
( ~ in(X0,sK3)
| subset(unordered_pair(sK4,X0),sK3) ),
inference(resolution,[],[f39,f40]) ).
fof(f67,plain,
subset(unordered_pair(sK4,sK2),sK3),
inference(resolution,[],[f63,f41]) ).
fof(f68,plain,
subset(unordered_pair(sK2,sK4),sK3),
inference(forward_demodulation,[],[f67,f28]) ).
fof(f81,plain,
sK3 = set_union2(unordered_pair(sK2,sK4),sK3),
inference(resolution,[],[f68,f36]) ).
fof(f82,plain,
$false,
inference(forward_subsumption_resolution,[],[f81,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET907+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n018.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
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:11:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.45 % (2957218)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (2957223)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1501711701_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % TRYING [1]
% 0.11/0.45 % TRYING [2]
% 0.11/0.45 % TRYING [3]
% 0.11/0.45 % TRYING [4]
% 0.11/0.45 % TRYING [5]
% 0.11/0.45 % TRYING [6]
% 0.11/0.45 % (2957224)% WARNING: option uhcvi not known.
% 0.11/0.45 % (2957225)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3255931512:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (2957228)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1397786529:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (2957226)dis+10_1_sil=32000:sp=arity:random_seed=1751090892:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (2957227)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1953002106:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (2957229)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2489309126:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % TRYING [7]
% 0.11/0.45 % (2957224)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3583143938:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % (2957228) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2957218-2957228"...
% 0.11/0.45 % (2957226) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2957218-2957226"...
% 0.11/0.45 % (2957227) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2957218-2957227"...
% 0.11/0.45 % (2957229) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2957218-2957229"...
% 0.11/0.45 % (2957224) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2957218-2957224"...
% 0.11/0.45 % (2957228)...printing done.
% 0.11/0.45 % (2957225) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2957218-2957225"...
% 0.11/0.45 % (2957226)...printing done.
% 0.11/0.45 % (2957227)...printing done.
% 0.11/0.45 % (2957229)...printing done.
% 0.11/0.45 % (2957228)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (2957228)------------------------------
% 0.11/0.45 % (2957228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (2957228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (2957228)CaDiCaL version: 2.1.3
% 0.11/0.45 % (2957228)Termination reason: Refutation
% 0.11/0.45 % (2957228)Time elapsed: 0.003 s
% 0.11/0.45 % (2957228)Peak memory usage: 11 MB
% 0.11/0.45 % (2957228)Instructions burned: 2 (million)
% 0.11/0.45 % (2957218)Success in time 0.035 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------