%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET886+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 : n020.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 12:44:55 PM UTC 2026
% Result : Theorem 0.12s 0.43s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 32 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 4 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),singleton(X2))
=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),singleton(X2))
=> unordered_pair(X0,X1) = singleton(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),singleton(X2))
=> unordered_pair(X0,X1) = singleton(X2) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f10,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ subset(unordered_pair(X0,X1),singleton(X2)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f11,plain,
? [X0,X1,X2] :
( unordered_pair(X0,X1) != singleton(X2)
& subset(unordered_pair(X0,X1),singleton(X2)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f14,plain,
( unordered_pair(sK2,sK3) != singleton(sK4)
& subset(unordered_pair(sK2,sK3),singleton(sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f11]) ).
fof(f15,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ subset(unordered_pair(X0,X1),singleton(X2)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
subset(unordered_pair(sK2,sK3),singleton(sK4)),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
unordered_pair(sK2,sK3) != singleton(sK4),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[],[f8]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),unordered_pair(X2,X2))
| X0 = X2 ),
inference(definition_unfolding,[],[f19,f22]) ).
fof(f24,plain,
unordered_pair(sK2,sK3) != unordered_pair(sK4,sK4),
inference(definition_unfolding,[],[f21,f22]) ).
fof(f25,plain,
subset(unordered_pair(sK2,sK3),unordered_pair(sK4,sK4)),
inference(definition_unfolding,[],[f20,f22]) ).
fof(f28,plain,
sK2 = sK4,
inference(resolution,[],[f23,f25]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ subset(unordered_pair(X0,X1),unordered_pair(X2,X2))
| X1 = X2 ),
inference(superposition,[],[f23,f15]) ).
fof(f32,plain,
subset(unordered_pair(sK2,sK3),unordered_pair(sK2,sK2)),
inference(superposition,[],[f25,f28]) ).
fof(f33,plain,
unordered_pair(sK2,sK3) != unordered_pair(sK2,sK2),
inference(superposition,[],[f24,f28]) ).
fof(f36,plain,
sK2 = sK3,
inference(resolution,[],[f31,f32]) ).
fof(f44,plain,
unordered_pair(sK2,sK2) != unordered_pair(sK2,sK2),
inference(superposition,[],[f33,f36]) ).
fof(f47,plain,
$false,
inference(trivial_inequality_removal,[],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET886+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 28 03:07:19 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 Running first-order model finding
% 0.12/0.39 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
% 0.12/0.43 % (3989784)Will run a generic schedule for satisfiability detection.
% 0.12/0.43 % (3989790)% WARNING: option uhcvi not known.
% 0.12/0.43 % (3989789)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=807657818_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.43 % (3989795)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=875518273:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.43 % (3989790)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3515236503:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.43 % (3989792)dis+10_1_sil=32000:sp=arity:random_seed=683819967:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.43 % (3989791)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3029361745:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.43 % (3989793)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3588449610:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.43 % (3989794)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3580158320:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.43 % TRYING [1]
% 0.12/0.43 % TRYING [2]
% 0.12/0.43 % TRYING [3]
% 0.12/0.43 % (3989795) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3989784-3989795"...
% 0.12/0.43 % (3989792) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3989784-3989792"...
% 0.12/0.43 % TRYING [4]
% 0.12/0.43 % (3989790) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3989784-3989790"...
% 0.12/0.43 % (3989793) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3989784-3989793"...
% 0.12/0.43 % (3989794) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3989784-3989794"...
% 0.12/0.43 % TRYING [5]
% 0.12/0.43 % (3989791) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3989784-3989791"...
% 0.12/0.43 % (3989795)...printing done.
% 0.12/0.43 % (3989792)...printing done.
% 0.12/0.43 % (3989790)...printing done.
% 0.12/0.43 % (3989793)...printing done.
% 0.12/0.43 % (3989794)...printing done.
% 0.12/0.43 % (3989795)Refutation found. Thanks to Tanya!
% 0.12/0.43 % SZS status Theorem for theBenchmark
% 0.12/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.43 % (3989795)------------------------------
% 0.12/0.43 % (3989795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.43 % (3989795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.43 % (3989795)CaDiCaL version: 2.1.3
% 0.12/0.43 % (3989795)Termination reason: Refutation
% 0.12/0.43 % (3989795)Time elapsed: 0.002 s
% 0.12/0.43 % (3989795)Peak memory usage: 11 MB
% 0.12/0.43 % (3989795)Instructions burned: 1 (million)
% 0.12/0.43 % (3989784)Success in time 0.033 s
% 0.12/0.43 % Vampire exiting
%------------------------------------------------------------------------------