%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 1.51s 0.66s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 99 ( 65 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 89 ( 29 ~; 55 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 70 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f9,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11,conjecture,
! [X0] : powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0] : powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0)),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f9]) ).
fof(f16,plain,
? [X0] : powerset(singleton(X0)) != unordered_pair(empty_set,singleton(X0)),
inference(ennf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0,X1] :
( subset(sK0(X0,X1),X0)
| in(sK0(X0,X1),X1)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1] :
( ~ subset(sK0(X0,X1),X0)
| ~ in(sK0(X0,X1),X1)
| powerset(X0) = X1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| X0 = X3
| ~ in(X3,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| in(X3,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( X0 != X3
| in(X3,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| empty_set = X0
| singleton(X1) = X0 ),
inference(cnf_transformation,[],[f6]) ).
fof(f32,plain,
! [X0,X1] :
( empty_set != X0
| subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f6]) ).
fof(f35,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f38,plain,
powerset(singleton(sK5)) != unordered_pair(empty_set,singleton(sK5)),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
! [X2,X3,X1] :
( in(X3,X2)
| unordered_pair(X3,X1) != X2 ),
inference(equality_resolution,[],[f28]) ).
fof(f42,plain,
! [X3,X1] : in(X3,unordered_pair(X3,X1)),
inference(equality_resolution,[],[f41]) ).
fof(f43,plain,
! [X2,X3,X0] :
( in(X3,X2)
| unordered_pair(X0,X3) != X2 ),
inference(equality_resolution,[],[f27]) ).
fof(f44,plain,
! [X3,X0] : in(X3,unordered_pair(X0,X3)),
inference(equality_resolution,[],[f43]) ).
fof(f45,plain,
! [X3,X0,X1] :
( ~ in(X3,unordered_pair(X0,X1))
| X0 = X3
| X1 = X3 ),
inference(equality_resolution,[],[f26]) ).
fof(f46,plain,
! [X1] : subset(empty_set,singleton(X1)),
inference(equality_resolution,[],[f32]) ).
fof(f88,plain,
! [X0,X1] :
( in(sK0(singleton(X0),X1),X1)
| powerset(singleton(X0)) = X1
| empty_set = sK0(singleton(X0),X1)
| singleton(X0) = sK0(singleton(X0),X1) ),
inference(resolution,[],[f21,f30]) ).
fof(f128,plain,
! [X2,X0,X1] :
( singleton(X0) = sK0(singleton(X0),unordered_pair(X1,X2))
| sK0(singleton(X0),unordered_pair(X1,X2)) = X1
| sK0(singleton(X0),unordered_pair(X1,X2)) = X2
| empty_set = sK0(singleton(X0),unordered_pair(X1,X2))
| powerset(singleton(X0)) = unordered_pair(X1,X2) ),
inference(resolution,[],[f88,f45]) ).
fof(f2288,plain,
! [X2,X0,X1] :
( empty_set != X1
| singleton(X0) = sK0(singleton(X0),unordered_pair(X1,X2))
| sK0(singleton(X0),unordered_pair(X1,X2)) = X2
| empty_set = sK0(singleton(X0),unordered_pair(X1,X2))
| powerset(singleton(X0)) = unordered_pair(X1,X2) ),
inference(equality_factoring,[],[f128]) ).
fof(f2495,plain,
! [X0,X1] :
( singleton(X0) = sK0(singleton(X0),unordered_pair(empty_set,X1))
| sK0(singleton(X0),unordered_pair(empty_set,X1)) = X1
| empty_set = sK0(singleton(X0),unordered_pair(empty_set,X1))
| powerset(singleton(X0)) = unordered_pair(empty_set,X1) ),
inference(equality_resolution,[],[f2288]) ).
fof(f2537,plain,
! [X0,X1] :
( singleton(X0) != X1
| sK0(singleton(X0),unordered_pair(empty_set,X1)) = X1
| empty_set = sK0(singleton(X0),unordered_pair(empty_set,X1))
| powerset(singleton(X0)) = unordered_pair(empty_set,X1) ),
inference(equality_factoring,[],[f2495]) ).
fof(f2564,plain,
! [X0] :
( singleton(X0) = sK0(singleton(X0),unordered_pair(empty_set,singleton(X0)))
| empty_set = sK0(singleton(X0),unordered_pair(empty_set,singleton(X0)))
| powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0)) ),
inference(equality_resolution,[],[f2537]) ).
fof(f2570,plain,
! [X0] :
( ~ subset(singleton(X0),singleton(X0))
| ~ in(singleton(X0),unordered_pair(empty_set,singleton(X0)))
| powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0))
| empty_set = sK0(singleton(X0),unordered_pair(empty_set,singleton(X0)))
| powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0)) ),
inference(superposition,[],[f22,f2564]) ).
fof(f2576,plain,
! [X0] :
( ~ subset(singleton(X0),singleton(X0))
| ~ in(singleton(X0),unordered_pair(empty_set,singleton(X0)))
| powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0))
| empty_set = sK0(singleton(X0),unordered_pair(empty_set,singleton(X0))) ),
inference(duplicate_literal_removal,[],[f2570]) ).
fof(f2581,plain,
! [X0] :
( ~ in(singleton(X0),unordered_pair(empty_set,singleton(X0)))
| powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0))
| empty_set = sK0(singleton(X0),unordered_pair(empty_set,singleton(X0))) ),
inference(forward_subsumption_resolution,[],[f2576,f35]) ).
fof(f2582,plain,
! [X0] :
( empty_set = sK0(singleton(X0),unordered_pair(empty_set,singleton(X0)))
| powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0)) ),
inference(forward_subsumption_resolution,[],[f2581,f44]) ).
fof(f2595,plain,
! [X0] :
( ~ subset(empty_set,singleton(X0))
| ~ in(empty_set,unordered_pair(empty_set,singleton(X0)))
| powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0))
| powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0)) ),
inference(superposition,[],[f22,f2582]) ).
fof(f2600,plain,
! [X0] :
( ~ subset(empty_set,singleton(X0))
| ~ in(empty_set,unordered_pair(empty_set,singleton(X0)))
| powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0)) ),
inference(duplicate_literal_removal,[],[f2595]) ).
fof(f2613,plain,
! [X0] :
( ~ in(empty_set,unordered_pair(empty_set,singleton(X0)))
| powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0)) ),
inference(forward_subsumption_resolution,[],[f2600,f46]) ).
fof(f2618,plain,
! [X0] : powerset(singleton(X0)) = unordered_pair(empty_set,singleton(X0)),
inference(forward_subsumption_resolution,[],[f2613,f42]) ).
fof(f2619,plain,
powerset(singleton(sK5)) != powerset(singleton(sK5)),
inference(superposition,[],[f38,f2618]) ).
fof(f2704,plain,
$false,
inference(trivial_inequality_removal,[],[f2619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n008.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 03:07:25 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 1.51/0.66 % (1828832)Will run a generic schedule for satisfiability detection.
% 1.51/0.66 % (1828842)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3132435331:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.51/0.66 % (1828837)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4155341980_2999 on theBenchmark for (2999ds/0Mi)
% 1.51/0.66 % (1828839)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2750522393:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.51/0.66 % (1828840)dis+10_1_sil=32000:sp=arity:random_seed=2876173616:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.51/0.66 % (1828841)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=807758852:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.51/0.66 % (1828843)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=48727672:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.51/0.66 % TRYING [1]
% 1.51/0.66 % TRYING [2]
% 1.51/0.66 % TRYING [3]
% 1.51/0.66 % TRYING [4]
% 1.51/0.66 % (1828838)% WARNING: option uhcvi not known.
% 1.51/0.66 % TRYING [5]
% 1.51/0.66 % (1828838)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=652713233:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.51/0.66 % TRYING [6]
% 1.51/0.66 % (1828842)Instruction limit reached!
% 1.51/0.66 % (1828842)------------------------------
% 1.51/0.66 % (1828842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.66 % (1828842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.66 % (1828842)CaDiCaL version: 2.1.3
% 1.51/0.66 % (1828842)Termination reason: Instruction limit
% 1.51/0.66 % (1828842)Termination phase: Saturation
% 1.51/0.66 % (1828842)Time elapsed: 0.035 s
% 1.51/0.66 % (1828842)Peak memory usage: 12 MB
% 1.51/0.66 % (1828842)Instructions burned: 133 (million)
% 1.51/0.66 % TRYING [7]
% 1.51/0.66 % (1828851)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3179327513:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.51/0.66 % TRYING [1]
% 1.51/0.66 % TRYING [2]
% 1.51/0.66 % TRYING [3]
% 1.51/0.66 % TRYING [4]
% 1.51/0.66 % TRYING [5]
% 1.51/0.66 % TRYING [6]
% 1.51/0.66 % (1828840)Instruction limit reached!
% 1.51/0.66 % (1828840)------------------------------
% 1.51/0.66 % (1828840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.66 % (1828840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.66 % (1828840)CaDiCaL version: 2.1.3
% 1.51/0.66 % (1828840)Termination reason: Instruction limit
% 1.51/0.66 % (1828840)Termination phase: Saturation
% 1.51/0.66 % (1828840)Time elapsed: 0.056 s
% 1.51/0.66 % (1828840)Peak memory usage: 11 MB
% 1.51/0.66 % (1828840)Instructions burned: 104 (million)
% 1.51/0.66 % (1828841)Instruction limit reached!
% 1.51/0.66 % (1828841)------------------------------
% 1.51/0.66 % (1828841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.66 % (1828841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.66 % (1828841)CaDiCaL version: 2.1.3
% 1.51/0.66 % (1828841)Termination reason: Instruction limit
% 1.51/0.66 % (1828841)Termination phase: Saturation
% 1.51/0.66 % (1828841)Time elapsed: 0.057 s
% 1.51/0.66 % (1828841)Peak memory usage: 11 MB
% 1.51/0.66 % (1828841)Instructions burned: 116 (million)
% 1.51/0.66 % TRYING [8]
% 1.51/0.66 % TRYING [7]
% 1.51/0.66 % (1828853)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2774146886:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.51/0.66 % (1828854)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4133918613:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.51/0.66 % (1828843)Instruction limit reached!
% 1.51/0.66 % (1828843)------------------------------
% 1.51/0.66 % (1828843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.66 % (1828843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.66 % (1828843)CaDiCaL version: 2.1.3
% 1.51/0.66 % (1828843)Termination reason: Instruction limit
% 1.51/0.66 % (1828843)Termination phase: Saturation
% 1.51/0.66 % (1828843)Time elapsed: 0.085 s
% 1.51/0.66 % (1828843)Peak memory usage: 12 MB
% 1.51/0.66 % (1828843)Instructions burned: 160 (million)
% 1.51/0.66 % TRYING [8]
% 1.51/0.66 % (1828857)ott-21_1_sil=16000:fs=off:random_seed=2395295329:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.51/0.66 % (1828853)Instruction limit reached!
% 1.51/0.66 % (1828853)------------------------------
% 1.51/0.66 % (1828853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.66 % (1828853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.66 % (1828853)CaDiCaL version: 2.1.3
% 1.51/0.66 % (1828853)Termination reason: Instruction limit
% 1.51/0.66 % (1828853)Termination phase: Saturation
% 1.51/0.66 % (1828853)Time elapsed: 0.070 s
% 1.51/0.66 % (1828853)Peak memory usage: 12 MB
% 1.51/0.66 % (1828853)Instructions burned: 133 (million)
% 1.51/0.66 % TRYING [9]
% 1.51/0.66 % (1828859)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=936031520:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.51/0.66 % TRYING [9]
% 1.51/0.66 % (1828857)Instruction limit reached!
% 1.51/0.66 % (1828857)------------------------------
% 1.51/0.66 % (1828857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.66 % (1828857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.66 % (1828857)CaDiCaL version: 2.1.3
% 1.51/0.66 % (1828857)Termination reason: Instruction limit
% 1.51/0.66 % (1828857)Termination phase: Saturation
% 1.51/0.66 % (1828857)Time elapsed: 0.087 s
% 1.51/0.66 % (1828857)Peak memory usage: 12 MB
% 1.51/0.66 % (1828857)Instructions burned: 182 (million)
% 1.51/0.66 % (1828851)Instruction limit reached!
% 1.51/0.66 % (1828851)------------------------------
% 1.51/0.66 % (1828851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.66 % (1828851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.66 % (1828851)CaDiCaL version: 2.1.3
% 1.51/0.66 % (1828851)Termination reason: Instruction limit
% 1.51/0.66 % (1828851)Termination phase: Finite model building constraint generation
% 1.51/0.66 % (1828851)Time elapsed: 0.160 s
% 1.51/0.66 % (1828851)Peak memory usage: 24 MB
% 1.51/0.66 % (1828851)Instructions burned: 719 (million)
% 1.51/0.66 % (1828854) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1828832-1828854"...
% 1.51/0.66 % (1828854)...printing done.
% 1.51/0.66 % (1828854)Refutation found. Thanks to Tanya!
% 1.51/0.66 % SZS status Theorem for theBenchmark
% 1.51/0.66 % SZS output start Proof for theBenchmark
% See solution above
% 1.51/0.66 % (1828854)------------------------------
% 1.51/0.66 % (1828854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.66 % (1828854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.66 % (1828854)CaDiCaL version: 2.1.3
% 1.51/0.66 % (1828854)Termination reason: Refutation
% 1.51/0.66 % (1828854)Time elapsed: 0.130 s
% 1.51/0.66 % (1828854)Peak memory usage: 13 MB
% 1.51/0.66 % (1828854)Instructions burned: 261 (million)
% 1.51/0.66 % (1828832)Success in time 0.242 s
% 1.51/0.66 % Vampire exiting
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