%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:42:16 PM UTC 2026
% Result : Theorem 3.37s 1.34s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 20 unt; 0 def)
% Number of atoms : 96 ( 84 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 101 ( 46 ~; 32 |; 22 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f6,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1,X2] :
~ ( singleton(X0) = set_union2(X1,X2)
& ~ ( X1 = singleton(X0)
& X2 = singleton(X0) )
& ~ ( X1 = empty_set
& X2 = singleton(X0) )
& ~ ( X1 = singleton(X0)
& X2 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( singleton(X0) = set_union2(X1,X2)
& ~ ( X1 = singleton(X0)
& X2 = singleton(X0) )
& ~ ( X1 = empty_set
& X2 = singleton(X0) )
& ~ ( X1 = singleton(X0)
& X2 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f14,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f5]) ).
fof(f16,plain,
? [X0,X1,X2] :
( singleton(X0) = set_union2(X1,X2)
& ( singleton(X0) != X1
| singleton(X0) != X2 )
& ( empty_set != X1
| singleton(X0) != X2 )
& ( singleton(X0) != X1
| empty_set != X2 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
( singleton(sK0) = set_union2(sK1,sK2)
& ( sK1 != singleton(sK0)
| sK2 != singleton(sK0) )
& ( empty_set != sK1
| sK2 != singleton(sK0) )
& ( sK1 != singleton(sK0)
| empty_set != sK2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f21,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f20]) ).
fof(f24,plain,
( sK1 != singleton(sK0)
| empty_set != sK2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f25,plain,
( sK2 != singleton(sK0)
| empty_set != sK1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f26,plain,
( sK2 != singleton(sK0)
| sK1 != singleton(sK0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
singleton(sK0) = set_union2(sK1,sK2),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f21]) ).
fof(f34,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f6]) ).
fof(f39,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f13]) ).
fof(f43,plain,
subset(sK1,singleton(sK0)),
inference(superposition,[],[f39,f27]) ).
fof(f51,plain,
! [X0,X1] : subset(X1,set_union2(X0,X1)),
inference(superposition,[],[f39,f29]) ).
fof(f55,plain,
subset(sK2,singleton(sK0)),
inference(superposition,[],[f51,f27]) ).
fof(f61,plain,
( sK1 = singleton(sK0)
| empty_set = sK1 ),
inference(resolution,[],[f31,f43]) ).
fof(f62,plain,
( sK2 = singleton(sK0)
| empty_set = sK2 ),
inference(resolution,[],[f31,f55]) ).
fof(f63,plain,
( sK1 != sK1
| empty_set != sK2
| empty_set = sK1 ),
inference(superposition,[],[f24,f61]) ).
fof(f65,plain,
( sK1 != sK2
| sK1 != sK1
| empty_set = sK1 ),
inference(superposition,[],[f26,f61]) ).
fof(f73,plain,
( sK1 != sK2
| empty_set = sK1 ),
inference(trivial_inequality_removal,[],[f65]) ).
fof(f74,plain,
( empty_set != sK2
| empty_set = sK1 ),
inference(trivial_inequality_removal,[],[f63]) ).
fof(f77,plain,
( sK2 != sK2
| empty_set != sK1
| empty_set = sK2 ),
inference(superposition,[],[f25,f62]) ).
fof(f83,plain,
( sK1 = sK2
| empty_set = sK1
| empty_set = sK2 ),
inference(superposition,[],[f61,f62]) ).
fof(f88,plain,
( empty_set != sK1
| empty_set = sK2 ),
inference(trivial_inequality_removal,[],[f77]) ).
fof(f89,plain,
( empty_set = sK1
| empty_set = sK2 ),
inference(forward_subsumption_resolution,[],[f83,f73]) ).
fof(f91,plain,
empty_set = sK1,
inference(forward_subsumption_resolution,[],[f89,f74]) ).
fof(f103,plain,
empty_set = sK2,
inference(forward_subsumption_resolution,[],[f88,f91]) ).
fof(f104,plain,
sK1 = sK2,
inference(forward_demodulation,[],[f103,f91]) ).
fof(f108,plain,
singleton(sK0) = set_union2(sK1,sK1),
inference(superposition,[],[f27,f104]) ).
fof(f110,plain,
sK1 = singleton(sK0),
inference(forward_demodulation,[],[f108,f28]) ).
fof(f123,plain,
empty_set != sK1,
inference(superposition,[],[f34,f110]) ).
fof(f126,plain,
$false,
inference(forward_subsumption_resolution,[],[f123,f91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n008.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 03:08:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.37/1.34 % (1830500)Detected formulas, will run a generic FOF schedule.
% 3.37/1.34 % (1830506)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1731651107:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.37/1.34 % (1830510)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4248671374:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.37/1.34 % (1830509)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1897352416:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.37/1.34 % (1830505)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=827232363:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.37/1.34 % (1830508)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1049941527:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.37/1.34 % (1830511)dis-21_1_sil=8000:lcm=predicate:random_seed=528850869:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.37/1.34 % (1830507)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3975629800:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.37/1.34 % (1830508)Refutation not found, incomplete strategy
% 3.37/1.34 % (1830508)------------------------------
% 3.37/1.34 % (1830508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.34 % (1830508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.34 % (1830511)Refutation not found, incomplete strategy
% 3.37/1.34 % (1830511)------------------------------
% 3.37/1.34 % (1830511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.34 % (1830508)CaDiCaL version: 2.1.3
% 3.37/1.34 % (1830508)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.34 % (1830508)Time elapsed: 0.001 s
% 3.37/1.34 % (1830508)Peak memory usage: 88 MB
% 3.37/1.34 % (1830511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.34 % (1830508)Instructions burned: 1 (million)
% 3.37/1.34 % (1830511)CaDiCaL version: 2.1.3
% 3.37/1.34 % (1830511)Termination reason: Refutation not found, incomplete strategy
% 3.37/1.34 % (1830511)Time elapsed: 0.002 s
% 3.37/1.34 % (1830511)Peak memory usage: 88 MB
% 3.37/1.34 % (1830511)Instructions burned: 1 (million)
% 3.37/1.34 % (1830509)First to succeed.
% 3.37/1.34 % (1830510)Also succeeded, but the first one will report.
% 3.37/1.34 % (1830509)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1830500"
% 3.37/1.34 % (1830508)------------------------------
% 3.37/1.34 % (1830508)------------------------------
% 3.37/1.34 % (1830511)------------------------------
% 3.37/1.34 % (1830511)------------------------------
% 3.37/1.34 % (1830509)Refutation found. Thanks to Tanya!
% 3.37/1.34 % SZS status Theorem for theBenchmark
% 3.37/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.34 % (1830509)------------------------------
% 3.37/1.34 % (1830509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.34 % (1830509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.34 % (1830509)CaDiCaL version: 2.1.3
% 3.37/1.34 % (1830509)Termination reason: Refutation
% 3.37/1.34 % (1830509)Time elapsed: 0.004 s
% 3.37/1.34 % (1830509)Peak memory usage: 88 MB
% 3.37/1.34 % (1830509)Instructions burned: 4 (million)
% 3.37/1.34 % (1830509)------------------------------
% 3.37/1.34 % (1830509)------------------------------
% 3.37/1.34 % (1830500)Success in time 0.406 s
% 3.37/1.34 % Vampire exiting
%------------------------------------------------------------------------------