%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET890+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 : n003.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 12:42:15 PM UTC 2026
% Result : Theorem 3.63s 1.48s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 135 ( 55 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 160 ( 57 ~; 74 |; 25 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 75 ( 65 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f10,conjecture,
! [X0] : union(singleton(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0] : union(singleton(X0)) = X0,
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f16,plain,
? [X0] : union(singleton(X0)) != X0,
inference(ennf_transformation,[],[f11]) ).
fof(f19,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,[],[f3]) ).
fof(f20,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,[],[f19]) ).
fof(f21,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))],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) ) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X2,X4)
& in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ? [X7] :
( in(X5,X7)
& in(X7,X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ( ( ! [X3] :
( ~ in(sK2(X0,X1),X3)
| ~ in(X3,X0) )
| ~ in(sK2(X0,X1),X1) )
& ( ( in(sK2(X0,X1),sK3(X0,X1))
& in(sK3(X0,X1),X0) )
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ( in(X5,sK4(X0,X5))
& in(sK4(X0,X5),X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X4,sK3(X0,X1)),skolemize(X7,sK4(X0,X5))],[f26]) ).
fof(f30,plain,
sK7 != union(singleton(sK7)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f16]) ).
fof(f35,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| union(X0) = X1
| in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X0,X1] :
( in(sK2(X0,X1),sK3(X0,X1))
| union(X0) = X1
| in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X3,X0,X1] :
( ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X3)
| ~ in(X3,X0)
| union(X0) = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f52,plain,
sK7 != union(singleton(sK7)),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f36]) ).
fof(f56,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f55]) ).
fof(f57,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f35]) ).
fof(f81,plain,
! [X0,X1] :
( sK3(singleton(X0),X1) = X0
| in(sK2(singleton(X0),X1),X1)
| union(singleton(X0)) = X1 ),
inference(resolution,[],[f45,f57]) ).
fof(f89,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| ~ in(X1,X0)
| union(X0) = X1 ),
inference(factoring,[],[f47]) ).
fof(f120,plain,
! [X0,X1] :
( in(sK2(singleton(X0),X1),X0)
| union(singleton(X0)) = X1
| in(sK2(singleton(X0),X1),X1)
| in(sK2(singleton(X0),X1),X1)
| union(singleton(X0)) = X1 ),
inference(superposition,[],[f46,f81]) ).
fof(f123,plain,
! [X0,X1] :
( in(sK2(singleton(X0),X1),X1)
| union(singleton(X0)) = X1
| in(sK2(singleton(X0),X1),X0) ),
inference(duplicate_literal_removal,[],[f120]) ).
fof(f250,plain,
! [X0,X1] :
( union(singleton(X0)) = X1
| in(sK2(singleton(X0),X1),X0)
| ~ in(X1,singleton(X0))
| union(singleton(X0)) = X1 ),
inference(resolution,[],[f123,f89]) ).
fof(f259,plain,
! [X0,X1] :
( in(sK2(singleton(X0),X1),X0)
| union(singleton(X0)) = X1
| ~ in(X1,singleton(X0)) ),
inference(duplicate_literal_removal,[],[f250]) ).
fof(f567,plain,
! [X0] :
( union(singleton(X0)) = X0
| ~ in(X0,singleton(X0))
| ~ in(X0,singleton(X0))
| union(singleton(X0)) = X0 ),
inference(resolution,[],[f259,f89]) ).
fof(f577,plain,
! [X0] :
( union(singleton(X0)) = X0
| ~ in(X0,singleton(X0)) ),
inference(duplicate_literal_removal,[],[f567]) ).
fof(f579,plain,
! [X0] : union(singleton(X0)) = X0,
inference(forward_subsumption_resolution,[],[f577,f56]) ).
fof(f647,plain,
sK7 != sK7,
inference(superposition,[],[f52,f579]) ).
fof(f683,plain,
$false,
inference(trivial_inequality_removal,[],[f647]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET890+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:08:27 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.63/1.48 % (1146142)Detected formulas, will run a generic FOF schedule.
% 3.63/1.48 % (1146149)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=2723874055:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.63/1.48 % (1146147)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=831481126:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.63/1.48 % (1146152)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4022743654:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.63/1.48 % (1146151)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3062695587:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.63/1.48 % (1146150)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2647140853:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.63/1.48 % (1146153)dis-21_1_sil=8000:lcm=predicate:random_seed=2644429395: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)
% 3.63/1.48 % (1146148)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=3110472566:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.63/1.48 % (1146150)Refutation not found, incomplete strategy
% 3.63/1.48 % (1146150)------------------------------
% 3.63/1.48 % (1146150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (1146150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (1146150)CaDiCaL version: 2.1.3
% 3.63/1.48 % (1146150)Termination reason: Refutation not found, incomplete strategy
% 3.63/1.48 % (1146150)Time elapsed: 0.001 s
% 3.63/1.48 % (1146150)Peak memory usage: 88 MB
% 3.63/1.48 % (1146150)Instructions burned: 1 (million)
% 3.63/1.48 % (1146152)First to succeed.
% 3.63/1.48 % (1146152)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1146142"
% 3.63/1.48 % (1146151)Instruction limit reached!
% 3.63/1.48 % (1146151)------------------------------
% 3.63/1.48 % (1146151)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (1146151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (1146151)CaDiCaL version: 2.1.3
% 3.63/1.48 % (1146151)Termination reason: Instruction limit
% 3.63/1.48 % (1146151)Termination phase: Saturation
% 3.63/1.48 % (1146151)Time elapsed: 0.073 s
% 3.63/1.48 % (1146151)Peak memory usage: 88 MB
% 3.63/1.48 % (1146151)Instructions burned: 119 (million)
% 3.63/1.48 % (1146153)Instruction limit reached!
% 3.63/1.48 % (1146153)------------------------------
% 3.63/1.48 % (1146153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (1146153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (1146153)CaDiCaL version: 2.1.3
% 3.63/1.48 % (1146153)Termination reason: Instruction limit
% 3.63/1.48 % (1146153)Termination phase: Saturation
% 3.63/1.48 % (1146153)Time elapsed: 0.074 s
% 3.63/1.48 % (1146153)Peak memory usage: 89 MB
% 3.63/1.48 % (1146153)Instructions burned: 129 (million)
% 3.63/1.48 % (1146161)lrs+10_1_sil=8000:sp=occurrence:random_seed=3459738149:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.63/1.48 % (1146162)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3768601155:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.63/1.48 % (1146161)Also succeeded, but the first one will report.
% 3.63/1.48 % (1146150)------------------------------
% 3.63/1.48 % (1146150)------------------------------
% 3.63/1.48 % (1146152)Refutation found. Thanks to Tanya!
% 3.63/1.48 % SZS status Theorem for theBenchmark
% 3.63/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.48 % (1146152)------------------------------
% 3.63/1.48 % (1146152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.48 % (1146152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.48 % (1146152)CaDiCaL version: 2.1.3
% 3.63/1.48 % (1146152)Termination reason: Refutation
% 3.63/1.48 % (1146152)Time elapsed: 0.031 s
% 3.63/1.48 % (1146152)Peak memory usage: 89 MB
% 3.63/1.48 % (1146152)Instructions burned: 38 (million)
% 3.63/1.48 % (1146152)------------------------------
% 3.63/1.48 % (1146152)------------------------------
% 3.63/1.48 % (1146142)Success in time 0.431 s
% 3.63/1.48 % Vampire exiting
%------------------------------------------------------------------------------