%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU127+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:47:19 PM UTC 2026
% Result : Theorem 2.69s 1.31s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 104 ( 10 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 128 ( 47 ~; 49 |; 27 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 64 ( 57 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f23,conjecture,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f24,negated_conjecture,
~ ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f43,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f48,plain,
? [X0,X1] : ~ subset(set_intersection2(X0,X1),X0),
inference(ennf_transformation,[],[f24]) ).
fof(f68,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f69,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X1) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f73]) ).
fof(f78,plain,
~ subset(set_intersection2(sK6,sK7),sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f48]) ).
fof(f96,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f97,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f99,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f74]) ).
fof(f116,plain,
~ subset(set_intersection2(sK6,sK7),sK6),
inference(cnf_transformation,[],[f78]) ).
fof(f139,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f99]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ in(sK2(X0,X1),set_intersection2(X1,X2))
| subset(X0,X1) ),
inference(resolution,[],[f139,f97]) ).
fof(f540,plain,
! [X0,X1] :
( subset(set_intersection2(X0,X1),X0)
| subset(set_intersection2(X0,X1),X0) ),
inference(resolution,[],[f168,f96]) ).
fof(f549,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(duplicate_literal_removal,[],[f540]) ).
fof(f677,plain,
$false,
inference(resolution,[],[f549,f116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU127+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n016.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 03:43:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.69/1.31 % (3237220)Detected formulas, will run a generic FOF schedule.
% 2.69/1.31 % (3237230)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2094856039:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.31 % (3237230)First to succeed.
% 2.69/1.31 % (3237230)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3237220"
% 2.69/1.31 % (3237231)dis-21_1_sil=8000:lcm=predicate:random_seed=2105300476: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)
% 2.69/1.31 % (3237231)Also succeeded, but the first one will report.
% 2.69/1.31 % (3237225)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=4238494033:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.31 % (3237229)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2617141526:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.31 % (3237228)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=716914711:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.31 % (3237226)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=2760782774:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.31 % (3237227)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=470985802:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.31 % (3237228)Instruction limit reached!
% 2.69/1.31 % (3237228)------------------------------
% 2.69/1.31 % (3237228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.31 % (3237228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.31 % (3237228)CaDiCaL version: 2.1.3
% 2.69/1.31 % (3237228)Termination reason: Instruction limit
% 2.69/1.31 % (3237228)Termination phase: Saturation
% 2.69/1.31 % (3237228)Time elapsed: 0.065 s
% 2.69/1.31 % (3237228)Peak memory usage: 89 MB
% 2.69/1.31 % (3237228)Instructions burned: 110 (million)
% 2.69/1.31 % (3237229)Also succeeded, but the first one will report.
% 2.69/1.31 % (3237230)Refutation found. Thanks to Tanya!
% 2.69/1.31 % SZS status Theorem for theBenchmark
% 2.69/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.31 % (3237230)------------------------------
% 2.69/1.31 % (3237230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.31 % (3237230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.31 % (3237230)CaDiCaL version: 2.1.3
% 2.69/1.31 % (3237230)Termination reason: Refutation
% 2.69/1.31 % (3237230)Time elapsed: 0.031 s
% 2.69/1.31 % (3237230)Peak memory usage: 89 MB
% 2.69/1.31 % (3237230)Instructions burned: 130 (million)
% 2.69/1.31 % (3237230)------------------------------
% 2.69/1.31 % (3237230)------------------------------
% 2.69/1.31 % (3237220)Success in time 0.295 s
% 2.69/1.31 % Vampire exiting
%------------------------------------------------------------------------------