%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET945+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 : n011.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 12:42:23 PM UTC 2026
% Result : Theorem 2.73s 1.36s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 13 unt; 0 def)
% Number of atoms : 184 ( 23 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 230 ( 91 ~; 84 |; 47 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 119 ( 104 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f4,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(f9,axiom,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X2] : in(X2,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f10,conjecture,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> disjoint(X2,X1) )
=> disjoint(union(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> disjoint(X2,X1) )
=> disjoint(union(X0),X1) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X0,X1))
& disjoint(X0,X1) ) ),
inference(rectify,[],[f9]) ).
fof(f16,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
? [X0,X1] :
( ~ disjoint(union(X0),X1)
& ! [X2] :
( disjoint(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f18,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,[],[f3]) ).
fof(f19,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,[],[f18]) ).
fof(f20,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,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),X0)
& in(sK0(X0,X1,X2),X1) )
| in(sK0(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,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f20]) ).
fof(f22,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,[],[f4]) ).
fof(f23,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,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ( ( ! [X3] :
( ~ in(sK1(X0,X1),X3)
| ~ in(X3,X0) )
| ~ in(sK1(X0,X1),X1) )
& ( ( in(sK1(X0,X1),sK2(X0,X1))
& in(sK2(X0,X1),X0) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ( in(X5,sK3(X0,X5))
& in(sK3(X0,X5),X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| in(sK6(X0,X1),set_intersection2(X0,X1)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f16]) ).
fof(f28,plain,
( ~ disjoint(union(sK7),sK8)
& ! [X2] :
( disjoint(X2,sK8)
| ~ in(X2,sK7) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f17]) ).
fof(f30,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f31,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f32,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
! [X0,X1,X5] :
( in(sK3(X0,X5),X0)
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
! [X0,X1,X5] :
( in(X5,sK3(X0,X5))
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f47,plain,
! [X3,X0,X1] :
( ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sK6(X0,X1),set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X2] :
( ~ in(X2,sK7)
| disjoint(X2,sK8) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
~ disjoint(union(sK7),sK8),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f33]) ).
fof(f52,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f32]) ).
fof(f53,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f31]) ).
fof(f55,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(X5,sK3(X0,X5)) ),
inference(equality_resolution,[],[f38]) ).
fof(f56,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK3(X0,X5),X0) ),
inference(equality_resolution,[],[f37]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X0)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(superposition,[],[f47,f30]) ).
fof(f67,plain,
in(sK6(union(sK7),sK8),set_intersection2(union(sK7),sK8)),
inference(resolution,[],[f48,f50]) ).
fof(f72,plain,
in(sK6(union(sK7),sK8),set_intersection2(sK8,union(sK7))),
inference(forward_demodulation,[],[f67,f30]) ).
fof(f73,plain,
in(sK6(union(sK7),sK8),union(sK7)),
inference(resolution,[],[f72,f53]) ).
fof(f74,plain,
in(sK6(union(sK7),sK8),sK8),
inference(resolution,[],[f72,f52]) ).
fof(f83,plain,
! [X0] :
( ~ in(sK6(union(sK7),sK8),X0)
| in(sK6(union(sK7),sK8),set_intersection2(sK8,X0)) ),
inference(resolution,[],[f74,f51]) ).
fof(f98,plain,
in(sK3(sK7,sK6(union(sK7),sK8)),sK7),
inference(resolution,[],[f73,f56]) ).
fof(f99,plain,
in(sK6(union(sK7),sK8),sK3(sK7,sK6(union(sK7),sK8))),
inference(resolution,[],[f73,f55]) ).
fof(f121,plain,
disjoint(sK3(sK7,sK6(union(sK7),sK8)),sK8),
inference(resolution,[],[f98,f49]) ).
fof(f127,plain,
! [X0] : ~ in(X0,set_intersection2(sK8,sK3(sK7,sK6(union(sK7),sK8)))),
inference(resolution,[],[f121,f63]) ).
fof(f449,plain,
in(sK6(union(sK7),sK8),set_intersection2(sK8,sK3(sK7,sK6(union(sK7),sK8)))),
inference(resolution,[],[f83,f99]) ).
fof(f452,plain,
$false,
inference(forward_subsumption_resolution,[],[f449,f127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET945+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n011.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Mon Sep 28 03:16:01 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 2.73/1.36 % (2982928)Detected formulas, will run a generic FOF schedule.
% 2.73/1.36 % (2983042)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1281237824:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/1.36 % (2983042)First to succeed.
% 2.73/1.36 % (2983042)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2982928"
% 2.73/1.36 % (2983038)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=3075710722:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/1.36 % (2983037)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=297386393:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/1.36 % (2983041)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=846481614:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/1.36 % (2983039)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=3345465449:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/1.36 % (2983040)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3568927616:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/1.36 % (2983040)Refutation not found, incomplete strategy
% 2.73/1.36 % (2983040)------------------------------
% 2.73/1.36 % (2983040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.36 % (2983040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.36 % (2983040)CaDiCaL version: 2.1.3
% 2.73/1.36 % (2983040)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.36 % (2983040)Time elapsed: 0.002 s
% 2.73/1.36 % (2983040)Peak memory usage: 88 MB
% 2.73/1.36 % (2983040)Instructions burned: 1 (million)
% 2.73/1.36 % (2983041)Also succeeded, but the first one will report.
% 2.73/1.36 % (2983043)dis-21_1_sil=8000:lcm=predicate:random_seed=942806122: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)
% 2.73/1.36 % (2983043)Also succeeded, but the first one will report.
% 2.73/1.36 % (2983042)Refutation found. Thanks to Tanya!
% 2.73/1.36 % SZS status Theorem for theBenchmark
% 2.73/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.36 % (2983042)------------------------------
% 2.73/1.36 % (2983042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.36 % (2983042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.36 % (2983042)CaDiCaL version: 2.1.3
% 2.73/1.36 % (2983042)Termination reason: Refutation
% 2.73/1.36 % (2983042)Time elapsed: 0.010 s
% 2.73/1.36 % (2983042)Peak memory usage: 89 MB
% 2.73/1.36 % (2983042)Instructions burned: 24 (million)
% 2.73/1.36 % (2983042)------------------------------
% 2.73/1.36 % (2983042)------------------------------
% 2.73/1.36 % (2982928)Success in time 0.294 s
% 2.73/1.36 % Vampire exiting
%------------------------------------------------------------------------------