%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET945+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:45:03 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 4 unt; 0 def)
% Number of atoms : 198 ( 21 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 254 ( 102 ~; 96 |; 47 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 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 : 129 ( 114 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f4,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f8,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
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/sandbox2/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/sandbox2/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(f15,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
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(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(f46,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f47,plain,
! [X3,X0,X1] :
( ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0,X1] :
( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(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,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ 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,sK3(X0,X5))
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f38]) ).
fof(f56,plain,
! [X0,X5] :
( in(sK3(X0,X5),X0)
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f37]) ).
fof(f70,plain,
! [X0] :
( disjoint(sK3(sK7,X0),sK8)
| ~ in(X0,union(sK7)) ),
inference(resolution,[],[f56,f49]) ).
fof(f78,plain,
! [X0,X1] :
( in(sK6(X0,X1),X1)
| disjoint(X0,X1) ),
inference(resolution,[],[f48,f53]) ).
fof(f79,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| disjoint(X0,X1) ),
inference(resolution,[],[f48,f52]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[],[f51,f47]) ).
fof(f271,plain,
! [X0,X1] :
( ~ in(X0,sK3(sK7,X1))
| ~ in(X0,sK8)
| ~ in(X1,union(sK7)) ),
inference(resolution,[],[f92,f70]) ).
fof(f328,plain,
! [X0] :
( ~ in(X0,sK8)
| ~ in(X0,union(sK7))
| ~ in(X0,union(sK7)) ),
inference(resolution,[],[f271,f55]) ).
fof(f344,plain,
! [X0] :
( ~ in(X0,union(sK7))
| ~ in(X0,sK8) ),
inference(duplicate_literal_removal,[],[f328]) ).
fof(f373,plain,
! [X0] :
( ~ in(sK6(X0,union(sK7)),sK8)
| disjoint(X0,union(sK7)) ),
inference(resolution,[],[f344,f78]) ).
fof(f390,plain,
( disjoint(sK8,union(sK7))
| disjoint(sK8,union(sK7)) ),
inference(resolution,[],[f373,f79]) ).
fof(f391,plain,
disjoint(sK8,union(sK7)),
inference(duplicate_literal_removal,[],[f390]) ).
fof(f405,plain,
disjoint(union(sK7),sK8),
inference(resolution,[],[f391,f46]) ).
fof(f406,plain,
$false,
inference(forward_subsumption_resolution,[],[f405,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET945+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n005.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 03:15:47 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
% 0.16/0.47 % (397679)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (397689)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2343259573:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (397685)% WARNING: option uhcvi not known.
% 0.16/0.47 % (397684)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3826285001_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (397688)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1738270577:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (397685)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2347895993:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (397687)dis+10_1_sil=32000:sp=arity:random_seed=2721348149:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (397686)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1572146581:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (397690)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2945170222:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % (397687) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-397679-397687"...
% 0.16/0.47 % (397687)...printing done.
% 0.16/0.47 % (397687)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (397687)------------------------------
% 0.16/0.47 % (397687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (397687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (397687)CaDiCaL version: 2.1.3
% 0.16/0.47 % (397687)Termination reason: Refutation
% 0.16/0.47 % (397687)Time elapsed: 0.013 s
% 0.16/0.47 % (397687)Peak memory usage: 11 MB
% 0.16/0.47 % (397687)Instructions burned: 20 (million)
% 0.16/0.47 % (397679)Success in time 0.056 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------