%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET173+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:43:21 PM UTC 2026
% Result : Theorem 1.32s 0.65s
% Output : Refutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 124 ( 35 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 135 ( 50 ~; 63 |; 18 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 86 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f5,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f9,conjecture,
! [X0,X1] : intersection(X0,union(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_absorbtion_for_intersection) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : intersection(X0,union(X0,X1)) = X0,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0,X1] : intersection(X0,union(X0,X1)) != X0,
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f23]) ).
fof(f25,plain,
sK2 != intersection(sK2,union(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f12]) ).
fof(f28,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f36,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f43,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| X0 = X1
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
sK2 != intersection(sK2,union(sK2,sK3)),
inference(cnf_transformation,[],[f25]) ).
fof(f95,plain,
! [X2,X0,X1] :
( member(sK1(X0,intersection(X1,X2)),X1)
| member(sK1(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0 ),
inference(resolution,[],[f43,f30]) ).
fof(f96,plain,
! [X2,X0,X1] :
( member(sK1(X0,intersection(X1,X2)),X2)
| member(sK1(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0 ),
inference(resolution,[],[f43,f29]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ member(sK1(X0,intersection(X1,X2)),X2)
| ~ member(sK1(X0,intersection(X1,X2)),X1)
| ~ member(sK1(X0,intersection(X1,X2)),X0)
| intersection(X1,X2) = X0 ),
inference(resolution,[],[f44,f31]) ).
fof(f1498,plain,
! [X0,X1] :
( ~ member(sK1(X0,intersection(X1,X0)),X1)
| ~ member(sK1(X0,intersection(X1,X0)),X0)
| intersection(X1,X0) = X0 ),
inference(factoring,[],[f101]) ).
fof(f1834,plain,
! [X0,X1] :
( ~ member(sK1(X0,intersection(X1,X0)),X1)
| intersection(X1,X0) = X0
| member(sK1(X0,intersection(X1,X0)),X0)
| intersection(X1,X0) = X0 ),
inference(resolution,[],[f1498,f96]) ).
fof(f1853,plain,
! [X0,X1] :
( member(sK1(X0,intersection(X1,X0)),X0)
| intersection(X1,X0) = X0
| ~ member(sK1(X0,intersection(X1,X0)),X1) ),
inference(duplicate_literal_removal,[],[f1834]) ).
fof(f1888,plain,
! [X0,X1] :
( intersection(X0,X1) = X1
| ~ member(sK1(X1,intersection(X0,X1)),X0)
| ~ member(sK1(X1,intersection(X0,X1)),X0)
| intersection(X0,X1) = X1 ),
inference(resolution,[],[f1853,f1498]) ).
fof(f1902,plain,
! [X0,X1] :
( ~ member(sK1(X1,intersection(X0,X1)),X0)
| intersection(X0,X1) = X1 ),
inference(duplicate_literal_removal,[],[f1888]) ).
fof(f1903,plain,
! [X0,X1] :
( intersection(X0,X1) = X1
| member(sK1(X1,intersection(X0,X1)),X1)
| intersection(X0,X1) = X1 ),
inference(resolution,[],[f1902,f95]) ).
fof(f1907,plain,
! [X2,X0,X1] :
( ~ member(sK1(X2,intersection(union(X0,X1),X2)),X0)
| intersection(union(X0,X1),X2) = X2 ),
inference(resolution,[],[f1902,f28]) ).
fof(f1923,plain,
! [X0,X1] :
( member(sK1(X1,intersection(X0,X1)),X1)
| intersection(X0,X1) = X1 ),
inference(duplicate_literal_removal,[],[f1903]) ).
fof(f2058,plain,
! [X0,X1] :
( intersection(union(X0,X1),X0) = X0
| intersection(union(X0,X1),X0) = X0 ),
inference(resolution,[],[f1907,f1923]) ).
fof(f2079,plain,
! [X0,X1] : intersection(union(X0,X1),X0) = X0,
inference(duplicate_literal_removal,[],[f2058]) ).
fof(f2090,plain,
! [X0,X1] : intersection(X0,union(X0,X1)) = X0,
inference(superposition,[],[f36,f2079]) ).
fof(f2184,plain,
sK2 != sK2,
inference(superposition,[],[f45,f2090]) ).
fof(f2185,plain,
$false,
inference(trivial_inequality_removal,[],[f2184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET173+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n004.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 01:00:37 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.44 Running first-order model finding
% 0.11/0.44 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.32/0.65 % (4046407)Will run a generic schedule for satisfiability detection.
% 1.32/0.65 % (4046415)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2475277079:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.32/0.65 % (4046414)% WARNING: option uhcvi not known.
% 1.32/0.65 % (4046414)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2832373255:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.32/0.65 % (4046417)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=849277365:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.32/0.65 % (4046416)dis+10_1_sil=32000:sp=arity:random_seed=1183825259:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.32/0.65 % (4046413)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3572215473_2999 on theBenchmark for (2999ds/0Mi)
% 1.32/0.65 % (4046418)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4009932714:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.32/0.65 % (4046419)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4045205942:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.32/0.65 % TRYING [1]
% 1.32/0.65 % TRYING [2]
% 1.32/0.65 % TRYING [3]
% 1.32/0.65 % TRYING [4]
% 1.32/0.65 % TRYING [5]
% 1.32/0.65 % TRYING [6]
% 1.32/0.65 % (4046416)Instruction limit reached!
% 1.32/0.65 % (4046416)------------------------------
% 1.32/0.65 % (4046416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.65 % (4046416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.65 % (4046416)CaDiCaL version: 2.1.3
% 1.32/0.65 % (4046416)Termination reason: Instruction limit
% 1.32/0.65 % (4046416)Termination phase: Saturation
% 1.32/0.65 % (4046416)Time elapsed: 0.103 s
% 1.32/0.65 % (4046416)Peak memory usage: 12 MB
% 1.32/0.65 % (4046416)Instructions burned: 104 (million)
% 1.32/0.65 % (4046417)Instruction limit reached!
% 1.32/0.65 % (4046417)------------------------------
% 1.32/0.65 % (4046417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.65 % (4046417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.65 % (4046417)CaDiCaL version: 2.1.3
% 1.32/0.65 % (4046417)Termination reason: Instruction limit
% 1.32/0.65 % (4046417)Termination phase: Saturation
% 1.32/0.65 % (4046417)Time elapsed: 0.104 s
% 1.32/0.65 % (4046417)Peak memory usage: 12 MB
% 1.32/0.65 % (4046417)Instructions burned: 116 (million)
% 1.32/0.65 % TRYING [7]
% 1.32/0.65 % (4046428)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1295623044:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.32/0.65 % TRYING [1]
% 1.32/0.65 % TRYING [2]
% 1.32/0.65 % (4046418)Instruction limit reached!
% 1.32/0.65 % (4046418)------------------------------
% 1.32/0.65 % (4046418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.65 % (4046418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.65 % (4046418)CaDiCaL version: 2.1.3
% 1.32/0.65 % (4046418)Termination reason: Instruction limit
% 1.32/0.65 % (4046418)Termination phase: Saturation
% 1.32/0.65 % (4046418)Time elapsed: 0.128 s
% 1.32/0.65 % (4046418)Peak memory usage: 12 MB
% 1.32/0.65 % (4046418)Instructions burned: 131 (million)
% 1.32/0.65 % TRYING [3]
% 1.32/0.65 % TRYING [4]
% 1.32/0.65 % (4046429)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1484044533:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.32/0.65 % (4046419) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4046407-4046419"...
% 1.32/0.65 % (4046419)...printing done.
% 1.32/0.65 % (4046419)Refutation found. Thanks to Tanya!
% 1.32/0.65 % SZS status Theorem for theBenchmark
% 1.32/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 1.32/0.65 % (4046419)------------------------------
% 1.32/0.65 % (4046419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.32/0.65 % (4046419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.32/0.65 % (4046419)CaDiCaL version: 2.1.3
% 1.32/0.65 % (4046419)Termination reason: Refutation
% 1.32/0.65 % (4046419)Time elapsed: 0.154 s
% 1.32/0.65 % (4046419)Peak memory usage: 13 MB
% 1.32/0.65 % (4046419)Instructions burned: 158 (million)
% 1.32/0.65 % (4046407)Success in time 0.194 s
% 1.32/0.65 % Vampire exiting
%------------------------------------------------------------------------------