%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET676+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 : 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 12:44:24 PM UTC 2026
% Result : Theorem 0.13s 0.46s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 7 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 59 ( 24 ~; 24 |; 3 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f20,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_41) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
! [X0] :
( ! [X1] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f45,plain,
? [X0] :
( ~ ilf_type(cross_product(X0,X0),identity_relation_of_type(X0))
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,relation_type(X0,X0)) )
& ( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f25]) ).
fof(f65,plain,
( ~ ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11))
& ilf_type(sK11,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f45]) ).
fof(f66,plain,
! [X0,X1] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f22]) ).
fof(f75,plain,
! [X0,X1] :
( ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f49]) ).
fof(f104,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f106,plain,
~ ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11)),
inference(cnf_transformation,[],[f65]) ).
fof(f108,plain,
! [X0,X1] :
( ~ ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ilf_type(X1,set_type)
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f66]) ).
fof(f116,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0))
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f75]) ).
fof(f146,plain,
! [X0] : ~ ilf_type(X0,set_type),
inference(consistent_polarity_flipping,[],[f104]) ).
fof(f147,plain,
ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11)),
inference(consistent_polarity_flipping,[],[f106]) ).
fof(f157,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ~ ilf_type(X0,identity_relation_of_type(X1))
| ilf_type(X0,relation_type(X1,X1)) ),
inference(resolution,[],[f116,f146]) ).
fof(f161,plain,
! [X0,X1] :
( ilf_type(X0,relation_type(X1,X1))
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(resolution,[],[f157,f146]) ).
fof(f162,plain,
! [X0] :
( ~ ilf_type(cross_product(X0,X0),identity_relation_of_type(X0))
| ilf_type(X0,set_type)
| ilf_type(X0,set_type) ),
inference(resolution,[],[f161,f108]) ).
fof(f165,plain,
! [X0] :
( ~ ilf_type(cross_product(X0,X0),identity_relation_of_type(X0))
| ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f162]) ).
fof(f166,plain,
ilf_type(sK11,set_type),
inference(resolution,[],[f165,f147]) ).
fof(f167,plain,
$false,
inference(resolution,[],[f166,f146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET676+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n016.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 02:34:18 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.13/0.46 % (3200193)Will run a generic schedule for satisfiability detection.
% 0.13/0.46 % (3200204)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1103350218:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.46 % (3200204) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3200193-3200204"...
% 0.13/0.46 % (3200199)% WARNING: option uhcvi not known.
% 0.13/0.46 % (3200204)...printing done.
% 0.13/0.46 % (3200204)Refutation found. Thanks to Tanya!
% 0.13/0.46 % SZS status Theorem for theBenchmark
% 0.13/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.46 % (3200204)------------------------------
% 0.13/0.46 % (3200204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.46 % (3200204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.46 % (3200204)CaDiCaL version: 2.1.3
% 0.13/0.46 % (3200204)Termination reason: Refutation
% 0.13/0.46 % (3200204)Time elapsed: 0.002 s
% 0.13/0.46 % (3200204)Peak memory usage: 12 MB
% 0.13/0.46 % (3200204)Instructions burned: 4 (million)
% 0.13/0.46 % (3200193)Success in time 0.028 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------