%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PHI010+1 : TPTP v9.3.1. Released v7.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 12:27:27 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 68 ( 11 unt; 2 def)
% Number of atoms : 273 ( 49 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 326 ( 121 ~; 123 |; 67 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 150 ( 136 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( object(X0)
=> ~ property(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',objects_are_not_properties) ).
fof(f2,axiom,
! [X0,X1] :
( exemplifies_property(X1,X0)
=> ( property(X1)
& object(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplifier_is_object_and_exemplified_is_property) ).
fof(f3,axiom,
! [X0,X1] :
( is_the(X0,X1)
=> ( property(X1)
& object(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',description_is_property_and_described_is_object) ).
fof(f4,axiom,
! [X0,X1,X2] :
( ( property(X0)
& object(X1)
& object(X2) )
=> ( ( is_the(X1,X0)
& X1 = X2 )
<=> ? [X3] :
( object(X3)
& exemplifies_property(X0,X3)
& ! [X4] :
( object(X4)
=> ( exemplifies_property(X0,X4)
=> X4 = X3 ) )
& X3 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',description_axiom_identity_instance) ).
fof(f5,conjecture,
! [X0,X1,X2] :
( ( object(X0)
& property(X1)
& object(X2) )
=> ( ( is_the(X0,X1)
& X0 = X2 )
=> exemplifies_property(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2] :
( ( object(X0)
& property(X1)
& object(X2) )
=> ( ( is_the(X0,X1)
& X0 = X2 )
=> exemplifies_property(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
! [X0] :
( ~ property(X0)
| ~ object(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f8,plain,
! [X0,X1] :
( ( property(X1)
& object(X0) )
| ~ exemplifies_property(X1,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0,X1] :
( ( property(X1)
& object(X0) )
| ~ is_the(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ( ( is_the(X1,X0)
& X1 = X2 )
<=> ? [X3] :
( object(X3)
& exemplifies_property(X0,X3)
& ! [X4] :
( X4 = X3
| ~ exemplifies_property(X0,X4)
| ~ object(X4) )
& X3 = X2 ) )
| ~ property(X0)
| ~ object(X1)
| ~ object(X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( ( is_the(X1,X0)
& X1 = X2 )
<=> ? [X3] :
( object(X3)
& exemplifies_property(X0,X3)
& ! [X4] :
( X4 = X3
| ~ exemplifies_property(X0,X4)
| ~ object(X4) )
& X3 = X2 ) )
| ~ property(X0)
| ~ object(X1)
| ~ object(X2) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
? [X0,X1,X2] :
( ~ exemplifies_property(X1,X2)
& is_the(X0,X1)
& X0 = X2
& object(X0)
& property(X1)
& object(X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f13,plain,
? [X0,X1,X2] :
( ~ exemplifies_property(X1,X2)
& is_the(X0,X1)
& X0 = X2
& object(X0)
& property(X1)
& object(X2) ),
inference(flattening,[],[f12]) ).
fof(f14,definition,
! [X0,X2] :
( sP0(X0,X2)
<=> ? [X3] :
( object(X3)
& exemplifies_property(X0,X3)
& ! [X4] :
( X4 = X3
| ~ exemplifies_property(X0,X4)
| ~ object(X4) )
& X3 = X2 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f15,definition,
! [X2,X0,X1] :
( ( ( is_the(X1,X0)
& X1 = X2 )
<=> sP0(X0,X2) )
| ~ sP1(X2,X0,X1) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f16,plain,
! [X0,X1,X2] :
( sP1(X2,X0,X1)
| ~ property(X0)
| ~ object(X1)
| ~ object(X2) ),
inference(definition_folding,[],[f11,f15,f14]) ).
fof(f17,plain,
! [X2,X0,X1] :
( ( ( ( is_the(X1,X0)
& X1 = X2 )
| ~ sP0(X0,X2) )
& ( sP0(X0,X2)
| ~ is_the(X1,X0)
| X1 != X2 ) )
| ~ sP1(X2,X0,X1) ),
inference(nnf_transformation,[],[f15]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ( ( ( is_the(X1,X0)
& X1 = X2 )
| ~ sP0(X0,X2) )
& ( sP0(X0,X2)
| ~ is_the(X1,X0)
| X1 != X2 ) )
| ~ sP1(X2,X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( ( ( is_the(X2,X1)
& X0 = X2 )
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ is_the(X2,X1)
| X0 != X2 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X2] :
( ( sP0(X0,X2)
| ! [X3] :
( ~ object(X3)
| ~ exemplifies_property(X0,X3)
| ? [X4] :
( X3 != X4
& exemplifies_property(X0,X4)
& object(X4) )
| X2 != X3 ) )
& ( ? [X3] :
( object(X3)
& exemplifies_property(X0,X3)
& ! [X4] :
( X4 = X3
| ~ exemplifies_property(X0,X4)
| ~ object(X4) )
& X3 = X2 )
| ~ sP0(X0,X2) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ object(X2)
| ~ exemplifies_property(X0,X2)
| ? [X3] :
( X2 != X3
& exemplifies_property(X0,X3)
& object(X3) )
| X1 != X2 ) )
& ( ? [X4] :
( object(X4)
& exemplifies_property(X0,X4)
& ! [X5] :
( X4 = X5
| ~ exemplifies_property(X0,X5)
| ~ object(X5) )
& X1 = X4 )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ object(X2)
| ~ exemplifies_property(X0,X2)
| ( sK2(X0,X2) != X2
& exemplifies_property(X0,sK2(X0,X2))
& object(sK2(X0,X2)) )
| X1 != X2 ) )
& ( ( object(sK3(X0,X1))
& exemplifies_property(X0,sK3(X0,X1))
& ! [X5] :
( sK3(X0,X1) = X5
| ~ exemplifies_property(X0,X5)
| ~ object(X5) )
& sK3(X0,X1) = X1 )
| ~ sP0(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X3,sK2(X0,X2)),skolemize(X4,sK3(X0,X1))],[f21]) ).
fof(f23,plain,
( ~ exemplifies_property(sK5,sK6)
& is_the(sK4,sK5)
& sK4 = sK6
& object(sK4)
& property(sK5)
& object(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f13]) ).
fof(f24,plain,
! [X0] :
( ~ property(X0)
| ~ object(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f25,plain,
! [X0,X1] :
( object(X0)
| ~ exemplifies_property(X1,X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] :
( property(X0)
| ~ exemplifies_property(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X0,X1] :
( object(X0)
| ~ is_the(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f28,plain,
! [X0,X1] :
( property(X0)
| ~ is_the(X1,X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f29,plain,
! [X2,X0,X1] :
( sP0(X1,X0)
| ~ is_the(X2,X1)
| X0 != X2
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ sP0(X1,X0)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X2,X0,X1] :
( is_the(X2,X1)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
! [X0,X1] :
( sK3(X0,X1) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X0,X1,X5] :
( sK3(X0,X1) = X5
| ~ exemplifies_property(X0,X5)
| ~ object(X5)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X0,X1] :
( exemplifies_property(X0,sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X0,X1] :
( object(sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X2,X0,X1] :
( sP0(X0,X1)
| ~ object(X2)
| ~ exemplifies_property(X0,X2)
| object(sK2(X0,X2))
| X1 != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X2,X0,X1] :
( sP0(X0,X1)
| ~ object(X2)
| ~ exemplifies_property(X0,X2)
| exemplifies_property(X0,sK2(X0,X2))
| X1 != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X0,X1] :
( sP0(X0,X1)
| ~ object(X2)
| ~ exemplifies_property(X0,X2)
| sK2(X0,X2) != X2
| X1 != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X2,X0,X1] :
( sP1(X2,X0,X1)
| ~ property(X0)
| ~ object(X1)
| ~ object(X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
object(sK6),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
property(sK5),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
object(sK4),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
is_the(sK4,sK5),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
~ exemplifies_property(sK5,sK6),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
is_the(sK6,sK5),
inference(definition_unfolding,[],[f44,f43]) ).
fof(f47,plain,
object(sK6),
inference(definition_unfolding,[],[f42,f43]) ).
fof(f48,plain,
! [X2,X1] :
( sP0(X1,X2)
| ~ is_the(X2,X1)
| ~ sP1(X2,X1,X2) ),
inference(equality_resolution,[],[f29]) ).
fof(f49,plain,
! [X2,X0] :
( sP0(X0,X2)
| ~ object(X2)
| ~ exemplifies_property(X0,X2)
| sK2(X0,X2) != X2 ),
inference(equality_resolution,[],[f38]) ).
fof(f50,plain,
! [X2,X0] :
( sP0(X0,X2)
| ~ object(X2)
| ~ exemplifies_property(X0,X2)
| exemplifies_property(X0,sK2(X0,X2)) ),
inference(equality_resolution,[],[f37]) ).
fof(f51,plain,
! [X2,X0] :
( sP0(X0,X2)
| ~ object(X2)
| ~ exemplifies_property(X0,X2)
| object(sK2(X0,X2)) ),
inference(equality_resolution,[],[f36]) ).
fof(f52,plain,
! [X0] :
( ~ property(X0)
| object(X0) ),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f53,plain,
! [X0,X1] :
( ~ object(X0)
| ~ exemplifies_property(X1,X0) ),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f54,plain,
! [X0,X1] :
( ~ object(X0)
| ~ is_the(X0,X1) ),
inference(consistent_polarity_flipping,[],[f27]) ).
fof(f55,plain,
! [X2,X0,X1] :
( is_the(X0,X1)
| sP0(X1,X2)
| sP1(X2,X1,X0) ),
inference(consistent_polarity_flipping,[],[f31]) ).
fof(f56,plain,
! [X2,X0,X1] :
( X0 = X1
| sP0(X2,X0)
| sP1(X0,X2,X1) ),
inference(consistent_polarity_flipping,[],[f30]) ).
fof(f57,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ~ is_the(X1,X0)
| sP1(X1,X0,X1) ),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f58,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| object(X1)
| ~ exemplifies_property(X0,X1)
| sK2(X0,X1) != X1 ),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f59,plain,
! [X2,X0] :
( ~ sP0(X0,X2)
| object(X2)
| ~ exemplifies_property(X0,X2)
| exemplifies_property(X0,sK2(X0,X2)) ),
inference(consistent_polarity_flipping,[],[f50]) ).
fof(f60,plain,
! [X2,X0] :
( ~ sP0(X0,X2)
| object(X2)
| ~ exemplifies_property(X0,X2)
| ~ object(sK2(X0,X2)) ),
inference(consistent_polarity_flipping,[],[f51]) ).
fof(f61,plain,
! [X0,X1] :
( ~ object(sK3(X0,X1))
| sP0(X0,X1) ),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f62,plain,
! [X0,X1] :
( exemplifies_property(X0,sK3(X0,X1))
| sP0(X0,X1) ),
inference(consistent_polarity_flipping,[],[f34]) ).
fof(f63,plain,
! [X2,X0,X1] :
( sK3(X0,X1) = X2
| ~ exemplifies_property(X0,X2)
| object(X2)
| sP0(X0,X1) ),
inference(consistent_polarity_flipping,[],[f33]) ).
fof(f64,plain,
! [X0,X1] :
( sK3(X0,X1) = X1
| sP0(X0,X1) ),
inference(consistent_polarity_flipping,[],[f32]) ).
fof(f65,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| ~ property(X1)
| object(X2)
| object(X0) ),
inference(consistent_polarity_flipping,[],[f39]) ).
fof(f66,plain,
~ object(sK6),
inference(consistent_polarity_flipping,[],[f47]) ).
fof(f67,plain,
~ object(sK6),
inference(consistent_polarity_flipping,[],[f40]) ).
fof(f77,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f52,f26,f53,f28,f54,f55,f56,f57,f58,f59,f60,f61,f62,f63,f64,f65,f45,f46,f66,f41,f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI010+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 22:09:24 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.15/0.46 % (2777830)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (2777835)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1137247246_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % TRYING [1]
% 0.15/0.46 % TRYING [2]
% 0.15/0.46 % (2777835) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2777830-2777835"...
% 0.15/0.46 % (2777835)...printing done.
% 0.15/0.46 % (2777836)% WARNING: option uhcvi not known.
% 0.15/0.46 % (2777835)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (2777835)------------------------------
% 0.15/0.46 % (2777835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (2777835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (2777835)CaDiCaL version: 2.1.3
% 0.15/0.46 % (2777835)Termination reason: Refutation
% 0.15/0.46 % (2777835)Time elapsed: 0.002 s
% 0.15/0.46 % (2777835)Peak memory usage: 11 MB
% 0.15/0.46 % (2777835)Instructions burned: 4 (million)
% 0.15/0.46 % (2777830)Success in time 0.037 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------