%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PHI012+1 : TPTP v9.3.1. Released v7.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:30:18 PM UTC 2026
% Result : Theorem 12.07s 2.17s
% Output : Proof 12.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 10 unt; 0 def)
% Number of atoms : 145 ( 18 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 172 ( 69 ~; 68 |; 26 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 15 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,conjecture,
( ? [X] :
( exemplifies_property(none_greater,X)
& object(X) )
=> ? [X] :
( ! [Y] :
( object(Y)
=> ( exemplifies_property(none_greater,Y)
=> Y = X ) )
& exemplifies_property(none_greater,X)
& object(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_2) ).
fof(f2_neg,negated_conjecture,
~ ( ? [X] :
( exemplifies_property(none_greater,X)
& object(X) )
=> ? [X] :
( ! [Y] :
( object(Y)
=> ( exemplifies_property(none_greater,Y)
=> Y = X ) )
& exemplifies_property(none_greater,X)
& object(X) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
( ! [X] :
( ? [Y] :
( Y != X
& exemplifies_property(none_greater,Y)
& object(Y) )
| ~ exemplifies_property(none_greater,X)
| ~ object(X) )
& ? [X] :
( exemplifies_property(none_greater,X)
& object(X) ) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
! [X] :
( ( ( sk2(X) != X
& exemplifies_property(none_greater,sk2(X))
& object(sk2(X)) )
| ~ exemplifies_property(none_greater,X)
| ~ object(X) )
& exemplifies_property(none_greater,sk1)
& object(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f2_nnf]) ).
cnf(c8,plain,
( object(sk2(X0))
| ~ exemplifies_property(none_greater,X0)
| ~ object(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(c6,plain,
object(sk1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p15,plain,
( object(sk2(sk1))
| ~ exemplifies_property(none_greater,sk1) ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(c7,plain,
exemplifies_property(none_greater,sk1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p21,plain,
object(sk2(sk1)),
inference(resolution,[status(thm)],[p15,c7]) ).
fof(f1,axiom,
! [X,Y] :
( ( object(Y)
& object(X) )
=> ( X = Y
| exemplifies_relation(greater_than,Y,X)
| exemplifies_relation(greater_than,X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_of_greater_than) ).
fof(f1_nnf,plain,
! [X,Y] :
( X = Y
| exemplifies_relation(greater_than,Y,X)
| exemplifies_relation(greater_than,X,Y)
| ~ object(Y)
| ~ object(X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( X = Y
| exemplifies_relation(greater_than,Y,X)
| exemplifies_relation(greater_than,X,Y)
| ~ object(Y)
| ~ object(X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c5,plain,
( X0 = X1
| exemplifies_relation(greater_than,X1,X0)
| exemplifies_relation(greater_than,X0,X1)
| ~ object(X1)
| ~ object(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p27,plain,
( sk2(sk1) = X0
| exemplifies_relation(greater_than,X0,sk2(sk1))
| exemplifies_relation(greater_than,sk2(sk1),X0)
| ~ object(X0) ),
inference(resolution,[status(thm)],[p21,c5]) ).
cnf(p36,plain,
( sk2(sk1) = sk1
| exemplifies_relation(greater_than,sk1,sk2(sk1))
| exemplifies_relation(greater_than,sk2(sk1),sk1) ),
inference(resolution,[status(thm)],[p27,c6]) ).
fof(f0,axiom,
! [X] :
( object(X)
=> ( exemplifies_property(none_greater,X)
<=> ( ~ ? [Y] :
( exemplifies_property(conceivable,Y)
& exemplifies_relation(greater_than,Y,X)
& object(Y) )
& exemplifies_property(conceivable,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_none_greater) ).
fof(f0_nnf,plain,
! [X] :
( ( ( ? [Y] :
( exemplifies_property(conceivable,Y)
& exemplifies_relation(greater_than,Y,X)
& object(Y) )
| ~ exemplifies_property(conceivable,X)
| exemplifies_property(none_greater,X) )
& ( ( ! [Y] :
( ~ exemplifies_property(conceivable,Y)
| ~ exemplifies_relation(greater_than,Y,X)
| ~ object(Y) )
& exemplifies_property(conceivable,X) )
| ~ exemplifies_property(none_greater,X) ) )
| ~ object(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ( ( exemplifies_property(conceivable,sk0(X))
& exemplifies_relation(greater_than,sk0(X),X)
& object(sk0(X)) )
| ~ exemplifies_property(conceivable,X)
| exemplifies_property(none_greater,X) )
& ( ( ( ~ exemplifies_property(conceivable,Y)
| ~ exemplifies_relation(greater_than,Y,X)
| ~ object(Y) )
& exemplifies_property(conceivable,X) )
| ~ exemplifies_property(none_greater,X) ) )
| ~ object(X) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( ~ exemplifies_property(conceivable,X1)
| ~ exemplifies_relation(greater_than,X1,X0)
| ~ object(X1)
| ~ exemplifies_property(none_greater,X0)
| ~ object(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p13,plain,
( ~ exemplifies_property(conceivable,X0)
| ~ exemplifies_relation(greater_than,X0,sk1)
| ~ object(X0)
| ~ exemplifies_property(none_greater,sk1) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(p20,plain,
( ~ exemplifies_property(conceivable,X0)
| ~ exemplifies_relation(greater_than,X0,sk1)
| ~ object(X0) ),
inference(resolution,[status(thm)],[p13,c7]) ).
cnf(p33,plain,
( ~ exemplifies_property(conceivable,sk2(sk1))
| ~ exemplifies_relation(greater_than,sk2(sk1),sk1) ),
inference(resolution,[status(thm)],[p21,p20]) ).
cnf(p43,plain,
( ~ exemplifies_property(conceivable,sk2(sk1))
| sk2(sk1) = sk1
| exemplifies_relation(greater_than,sk1,sk2(sk1)) ),
inference(resolution,[status(thm)],[p36,p33]) ).
cnf(c0,plain,
( exemplifies_property(conceivable,X0)
| ~ exemplifies_property(none_greater,X0)
| ~ object(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p25,plain,
( exemplifies_property(conceivable,sk2(sk1))
| ~ exemplifies_property(none_greater,sk2(sk1)) ),
inference(resolution,[status(thm)],[p21,c0]) ).
cnf(c9,plain,
( exemplifies_property(none_greater,sk2(X0))
| ~ exemplifies_property(none_greater,X0)
| ~ object(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p16,plain,
( exemplifies_property(none_greater,sk2(sk1))
| ~ exemplifies_property(none_greater,sk1) ),
inference(resolution,[status(thm)],[c9,c6]) ).
cnf(p22,plain,
exemplifies_property(none_greater,sk2(sk1)),
inference(resolution,[status(thm)],[p16,c7]) ).
cnf(p34,plain,
exemplifies_property(conceivable,sk2(sk1)),
inference(resolution,[status(thm)],[p25,p22]) ).
cnf(p56,plain,
( sk2(sk1) = sk1
| exemplifies_relation(greater_than,sk1,sk2(sk1)) ),
inference(resolution,[status(thm)],[p43,p34]) ).
cnf(p26,plain,
( ~ exemplifies_property(conceivable,X0)
| ~ exemplifies_relation(greater_than,X0,sk2(sk1))
| ~ object(X0)
| ~ exemplifies_property(none_greater,sk2(sk1)) ),
inference(resolution,[status(thm)],[p21,c1]) ).
cnf(p35,plain,
( ~ exemplifies_property(conceivable,X0)
| ~ exemplifies_relation(greater_than,X0,sk2(sk1))
| ~ object(X0) ),
inference(resolution,[status(thm)],[p26,p22]) ).
cnf(p42,plain,
( ~ exemplifies_property(conceivable,sk1)
| ~ exemplifies_relation(greater_than,sk1,sk2(sk1)) ),
inference(resolution,[status(thm)],[p35,c6]) ).
cnf(p68,plain,
( ~ exemplifies_property(conceivable,sk1)
| sk2(sk1) = sk1 ),
inference(resolution,[status(thm)],[p56,p42]) ).
cnf(p12,plain,
( exemplifies_property(conceivable,sk1)
| ~ exemplifies_property(none_greater,sk1) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(p19,plain,
exemplifies_property(conceivable,sk1),
inference(resolution,[status(thm)],[p12,c7]) ).
cnf(p89,plain,
sk2(sk1) = sk1,
inference(resolution,[status(thm)],[p68,p19]) ).
cnf(c10,plain,
( sk2(X0) != X0
| ~ exemplifies_property(none_greater,X0)
| ~ object(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p17,plain,
( sk2(sk1) != sk1
| ~ exemplifies_property(none_greater,sk1) ),
inference(resolution,[status(thm)],[c10,c6]) ).
cnf(p23,plain,
sk2(sk1) != sk1,
inference(resolution,[status(thm)],[p17,c7]) ).
cnf(p90,plain,
sk1 != sk1,
inference(demodulation,[status(thm)],[p89,p23]) ).
cnf(p112,plain,
$false,
inference(equality_resolution,[status(thm)],[p90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI012+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 06:05:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.07/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.07/2.17 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------