%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PHI011+1 : TPTP v9.3.1. Released v7.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 5.82s 1.29s
% Output : Proof 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 60 ( 48 unt; 0 def)
% Number of atoms : 104 ( 46 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 78 ( 34 ~; 18 |; 15 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 46 ( 2 sgn 16 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X] :
( object(X)
=> ~ property(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',objects_are_not_properties) ).
fof(f0_nnf,plain,
! [X] :
( ~ property(X)
| ~ object(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] :
( ~ property(X)
| ~ object(X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ property(X0)
| ~ object(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t11,plain,
ifeq(object(X1),true,ifeq(property(X1),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t16,plain,
ifeq(object(X1),true,ifeq(property(X1),true,false,true),true) = true,
inference(orient,[status(thm)],[t11]) ).
fof(f4,conjecture,
! [F] :
( property(F)
=> ( ? [Y] :
( is_the(Y,F)
& object(Y) )
=> ! [Z] :
( object(Z)
=> ( is_the(Z,F)
=> exemplifies_property(F,Z) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',description_theorem_2) ).
fof(f4_neg,negated_conjecture,
~ ! [F] :
( property(F)
=> ( ? [Y] :
( is_the(Y,F)
& object(Y) )
=> ! [Z] :
( object(Z)
=> ( is_the(Z,F)
=> exemplifies_property(F,Z) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
? [F] :
( ? [Z] :
( ~ exemplifies_property(F,Z)
& is_the(Z,F)
& object(Z) )
& ? [Y] :
( is_the(Y,F)
& object(Y) )
& property(F) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
( ~ exemplifies_property(sk0,sk2)
& is_the(sk2,sk0)
& object(sk2)
& is_the(sk1,sk0)
& object(sk1)
& property(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f4_nnf]) ).
cnf(c9,plain,
object(sk2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t1,plain,
object(sk2) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t22,plain,
object(sk2) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t25,plain,
true = ifeq(true,true,ifeq(property(sk2),true,false,true),true),
inference(cp,[status(thm)],[t16,t22]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t59,plain,
true = ifeq(property(sk2),true,false,true),
inference(step,[status(thm)],[t25,t13]) ).
cnf(t43,plain,
ifeq(property(sk2),true,false,true) = true,
inference(orient,[status(thm)],[t59]) ).
cnf(c7,plain,
object(sk1),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t0,plain,
object(sk1) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t28,plain,
object(sk1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t31,plain,
true = ifeq(true,true,ifeq(property(sk1),true,false,true),true),
inference(cp,[status(thm)],[t16,t28]) ).
cnf(t60,plain,
true = ifeq(property(sk1),true,false,true),
inference(step,[status(thm)],[t31,t13]) ).
cnf(t44,plain,
ifeq(property(sk1),true,false,true) = true,
inference(orient,[status(thm)],[t60]) ).
cnf(c6,plain,
property(sk0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t2,plain,
property(sk0) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t34,plain,
property(sk0) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t37,plain,
true = ifeq(object(sk0),true,ifeq(true,true,false,true),true),
inference(cp,[status(thm)],[t16,t34]) ).
cnf(t61,plain,
true = ifeq(object(sk0),true,false,true),
inference(step,[status(thm)],[t37,t13]) ).
cnf(t45,plain,
ifeq(object(sk0),true,false,true) = true,
inference(orient,[status(thm)],[t61]) ).
fof(f3,axiom,
! [X,F,Y] :
( ( object(Y)
& property(F)
& object(X) )
=> ( ( X = Y
& is_the(X,F) )
=> exemplifies_property(F,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).
fof(f3_nnf,plain,
! [X,F,Y] :
( exemplifies_property(F,Y)
| X != Y
| ~ is_the(X,F)
| ~ object(Y)
| ~ property(F)
| ~ object(X) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,F,Y] :
( exemplifies_property(F,Y)
| X != Y
| ~ is_the(X,F)
| ~ object(Y)
| ~ property(F)
| ~ object(X) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( exemplifies_property(X1,X2)
| X0 != X2
| ~ is_the(X0,X1)
| ~ object(X2)
| ~ property(X1)
| ~ object(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t12,plain,
ifeq(object(X1),true,ifeq(property(X2),true,ifeq(object(X3),true,ifeq(is_the(X1,X2),true,ifeq(X1,X3,exemplifies_property(X2,X3),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t14,plain,
ifeq(object(X1),true,ifeq(property(X2),true,ifeq(object(X3),true,ifeq(is_the(X1,X2),true,ifeq(X1,X3,exemplifies_property(X2,X3),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(c10,plain,
is_the(sk2,sk0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t4,plain,
is_the(sk2,sk0) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t39,plain,
is_the(sk2,sk0) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t40,plain,
true = ifeq(object(sk2),true,ifeq(property(sk0),true,ifeq(object(X1),true,ifeq(true,true,ifeq(sk2,X1,exemplifies_property(sk0,X1),true),true),true),true),true),
inference(cp,[status(thm)],[t14,t39]) ).
cnf(t62,plain,
true = ifeq(true,true,ifeq(property(sk0),true,ifeq(object(X1),true,ifeq(true,true,ifeq(sk2,X1,exemplifies_property(sk0,X1),true),true),true),true),true),
inference(step,[status(thm)],[t40,t22]) ).
cnf(t63,plain,
true = ifeq(property(sk0),true,ifeq(object(X1),true,ifeq(true,true,ifeq(sk2,X1,exemplifies_property(sk0,X1),true),true),true),true),
inference(step,[status(thm)],[t62,t13]) ).
cnf(t64,plain,
true = ifeq(true,true,ifeq(object(X1),true,ifeq(true,true,ifeq(sk2,X1,exemplifies_property(sk0,X1),true),true),true),true),
inference(step,[status(thm)],[t63,t34]) ).
cnf(t65,plain,
true = ifeq(object(X1),true,ifeq(true,true,ifeq(sk2,X1,exemplifies_property(sk0,X1),true),true),true),
inference(step,[status(thm)],[t64,t13]) ).
cnf(t66,plain,
true = ifeq(object(X1),true,ifeq(sk2,X1,exemplifies_property(sk0,X1),true),true),
inference(step,[status(thm)],[t65,t13]) ).
cnf(t52,plain,
ifeq(object(X1),true,ifeq(sk2,X1,exemplifies_property(sk0,X1),true),true) = true,
inference(orient,[status(thm)],[t66]) ).
cnf(t53,plain,
true = ifeq(true,true,ifeq(sk2,sk2,exemplifies_property(sk0,sk2),true),true),
inference(cp,[status(thm)],[t52,t22]) ).
cnf(t67,plain,
true = ifeq(sk2,sk2,exemplifies_property(sk0,sk2),true),
inference(step,[status(thm)],[t53,t13]) ).
cnf(t68,plain,
true = exemplifies_property(sk0,sk2),
inference(step,[status(thm)],[t67,t13]) ).
cnf(t56,plain,
exemplifies_property(sk0,sk2) = true,
inference(orient,[status(thm)],[t68]) ).
cnf(c11,plain,
~ exemplifies_property(sk0,sk2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c11]) ).
cnf(g0_0,plain,
true != ifeq(exemplifies_property(sk0,sk2),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(exemplifies_property(sk0,sk2),true,false,ifeq(property(sk2),true,false,true)),
inference(rw,[status(thm)],[g0_0,t43]) ).
cnf(g0_2,plain,
true != ifeq(exemplifies_property(sk0,sk2),true,false,ifeq(property(sk2),true,false,ifeq(property(sk1),true,false,true))),
inference(rw,[status(thm)],[g0_1,t44]) ).
cnf(g0_3,plain,
true != ifeq(exemplifies_property(sk0,sk2),true,false,ifeq(property(sk2),true,false,ifeq(property(sk1),true,false,ifeq(object(sk0),true,false,true)))),
inference(rw,[status(thm)],[g0_2,t45]) ).
cnf(g0_4,plain,
true != ifeq(exemplifies_property(sk0,sk2),true,false,ifeq(property(sk2),true,false,ifeq(property(sk1),true,false,ifeq(object(sk0),true,false,exemplifies_property(sk0,sk2))))),
inference(rw,[status(thm)],[g0_3,t56]) ).
cnf(g0_5,plain,
true != ifeq(true,true,false,ifeq(property(sk2),true,false,ifeq(property(sk1),true,false,ifeq(object(sk0),true,false,exemplifies_property(sk0,sk2))))),
inference(rw,[status(thm)],[g0_4,t56]) ).
cnf(g0_6,plain,
true != false,
inference(rw,[status(thm)],[g0_5,t13]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI011+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 06:05:57 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.82/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.82/1.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------