%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PHI022+1 : TPTP v9.3.1. Released v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 : Sun Sep 27 08:19:50 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 53 ( 22 ~; 18 |; 5 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 20 ( 0 sgn 8 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(self_caused,axiom,
! [X] :
( selfCaused(X)
<=> ( natureConcOnlyByExistence(X)
& essenceInvExistence(X) ) ),
file('theBenchmark.p',self_caused) ).
fof(substance,axiom,
! [X] :
( substance(X)
<=> ( conceivedThruItself(X)
& inItself(X) ) ),
file('theBenchmark.p',substance) ).
fof(has_substance_being,axiom,
! [X] :
( substance(X)
=> being(X) ),
file('theBenchmark.p',has_substance_being) ).
fof(is_in_itself_is_self_caused,axiom,
! [X] :
( inItself(X)
=> selfCaused(X) ),
file('theBenchmark.p',is_in_itself_is_self_caused) ).
fof(being_has_essense,axiom,
! [X] :
( being(X)
=> hasEssence(X) ),
file('theBenchmark.p',being_has_essense) ).
fof(essence_involves_existence_exists,axiom,
! [X] :
( ( hasEssence(X)
& essenceInvExistence(X) )
=> exists(X) ),
file('theBenchmark.p',essence_involves_existence_exists) ).
fof(has_substance_exists,conjecture,
! [X] :
( substance(X)
=> exists(X) ),
file('theBenchmark.p',has_substance_exists) ).
fof(has_substance_exists_neg,negated_conjecture,
~ ! [X] :
( substance(X)
=> exists(X) ),
inference(assume_negation,[status(cth)],[has_substance_exists]) ).
cnf(c_25,plain,
( essenceInvExistence(A)
| ~ selfCaused(A) ),
inference(clausify,[status(thm)],[self_caused]) ).
cnf(c_26,plain,
( selfCaused(A)
| ~ inItself(A) ),
inference(clausify,[status(thm)],[is_in_itself_is_self_caused]) ).
cnf(c_27,plain,
( exists(A)
| ~ hasEssence(A)
| ~ essenceInvExistence(A) ),
inference(clausify,[status(thm)],[essence_involves_existence_exists]) ).
cnf(c_28,plain,
( essenceInvExistence(A)
| ~ inItself(A) ),
inference(resolve,[status(thm)],[c_26,c_25]) ).
cnf(c_33,plain,
( ~ conceivedThruItself(A)
| ~ inItself(A)
| substance(A) ),
inference(clausify,[status(thm)],[substance]) ).
cnf(c_34,plain,
( conceivedThruItself(A)
| ~ substance(A) ),
inference(clausify,[status(thm)],[substance]) ).
cnf(c_35,plain,
( inItself(A)
| ~ substance(A) ),
inference(clausify,[status(thm)],[substance]) ).
cnf(c_42,plain,
( being(A)
| ~ substance(A) ),
inference(clausify,[status(thm)],[has_substance_being]) ).
fof(nnf_22,plain,
? [X] :
( ~ exists(X)
& substance(X) ),
inference(fof_nnf,[status(thm)],[has_substance_exists_neg]) ).
fof(sk_has_substance_exists_neg,plain,
( ~ exists(sK0)
& substance(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_22]) ).
cnf(c_43,negated_conjecture,
substance(sK0),
inference(split_conjunct,[status(thm)],[sk_has_substance_exists_neg]) ).
cnf(c_44,plain,
( ~ conceivedThruItself(A)
| ~ inItself(A)
| being(A) ),
inference(resolve,[status(thm)],[c_42,c_33]) ).
cnf(c_45,negated_conjecture,
inItself(sK0),
inference(resolve,[status(thm)],[c_43,c_35]) ).
cnf(c_52,plain,
( ~ inItself(A)
| exists(A)
| ~ hasEssence(A) ),
inference(resolve,[status(thm)],[c_27,c_28]) ).
cnf(c_59,plain,
( hasEssence(A)
| ~ being(A) ),
inference(clausify,[status(thm)],[being_has_essense]) ).
cnf(c_60,negated_conjecture,
( ~ conceivedThruItself(sK0)
| being(sK0) ),
inference(resolve,[status(thm)],[c_44,c_45]) ).
cnf(c_145,negated_conjecture,
( exists(sK0)
| ~ hasEssence(sK0) ),
inference(resolve,[status(thm)],[c_52,c_45]) ).
cnf(c_164,negated_conjecture,
~ exists(sK0),
inference(split_conjunct,[status(thm)],[sk_has_substance_exists_neg]) ).
cnf(c_170,negated_conjecture,
conceivedThruItself(sK0),
inference(resolve,[status(thm)],[c_43,c_34]) ).
cnf(c_171,negated_conjecture,
( ~ conceivedThruItself(sK0)
| hasEssence(sK0) ),
inference(resolve,[status(thm)],[c_59,c_60]) ).
cnf(c_172,negated_conjecture,
hasEssence(sK0),
inference(resolve,[status(thm)],[c_170,c_171]) ).
cnf(c_186,negated_conjecture,
exists(sK0),
inference(resolve,[status(thm)],[c_172,c_145]) ).
cnf(c_185,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_164,c_186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI022+1 : TPTP v9.3.1. Released v7.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.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 : Sat Sep 26 04:45:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 930385 was started by sandbox2 on n001,
% 0.09/0.36 % Sat Sep 26 04:45:41 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.40
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40
% 0.13/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.40 % Length of proof is 27.
% 0.13/0.40 % Level of proof is 6.
% 0.13/0.40 % Maximum clause weight is 9.000.
% 0.13/0.40 % Given clauses 0.
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------