%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PHI023+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 : n012.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 0.07s 10.58s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 55 ( 20 ~; 16 |; 9 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 23 ( 0 sgn 10 !; 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(god,axiom,
! [X] :
( god(X)
<=> ( absolutelyInfinite(X)
& being(X) ) ),
file('theBenchmark.p',god) ).
fof(absolutely_infinite,axiom,
! [X,Y] :
( absolutelyInfinite(X)
<=> ( ( attributeOf(Y,X)
=> ( expressesInfiniteEssentiality(Y)
& expressesEternalEssentiality(Y) ) )
& constInInfAttributes(X)
& substance(X) ) ),
file('theBenchmark.p',absolutely_infinite) ).
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(if_god_then_exists,conjecture,
! [X] :
( god(X)
=> exists(X) ),
file('theBenchmark.p',if_god_then_exists) ).
fof(if_god_then_exists_neg,negated_conjecture,
~ ! [X] :
( god(X)
=> exists(X) ),
inference(assume_negation,[status(cth)],[if_god_then_exists]) ).
cnf(c_24,plain,
( essenceInvExistence(A)
| ~ selfCaused(A) ),
inference(clausify,[status(thm)],[self_caused]) ).
cnf(c_25,plain,
( selfCaused(A)
| ~ inItself(A) ),
inference(clausify,[status(thm)],[is_in_itself_is_self_caused]) ).
cnf(c_26,plain,
( exists(A)
| ~ hasEssence(A)
| ~ essenceInvExistence(A) ),
inference(clausify,[status(thm)],[essence_involves_existence_exists]) ).
cnf(c_27,plain,
( essenceInvExistence(A)
| ~ inItself(A) ),
inference(resolve,[status(thm)],[c_25,c_24]) ).
cnf(c_34,plain,
( inItself(A)
| ~ substance(A) ),
inference(clausify,[status(thm)],[substance]) ).
cnf(c_38,plain,
( substance(A)
| ~ absolutelyInfinite(A) ),
inference(clausify,[status(thm)],[absolutely_infinite]) ).
cnf(c_41,plain,
( inItself(A)
| ~ absolutelyInfinite(A) ),
inference(resolve,[status(thm)],[c_38,c_34]) ).
cnf(c_47,plain,
( ~ inItself(A)
| exists(A)
| ~ hasEssence(A) ),
inference(resolve,[status(thm)],[c_26,c_27]) ).
cnf(c_77,plain,
( absolutelyInfinite(A)
| ~ god(A) ),
inference(clausify,[status(thm)],[god]) ).
cnf(c_78,plain,
( being(A)
| ~ god(A) ),
inference(clausify,[status(thm)],[god]) ).
fof(nnf_21,plain,
? [X] :
( ~ exists(X)
& god(X) ),
inference(fof_nnf,[status(thm)],[if_god_then_exists_neg]) ).
fof(sk_if_god_then_exists_neg,plain,
( ~ exists(sK0)
& god(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_21]) ).
cnf(c_79,negated_conjecture,
god(sK0),
inference(split_conjunct,[status(thm)],[sk_if_god_then_exists_neg]) ).
cnf(c_80,plain,
( hasEssence(A)
| ~ being(A) ),
inference(clausify,[status(thm)],[being_has_essense]) ).
cnf(c_81,negated_conjecture,
being(sK0),
inference(resolve,[status(thm)],[c_79,c_78]) ).
cnf(c_87,plain,
( ~ absolutelyInfinite(A)
| exists(A)
| ~ hasEssence(A) ),
inference(resolve,[status(thm)],[c_47,c_41]) ).
cnf(c_91,negated_conjecture,
absolutelyInfinite(sK0),
inference(resolve,[status(thm)],[c_79,c_77]) ).
cnf(c_131,negated_conjecture,
hasEssence(sK0),
inference(resolve,[status(thm)],[c_80,c_81]) ).
cnf(c_146,negated_conjecture,
~ exists(sK0),
inference(split_conjunct,[status(thm)],[sk_if_god_then_exists_neg]) ).
cnf(c_149,negated_conjecture,
( exists(sK0)
| ~ hasEssence(sK0) ),
inference(resolve,[status(thm)],[c_91,c_87]) ).
cnf(c_151,negated_conjecture,
exists(sK0),
inference(resolve,[status(thm)],[c_131,c_149]) ).
cnf(c_150,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_146,c_151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI023+1 : TPTP v9.3.1. Released v7.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/10.56 % Computer : n012.cluster.edu
% 0.07/10.56 % Model : x86_64 x86_64
% 0.07/10.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/10.56 % Memory : 8046.5625MB
% 0.07/10.56 % OS : Linux 6.8.0-71-generic
% 0.07/10.56 % CPULimit : 300
% 0.07/10.56 % WCLimit : 300
% 0.07/10.56 % DateTime : Sat Sep 26 04:40:06 UTC 2026
% 0.07/10.56 % CPUTime :
% 0.07/10.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/10.57 % Process 3921026 was started by sandbox2 on n012,
% 0.07/10.57 % Sat Sep 26 04:40:06 2026
% 0.07/10.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/10.57
% 0.07/10.57 % From the command line: assign(max_seconds, 300).
% 0.07/10.58
% 0.07/10.58 % SZS status Theorem for theBenchmark
% 0.07/10.58
% 0.07/10.58 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.07/10.58 % Length of proof is 27.
% 0.07/10.58 % Level of proof is 6.
% 0.07/10.58 % Maximum clause weight is 2.000.
% 0.07/10.58 % Given clauses 0.
% 0.07/10.58
% 0.07/10.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------