%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PHI014+1 : TPTP v9.3.1. Released v7.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:19:49 AM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 11 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 175 ( 75 ~; 77 |; 14 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 40 ( 3 sgn 11 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(description_theorem_2,axiom,
! [F] :
( property(F)
=> ( ? [Y] :
( is_the(Y,F)
& object(Y) )
=> ! [Z] :
( object(Z)
=> ( is_the(Z,F)
=> exemplifies_property(F,Z) ) ) ) ),
file('theBenchmark.p',description_theorem_2) ).
fof(description_is_property_and_described_is_object,axiom,
! [X,F] :
( is_the(X,F)
=> ( object(X)
& property(F) ) ),
file('theBenchmark.p',description_is_property_and_described_is_object) ).
fof(definition_none_greater,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('theBenchmark.p',definition_none_greater) ).
fof(premise_2,axiom,
! [X] :
( object(X)
=> ( ( ~ exemplifies_property(existence,X)
& is_the(X,none_greater) )
=> ? [Y] :
( exemplifies_property(conceivable,Y)
& exemplifies_relation(greater_than,Y,X)
& object(Y) ) ) ),
file('theBenchmark.p',premise_2) ).
fof(god_exists,conjecture,
exemplifies_property(existence,god),
file('theBenchmark.p',god_exists) ).
fof(god_exists_neg,negated_conjecture,
~ exemplifies_property(existence,god),
inference(assume_negation,[status(cth)],[god_exists]) ).
cnf(c_6,plain,
( property(B)
| ~ is_the(A,B) ),
inference(clausify,[status(thm)],[description_is_property_and_described_is_object]) ).
cnf(c_7,plain,
( exemplifies_property(A,C)
| ~ is_the(C,A)
| ~ object(C)
| ~ is_the(B,A)
| ~ object(B)
| ~ property(A) ),
inference(clausify,[status(thm)],[description_theorem_2]) ).
cnf(c_8,plain,
( ~ exemplifies_property(conceivable,B)
| ~ exemplifies_relation(greater_than,B,A)
| ~ object(B)
| ~ exemplifies_property(none_greater,A)
| ~ object(A) ),
inference(clausify,[status(thm)],[definition_none_greater]) ).
fof(nnf_4,plain,
! [X] :
( ? [Y] :
( exemplifies_property(conceivable,Y)
& exemplifies_relation(greater_than,Y,X)
& object(Y) )
| exemplifies_property(existence,X)
| ~ is_the(X,none_greater)
| ~ object(X) ),
inference(fof_nnf,[status(thm)],[premise_2]) ).
fof(sk_premise_2_sk,plain,
! [X] :
( ( exemplifies_property(conceivable,sK0(X))
& exemplifies_relation(greater_than,sK0(X),X)
& object(sK0(X)) )
| exemplifies_property(existence,X)
| ~ is_the(X,none_greater)
| ~ object(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(X))],[nnf_4]) ).
fof(sk_premise_2,plain,
( ! [VAR_0] :
( exemplifies_property(conceivable,sK0(VAR_0))
| exemplifies_property(existence,VAR_0)
| ~ is_the(VAR_0,none_greater)
| ~ object(VAR_0) )
& ! [VAR_0] :
( exemplifies_relation(greater_than,sK0(VAR_0),VAR_0)
| exemplifies_property(existence,VAR_0)
| ~ is_the(VAR_0,none_greater)
| ~ object(VAR_0) )
& ! [VAR_0] :
( object(sK0(VAR_0))
| exemplifies_property(existence,VAR_0)
| ~ is_the(VAR_0,none_greater)
| ~ object(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_premise_2_sk]) ).
cnf(c_10,plain,
( exemplifies_relation(greater_than,sK0(A),A)
| exemplifies_property(existence,A)
| ~ is_the(A,none_greater)
| ~ object(A) ),
inference(split_conjunct,[status(thm)],[sk_premise_2]) ).
cnf(c_11,plain,
( exemplifies_property(existence,A)
| ~ is_the(A,none_greater)
| ~ object(A)
| ~ exemplifies_property(conceivable,sK0(A))
| ~ object(sK0(A))
| ~ exemplifies_property(none_greater,A)
| ~ object(A) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_12,plain,
( exemplifies_property(existence,A)
| ~ is_the(A,none_greater)
| ~ exemplifies_property(conceivable,sK0(A))
| ~ object(sK0(A))
| ~ exemplifies_property(none_greater,A)
| ~ object(A) ),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_13,plain,
( object(A)
| ~ is_the(A,B) ),
inference(clausify,[status(thm)],[description_is_property_and_described_is_object]) ).
cnf(c_17,plain,
( object(sK0(A))
| exemplifies_property(existence,A)
| ~ is_the(A,none_greater)
| ~ object(A) ),
inference(split_conjunct,[status(thm)],[sk_premise_2]) ).
cnf(c_18,plain,
( exemplifies_property(conceivable,sK0(A))
| exemplifies_property(existence,A)
| ~ is_the(A,none_greater)
| ~ object(A) ),
inference(split_conjunct,[status(thm)],[sk_premise_2]) ).
fof(definition_god,axiom,
is_the(god,none_greater),
file('theBenchmark.p',definition_god) ).
cnf(c_19,plain,
is_the(god,none_greater),
inference(clausify,[status(thm)],[definition_god]) ).
cnf(c_20,negated_conjecture,
~ exemplifies_property(existence,god),
inference(clausify,[status(thm)],[god_exists_neg]) ).
cnf(c_21,plain,
( exemplifies_property(B,D)
| ~ is_the(D,B)
| ~ object(D)
| ~ is_the(C,B)
| ~ object(C)
| ~ is_the(A,B) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_22,plain,
( exemplifies_property(B,C)
| ~ is_the(C,B)
| ~ object(C)
| ~ object(A)
| ~ is_the(A,B) ),
inference(factor,[status(thm)],[c_21]) ).
cnf(c_33,plain,
( exemplifies_property(B,A)
| ~ object(A)
| ~ object(A)
| ~ is_the(A,B) ),
inference(factor,[status(thm)],[c_22]) ).
cnf(c_24,plain,
( exemplifies_property(B,A)
| ~ object(A)
| ~ is_the(A,B) ),
inference(copy,[status(thm)],[c_33]) ).
cnf(c_34,plain,
( exemplifies_property(conceivable,sK0(god))
| exemplifies_property(existence,god)
| ~ object(god) ),
inference(resolve,[status(thm)],[c_19,c_18]) ).
cnf(c_25,negated_conjecture,
( exemplifies_property(conceivable,sK0(god))
| ~ object(god) ),
inference(resolve,[status(thm)],[c_20,c_34]) ).
cnf(c_35,plain,
( object(sK0(god))
| exemplifies_property(existence,god)
| ~ object(god) ),
inference(resolve,[status(thm)],[c_19,c_17]) ).
cnf(c_26,negated_conjecture,
( object(sK0(god))
| ~ object(god) ),
inference(resolve,[status(thm)],[c_20,c_35]) ).
cnf(c_27,plain,
object(god),
inference(resolve,[status(thm)],[c_19,c_13]) ).
cnf(c_36,plain,
( exemplifies_property(existence,god)
| ~ exemplifies_property(conceivable,sK0(god))
| ~ object(sK0(god))
| ~ exemplifies_property(none_greater,god)
| ~ object(god) ),
inference(resolve,[status(thm)],[c_19,c_12]) ).
cnf(c_37,plain,
( exemplifies_property(existence,god)
| ~ exemplifies_property(conceivable,sK0(god))
| ~ object(sK0(god))
| ~ exemplifies_property(none_greater,god) ),
inference(resolve,[status(thm)],[c_27,c_36]) ).
cnf(c_28,negated_conjecture,
( ~ exemplifies_property(conceivable,sK0(god))
| ~ object(sK0(god))
| ~ exemplifies_property(none_greater,god) ),
inference(resolve,[status(thm)],[c_20,c_37]) ).
cnf(c_29,negated_conjecture,
object(sK0(god)),
inference(resolve,[status(thm)],[c_27,c_26]) ).
cnf(c_30,negated_conjecture,
exemplifies_property(conceivable,sK0(god)),
inference(resolve,[status(thm)],[c_27,c_25]) ).
cnf(c_38,negated_conjecture,
( ~ exemplifies_property(conceivable,sK0(god))
| ~ exemplifies_property(none_greater,god) ),
inference(resolve,[status(thm)],[c_29,c_28]) ).
cnf(c_31,negated_conjecture,
~ exemplifies_property(none_greater,god),
inference(resolve,[status(thm)],[c_30,c_38]) ).
cnf(c_39,plain,
( exemplifies_property(none_greater,god)
| ~ object(god) ),
inference(resolve,[status(thm)],[c_24,c_19]) ).
cnf(c_40,plain,
exemplifies_property(none_greater,god),
inference(resolve,[status(thm)],[c_27,c_39]) ).
cnf(c_32,plain,
$false,
inference(resolve,[status(thm)],[c_31,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : PHI014+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n011.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 04:39:44 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 3785469 was started by sandbox on n011,
% 0.17/0.44 % Sat Sep 26 04:39:44 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.46
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 27.
% 0.17/0.46 % Level of proof is 6.
% 0.17/0.46 % Maximum clause weight is 18.000.
% 0.17/0.46 % Given clauses 10.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------