%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PHI015+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 : n020.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 1.32s 0.59s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 15 unt; 0 def)
% Number of atoms : 290 ( 52 equ)
% Maximal formula atoms : 74 ( 5 avg)
% Number of connectives : 402 ( 170 ~; 176 |; 46 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 96 ( 2 sgn 62 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(exemplifier_is_object_and_exemplified_is_property,axiom,
! [X,F] :
( exemplifies_property(F,X)
=> ( object(X)
& property(F) ) ),
file('theBenchmark.p',exemplifier_is_object_and_exemplified_is_property) ).
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(description_axiom_identity_instance,axiom,
! [F,X,W] :
( ( object(W)
& object(X)
& property(F) )
=> ( ( X = W
& is_the(X,F) )
<=> ? [Y] :
( Y = W
& ! [Z] :
( object(Z)
=> ( exemplifies_property(F,Z)
=> Z = Y ) )
& exemplifies_property(F,Y)
& object(Y) ) ) ),
file('theBenchmark.p',description_axiom_identity_instance) ).
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_1,axiom,
? [X] :
( exemplifies_property(none_greater,X)
& object(X) ),
file('theBenchmark.p',premise_1) ).
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_12,plain,
( property(A)
| ~ exemplifies_property(A,B) ),
inference(clausify,[status(thm)],[exemplifier_is_object_and_exemplified_is_property]) ).
cnf(c_15,plain,
( object(A)
| ~ is_the(A,B) ),
inference(clausify,[status(thm)],[description_is_property_and_described_is_object]) ).
fof(nnf_5,plain,
! [F,X,W] :
( ( ( ! [Y] :
( W != Y
| ? [Z] :
( Z != Y
& exemplifies_property(F,Z)
& object(Z) )
| ~ exemplifies_property(F,Y)
| ~ object(Y) )
| ( W = X
& is_the(X,F) ) )
& ( ? [X0] :
( W = X0
& ! [X1] :
( X1 = X0
| ~ exemplifies_property(F,X1)
| ~ object(X1) )
& exemplifies_property(F,X0)
& object(X0) )
| W != X
| ~ is_the(X,F) ) )
| ~ object(W)
| ~ object(X)
| ~ property(F) ),
inference(fof_nnf,[status(thm)],[description_axiom_identity_instance]) ).
fof(sk_description_axiom_identity_instance_sk,plain,
! [F,X,W] :
( ( ( ! [Y] :
( W != Y
| ( sK3(F,X,W,Y) != Y
& exemplifies_property(F,sK3(F,X,W,Y))
& object(sK3(F,X,W,Y)) )
| ~ exemplifies_property(F,Y)
| ~ object(Y) )
| ( W = X
& is_the(X,F) ) )
& ( ( W = sK0(F,X,W)
& ! [X1] :
( X1 = sK0(F,X,W)
| ~ exemplifies_property(F,X1)
| ~ object(X1) )
& exemplifies_property(F,sK0(F,X,W))
& object(sK0(F,X,W)) )
| W != X
| ~ is_the(X,F) ) )
| ~ object(W)
| ~ object(X)
| ~ property(F) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3]),skolemize(X0,sK0(F,X,W)),skolemize(Z,sK3(F,X,W,Y))],[nnf_5]) ).
fof(sk_description_axiom_identity_instance,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 != VAR_3
| sK3(VAR_0,VAR_1,VAR_2,VAR_3) != VAR_3
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| VAR_2 = VAR_1
| ~ object(VAR_2)
| ~ object(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 != VAR_3
| exemplifies_property(VAR_0,sK3(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| VAR_2 = VAR_1
| ~ object(VAR_2)
| ~ object(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 != VAR_3
| object(sK3(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| VAR_2 = VAR_1
| ~ object(VAR_2)
| ~ object(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 != VAR_3
| sK3(VAR_0,VAR_1,VAR_2,VAR_3) != VAR_3
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| is_the(VAR_1,VAR_0)
| ~ object(VAR_2)
| ~ object(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 != VAR_3
| exemplifies_property(VAR_0,sK3(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| is_the(VAR_1,VAR_0)
| ~ object(VAR_2)
| ~ object(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 != VAR_3
| object(sK3(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| is_the(VAR_1,VAR_0)
| ~ object(VAR_2)
| ~ object(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = sK0(VAR_0,VAR_1,VAR_2)
| VAR_2 != VAR_1
| ~ is_the(VAR_1,VAR_0)
| ~ object(VAR_2)
| ~ object(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = sK0(VAR_0,VAR_1,VAR_2)
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| VAR_2 != VAR_1
| ~ is_the(VAR_1,VAR_0)
| ~ object(VAR_2)
| ~ object(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( exemplifies_property(VAR_0,sK0(VAR_0,VAR_1,VAR_2))
| VAR_2 != VAR_1
| ~ is_the(VAR_1,VAR_0)
| ~ object(VAR_2)
| ~ object(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( object(sK0(VAR_0,VAR_1,VAR_2))
| VAR_2 != VAR_1
| ~ is_the(VAR_1,VAR_0)
| ~ object(VAR_2)
| ~ object(VAR_1)
| ~ property(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_description_axiom_identity_instance_sk]) ).
cnf(c_28,plain,
( exemplifies_property(A,sK0(A,B,C))
| C != B
| ~ is_the(B,A)
| ~ object(C)
| ~ object(B)
| ~ property(A) ),
inference(split_conjunct,[status(thm)],[sk_description_axiom_identity_instance]) ).
cnf(c_31,plain,
( C = sK0(A,B,C)
| C != B
| ~ is_the(B,A)
| ~ object(C)
| ~ object(B)
| ~ property(A) ),
inference(split_conjunct,[status(thm)],[sk_description_axiom_identity_instance]) ).
cnf(c_32,plain,
( sK0(A,B,C) = C
| C != B
| ~ is_the(B,A)
| ~ object(C)
| ~ object(B)
| ~ property(A) ),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_41,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_8,plain,
? [X] :
( exemplifies_property(none_greater,X)
& object(X) ),
inference(fof_nnf,[status(thm)],[premise_1]) ).
fof(sk_premise_1,plain,
( exemplifies_property(none_greater,sK1)
& object(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X,sK1)],[nnf_8]) ).
cnf(c_46,plain,
exemplifies_property(none_greater,sK1),
inference(split_conjunct,[status(thm)],[sk_premise_1]) ).
fof(nnf_9,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,sK2(X))
& exemplifies_relation(greater_than,sK2(X),X)
& object(sK2(X)) )
| exemplifies_property(existence,X)
| ~ is_the(X,none_greater)
| ~ object(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(Y,sK2(X))],[nnf_9]) ).
fof(sk_premise_2,plain,
( ! [VAR_0] :
( exemplifies_property(conceivable,sK2(VAR_0))
| exemplifies_property(existence,VAR_0)
| ~ is_the(VAR_0,none_greater)
| ~ object(VAR_0) )
& ! [VAR_0] :
( exemplifies_relation(greater_than,sK2(VAR_0),VAR_0)
| exemplifies_property(existence,VAR_0)
| ~ is_the(VAR_0,none_greater)
| ~ object(VAR_0) )
& ! [VAR_0] :
( object(sK2(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_47,plain,
( object(sK2(A))
| exemplifies_property(existence,A)
| ~ is_the(A,none_greater)
| ~ object(A) ),
inference(split_conjunct,[status(thm)],[sk_premise_2]) ).
cnf(c_48,plain,
( exemplifies_relation(greater_than,sK2(A),A)
| exemplifies_property(existence,A)
| ~ is_the(A,none_greater)
| ~ object(A) ),
inference(split_conjunct,[status(thm)],[sk_premise_2]) ).
cnf(c_49,plain,
( exemplifies_property(conceivable,sK2(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_50,plain,
is_the(god,none_greater),
inference(clausify,[status(thm)],[definition_god]) ).
cnf(c_51,negated_conjecture,
~ exemplifies_property(existence,god),
inference(clausify,[status(thm)],[god_exists_neg]) ).
cnf(c_111,plain,
property(none_greater),
inference(resolve,[status(thm)],[c_46,c_12]) ).
cnf(c_427,plain,
( exemplifies_property(conceivable,sK2(god))
| exemplifies_property(existence,god)
| ~ object(god) ),
inference(resolve,[status(thm)],[c_50,c_49]) ).
cnf(c_139,negated_conjecture,
( exemplifies_property(conceivable,sK2(god))
| ~ object(god) ),
inference(resolve,[status(thm)],[c_51,c_427]) ).
cnf(c_428,plain,
( exemplifies_relation(greater_than,sK2(god),god)
| exemplifies_property(existence,god)
| ~ object(god) ),
inference(resolve,[status(thm)],[c_50,c_48]) ).
cnf(c_140,negated_conjecture,
( exemplifies_relation(greater_than,sK2(god),god)
| ~ object(god) ),
inference(resolve,[status(thm)],[c_51,c_428]) ).
cnf(c_429,plain,
( object(sK2(god))
| exemplifies_property(existence,god)
| ~ object(god) ),
inference(resolve,[status(thm)],[c_50,c_47]) ).
cnf(c_141,negated_conjecture,
( object(sK2(god))
| ~ object(god) ),
inference(resolve,[status(thm)],[c_51,c_429]) ).
cnf(c_430,plain,
( sK0(none_greater,god,A) = A
| A != god
| ~ object(A)
| ~ object(god)
| ~ property(none_greater) ),
inference(resolve,[status(thm)],[c_50,c_32]) ).
cnf(c_431,plain,
( sK0(none_greater,god,A) = A
| god != A
| ~ object(A)
| ~ object(god)
| ~ property(none_greater) ),
inference(copy,[status(thm)],[c_430]) ).
cnf(c_142,plain,
( sK0(none_greater,god,A) = A
| god != A
| ~ object(A)
| ~ object(god) ),
inference(resolve,[status(thm)],[c_111,c_431]) ).
cnf(c_432,plain,
( exemplifies_property(none_greater,sK0(none_greater,god,A))
| A != god
| ~ object(A)
| ~ object(god)
| ~ property(none_greater) ),
inference(resolve,[status(thm)],[c_50,c_28]) ).
cnf(c_433,plain,
( exemplifies_property(none_greater,sK0(none_greater,god,A))
| god != A
| ~ object(A)
| ~ object(god)
| ~ property(none_greater) ),
inference(copy,[status(thm)],[c_432]) ).
cnf(c_144,plain,
( exemplifies_property(none_greater,sK0(none_greater,god,A))
| god != A
| ~ object(A)
| ~ object(god) ),
inference(resolve,[status(thm)],[c_111,c_433]) ).
cnf(c_150,plain,
object(god),
inference(resolve,[status(thm)],[c_50,c_15]) ).
cnf(c_434,plain,
( sK0(none_greater,god,god) = god
| god != god
| ~ object(god) ),
inference(factor,[status(thm)],[c_142]) ).
cnf(c_435,plain,
( sK0(none_greater,god,god) = god
| ~ object(god) ),
inference(copy,[status(thm)],[c_434]) ).
cnf(c_151,plain,
sK0(none_greater,god,god) = god,
inference(resolve,[status(thm)],[c_150,c_435]) ).
cnf(c_436,plain,
( exemplifies_property(none_greater,sK0(none_greater,god,god))
| god != god
| ~ object(god) ),
inference(factor,[status(thm)],[c_144]) ).
cnf(c_437,plain,
( exemplifies_property(none_greater,god)
| god != god
| ~ object(god) ),
inference(paramod,[status(thm)],[c_151,c_436]) ).
cnf(c_438,plain,
( exemplifies_property(none_greater,god)
| ~ object(god) ),
inference(copy,[status(thm)],[c_437]) ).
cnf(c_155,plain,
exemplifies_property(none_greater,god),
inference(resolve,[status(thm)],[c_150,c_438]) ).
cnf(c_166,negated_conjecture,
object(sK2(god)),
inference(resolve,[status(thm)],[c_150,c_141]) ).
cnf(c_167,negated_conjecture,
exemplifies_relation(greater_than,sK2(god),god),
inference(resolve,[status(thm)],[c_150,c_140]) ).
cnf(c_168,negated_conjecture,
exemplifies_property(conceivable,sK2(god)),
inference(resolve,[status(thm)],[c_150,c_139]) ).
cnf(c_439,plain,
( ~ exemplifies_property(conceivable,A)
| ~ exemplifies_relation(greater_than,A,god)
| ~ object(A)
| ~ exemplifies_property(none_greater,god) ),
inference(resolve,[status(thm)],[c_41,c_150]) ).
cnf(c_440,plain,
( ~ exemplifies_property(conceivable,A)
| ~ exemplifies_relation(greater_than,A,god)
| ~ object(A) ),
inference(resolve,[status(thm)],[c_439,c_155]) ).
cnf(c_441,plain,
( ~ exemplifies_property(conceivable,sK2(god))
| ~ exemplifies_relation(greater_than,sK2(god),god) ),
inference(resolve,[status(thm)],[c_440,c_166]) ).
cnf(c_442,plain,
~ exemplifies_relation(greater_than,sK2(god),god),
inference(resolve,[status(thm)],[c_441,c_168]) ).
cnf(c_426,plain,
$false,
inference(resolve,[status(thm)],[c_167,c_442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI015+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.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 : Sat Sep 26 04:40:34 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 627316 was started by sandbox on n020,
% 0.09/0.36 % Sat Sep 26 04:40:34 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 1.32/0.59
% 1.32/0.59 % SZS status Theorem for theBenchmark
% 1.32/0.59
% 1.32/0.59 % Proof 1 at 0.17 (+ 0.02) seconds.
% 1.32/0.59 % Length of proof is 32.
% 1.32/0.59 % Level of proof is 6.
% 1.32/0.59 % Maximum clause weight is 28.000.
% 1.32/0.59 % Given clauses 103.
% 1.32/0.59
% 1.32/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------