%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PHI012+1 : TPTP v9.3.1. Released v7.2.0.
% 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 08:19:49 AM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 123 ( 13 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 143 ( 59 ~; 53 |; 22 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 30 ( 0 sgn 10 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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(connectedness_of_greater_than,axiom,
! [X,Y] :
( ( object(Y)
& object(X) )
=> ( X = Y
| exemplifies_relation(greater_than,Y,X)
| exemplifies_relation(greater_than,X,Y) ) ),
file('theBenchmark.p',connectedness_of_greater_than) ).
fof(lemma_2,conjecture,
( ? [X] :
( exemplifies_property(none_greater,X)
& object(X) )
=> ? [X] :
( ! [Y] :
( object(Y)
=> ( exemplifies_property(none_greater,Y)
=> Y = X ) )
& exemplifies_property(none_greater,X)
& object(X) ) ),
file('theBenchmark.p',lemma_2) ).
fof(lemma_2_neg,negated_conjecture,
~ ( ? [X] :
( exemplifies_property(none_greater,X)
& object(X) )
=> ? [X] :
( ! [Y] :
( object(Y)
=> ( exemplifies_property(none_greater,Y)
=> Y = X ) )
& exemplifies_property(none_greater,X)
& object(X) ) ),
inference(assume_negation,[status(cth)],[lemma_2]) ).
cnf(c_4,plain,
( exemplifies_property(conceivable,A)
| ~ exemplifies_property(none_greater,A)
| ~ object(A) ),
inference(clausify,[status(thm)],[definition_none_greater]) ).
cnf(c_5,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]) ).
cnf(c_9,plain,
( B = A
| exemplifies_relation(greater_than,B,A)
| exemplifies_relation(greater_than,A,B)
| ~ object(B)
| ~ object(A) ),
inference(clausify,[status(thm)],[connectedness_of_greater_than]) ).
fof(nnf_3,plain,
( ! [X] :
( ? [Y] :
( Y != X
& exemplifies_property(none_greater,Y)
& object(Y) )
| ~ exemplifies_property(none_greater,X)
| ~ object(X) )
& ? [X0] :
( exemplifies_property(none_greater,X0)
& object(X0) ) ),
inference(fof_nnf,[status(thm)],[lemma_2_neg]) ).
fof(sk_lemma_2_neg_sk,plain,
( ! [X] :
( ( sK1(X) != X
& exemplifies_property(none_greater,sK1(X))
& object(sK1(X)) )
| ~ exemplifies_property(none_greater,X)
| ~ object(X) )
& exemplifies_property(none_greater,sK0)
& object(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(Y,sK1(X))],[nnf_3]) ).
fof(sk_lemma_2_neg,plain,
( ! [VAR_0] :
( sK1(VAR_0) != VAR_0
| ~ exemplifies_property(none_greater,VAR_0)
| ~ object(VAR_0) )
& ! [VAR_0] :
( exemplifies_property(none_greater,sK1(VAR_0))
| ~ exemplifies_property(none_greater,VAR_0)
| ~ object(VAR_0) )
& ! [VAR_0] :
( object(sK1(VAR_0))
| ~ exemplifies_property(none_greater,VAR_0)
| ~ object(VAR_0) )
& exemplifies_property(none_greater,sK0)
& object(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_lemma_2_neg_sk]) ).
cnf(c_10,negated_conjecture,
object(sK0),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_11,negated_conjecture,
exemplifies_property(none_greater,sK0),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_12,negated_conjecture,
( object(sK1(A))
| ~ exemplifies_property(none_greater,A)
| ~ object(A) ),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_13,negated_conjecture,
( exemplifies_property(none_greater,sK1(A))
| ~ exemplifies_property(none_greater,A)
| ~ object(A) ),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_14,negated_conjecture,
( sK1(A) != A
| ~ exemplifies_property(none_greater,A)
| ~ object(A) ),
inference(split_conjunct,[status(thm)],[sk_lemma_2_neg]) ).
cnf(c_16,plain,
( sK0 = A
| exemplifies_relation(greater_than,sK0,A)
| exemplifies_relation(greater_than,A,sK0)
| ~ object(A) ),
inference(resolve,[status(thm)],[c_10,c_9]) ).
cnf(c_34,negated_conjecture,
( exemplifies_property(conceivable,sK0)
| ~ object(sK0) ),
inference(resolve,[status(thm)],[c_11,c_4]) ).
cnf(c_17,negated_conjecture,
exemplifies_property(conceivable,sK0),
inference(resolve,[status(thm)],[c_10,c_34]) ).
cnf(c_35,negated_conjecture,
( object(sK1(sK0))
| ~ object(sK0) ),
inference(resolve,[status(thm)],[c_12,c_11]) ).
cnf(c_18,negated_conjecture,
object(sK1(sK0)),
inference(resolve,[status(thm)],[c_10,c_35]) ).
cnf(c_36,negated_conjecture,
( exemplifies_property(none_greater,sK1(sK0))
| ~ object(sK0) ),
inference(resolve,[status(thm)],[c_13,c_11]) ).
cnf(c_19,negated_conjecture,
exemplifies_property(none_greater,sK1(sK0)),
inference(resolve,[status(thm)],[c_10,c_36]) ).
cnf(c_37,negated_conjecture,
( sK1(sK0) != sK0
| ~ object(sK0) ),
inference(resolve,[status(thm)],[c_14,c_11]) ).
cnf(c_20,negated_conjecture,
sK1(sK0) != sK0,
inference(resolve,[status(thm)],[c_10,c_37]) ).
cnf(c_38,plain,
( sK0 = sK1(sK0)
| exemplifies_relation(greater_than,sK0,sK1(sK0))
| exemplifies_relation(greater_than,sK1(sK0),sK0) ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_39,plain,
( sK1(sK0) = sK0
| exemplifies_relation(greater_than,sK0,sK1(sK0))
| exemplifies_relation(greater_than,sK1(sK0),sK0) ),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_22,plain,
( exemplifies_relation(greater_than,sK0,sK1(sK0))
| exemplifies_relation(greater_than,sK1(sK0),sK0) ),
inference(resolve,[status(thm)],[c_20,c_39]) ).
cnf(c_40,plain,
( exemplifies_property(conceivable,sK1(sK0))
| ~ object(sK1(sK0)) ),
inference(resolve,[status(thm)],[c_19,c_4]) ).
cnf(c_27,plain,
exemplifies_property(conceivable,sK1(sK0)),
inference(resolve,[status(thm)],[c_18,c_40]) ).
cnf(c_41,plain,
( ~ exemplifies_property(conceivable,A)
| ~ exemplifies_relation(greater_than,A,sK1(sK0))
| ~ object(A)
| ~ exemplifies_property(none_greater,sK1(sK0)) ),
inference(resolve,[status(thm)],[c_5,c_18]) ).
cnf(c_42,plain,
( ~ exemplifies_property(conceivable,A)
| ~ exemplifies_relation(greater_than,A,sK1(sK0))
| ~ object(A) ),
inference(resolve,[status(thm)],[c_41,c_19]) ).
cnf(c_43,negated_conjecture,
( ~ exemplifies_property(conceivable,sK0)
| ~ exemplifies_relation(greater_than,sK0,sK1(sK0)) ),
inference(resolve,[status(thm)],[c_42,c_10]) ).
cnf(c_28,negated_conjecture,
~ exemplifies_relation(greater_than,sK0,sK1(sK0)),
inference(resolve,[status(thm)],[c_43,c_17]) ).
cnf(c_29,plain,
exemplifies_relation(greater_than,sK1(sK0),sK0),
inference(resolve,[status(thm)],[c_28,c_22]) ).
cnf(c_44,negated_conjecture,
( ~ exemplifies_property(conceivable,A)
| ~ exemplifies_relation(greater_than,A,sK0)
| ~ object(A)
| ~ exemplifies_property(none_greater,sK0) ),
inference(resolve,[status(thm)],[c_5,c_10]) ).
cnf(c_45,negated_conjecture,
( ~ exemplifies_property(conceivable,A)
| ~ exemplifies_relation(greater_than,A,sK0)
| ~ object(A) ),
inference(resolve,[status(thm)],[c_44,c_11]) ).
cnf(c_46,negated_conjecture,
( ~ exemplifies_property(conceivable,sK1(sK0))
| ~ exemplifies_relation(greater_than,sK1(sK0),sK0) ),
inference(resolve,[status(thm)],[c_45,c_18]) ).
cnf(c_47,negated_conjecture,
~ exemplifies_relation(greater_than,sK1(sK0),sK0),
inference(resolve,[status(thm)],[c_46,c_27]) ).
cnf(c_33,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_29,c_47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI012+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n001.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 04:44:57 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 928239 was started by sandbox2 on n001,
% 0.09/0.35 % Sat Sep 26 04:44:57 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 21.
% 0.13/0.37 % Level of proof is 5.
% 0.13/0.37 % Maximum clause weight is 15.000.
% 0.13/0.37 % Given clauses 22.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------