%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PHI010+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 : n009.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 08:19:48 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 215 ( 50 equ)
% Maximal formula atoms : 74 ( 6 avg)
% Number of connectives : 312 ( 129 ~; 128 |; 46 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 97 ( 7 sgn 59 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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(lemma_1,conjecture,
! [X,F,Y] :
( ( object(Y)
& property(F)
& object(X) )
=> ( ( X = Y
& is_the(X,F) )
=> exemplifies_property(F,Y) ) ),
file('theBenchmark.p',lemma_1) ).
fof(lemma_1_neg,negated_conjecture,
~ ! [X,F,Y] :
( ( object(Y)
& property(F)
& object(X) )
=> ( ( X = Y
& is_the(X,F) )
=> exemplifies_property(F,Y) ) ),
inference(assume_negation,[status(cth)],[lemma_1]) ).
cnf(c_8,plain,
( property(B)
| ~ is_the(A,B) ),
inference(clausify,[status(thm)],[description_is_property_and_described_is_object]) ).
fof(nnf_4,plain,
! [F,X,W] :
( ( ( ! [Y] :
( Y != W
| ? [Z] :
( Z != Y
& exemplifies_property(F,Z)
& object(Z) )
| ~ exemplifies_property(F,Y)
| ~ object(Y) )
| ( W = X
& is_the(X,F) ) )
& ( ? [X0] :
( X0 = W
& ! [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] :
( Y != W
| ( sK4(F,X,W,Y) != Y
& exemplifies_property(F,sK4(F,X,W,Y))
& object(sK4(F,X,W,Y)) )
| ~ exemplifies_property(F,Y)
| ~ object(Y) )
| ( W = X
& is_the(X,F) ) )
& ( ( sK0(F,X,W) = 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,sK4]),skolemize(X0,sK0(F,X,W)),skolemize(Z,sK4(F,X,W,Y))],[nnf_4]) ).
fof(sk_description_axiom_identity_instance,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 != VAR_2
| sK4(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_3 != VAR_2
| exemplifies_property(VAR_0,sK4(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_3 != VAR_2
| object(sK4(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_3 != VAR_2
| sK4(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_3 != VAR_2
| exemplifies_property(VAR_0,sK4(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_3 != VAR_2
| object(sK4(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] :
( sK0(VAR_0,VAR_1,VAR_2) = 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_10,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_12,plain,
( sK0(A,B,C) = 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_33,plain,
( ~ is_the(D,C)
| sK0(C,A,B) = B
| B != A
| ~ is_the(A,C)
| ~ object(B)
| ~ object(A) ),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_36,plain,
( ~ is_the(D,C)
| exemplifies_property(C,sK0(C,A,B))
| B != A
| ~ is_the(A,C)
| ~ object(B)
| ~ object(A) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
fof(nnf_5,plain,
? [X,F,Y] :
( ~ exemplifies_property(F,Y)
& Y = X
& is_the(X,F)
& object(Y)
& property(F)
& object(X) ),
inference(fof_nnf,[status(thm)],[lemma_1_neg]) ).
fof(sk_lemma_1_neg,plain,
( ~ exemplifies_property(sK1,sK2)
& sK2 = sK3
& is_the(sK3,sK1)
& object(sK2)
& property(sK1)
& object(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK2]),skolemize(X,sK3),skolemize(F,sK1),skolemize(Y,sK2)],[nnf_5]) ).
cnf(c_40,negated_conjecture,
~ exemplifies_property(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_lemma_1_neg]) ).
cnf(c_41,negated_conjecture,
sK2 = sK3,
inference(split_conjunct,[status(thm)],[sk_lemma_1_neg]) ).
cnf(c_42,negated_conjecture,
is_the(sK3,sK1),
inference(split_conjunct,[status(thm)],[sk_lemma_1_neg]) ).
cnf(c_43,negated_conjecture,
object(sK2),
inference(split_conjunct,[status(thm)],[sk_lemma_1_neg]) ).
cnf(c_44,negated_conjecture,
object(sK3),
inference(paramod,[status(thm)],[c_41,c_43]) ).
cnf(c_133,plain,
( ~ is_the(C,B)
| sK0(B,A,A) = A
| A != A
| ~ is_the(A,B)
| ~ object(A) ),
inference(factor,[status(thm)],[c_33]) ).
cnf(c_83,plain,
( ~ is_the(C,B)
| sK0(B,A,A) = A
| ~ is_the(A,B)
| ~ object(A) ),
inference(copy,[status(thm)],[c_133]) ).
cnf(c_134,plain,
( ~ is_the(C,B)
| exemplifies_property(B,sK0(B,A,A))
| A != A
| ~ is_the(A,B)
| ~ object(A) ),
inference(factor,[status(thm)],[c_36]) ).
cnf(c_88,plain,
( ~ is_the(C,B)
| exemplifies_property(B,sK0(B,A,A))
| ~ is_the(A,B)
| ~ object(A) ),
inference(copy,[status(thm)],[c_134]) ).
cnf(c_92,negated_conjecture,
~ exemplifies_property(sK1,sK3),
inference(paramod,[status(thm)],[c_41,c_40]) ).
cnf(c_114,plain,
( sK0(B,A,A) = A
| ~ is_the(A,B)
| ~ object(A) ),
inference(factor,[status(thm)],[c_83]) ).
cnf(c_117,plain,
( exemplifies_property(B,sK0(B,A,A))
| ~ is_the(A,B)
| ~ object(A) ),
inference(factor,[status(thm)],[c_88]) ).
cnf(c_135,negated_conjecture,
( sK0(sK1,sK3,sK3) = sK3
| ~ object(sK3) ),
inference(resolve,[status(thm)],[c_114,c_42]) ).
cnf(c_130,negated_conjecture,
sK0(sK1,sK3,sK3) = sK3,
inference(resolve,[status(thm)],[c_44,c_135]) ).
cnf(c_136,negated_conjecture,
( exemplifies_property(sK1,sK0(sK1,sK3,sK3))
| ~ object(sK3) ),
inference(resolve,[status(thm)],[c_117,c_42]) ).
cnf(c_137,negated_conjecture,
( exemplifies_property(sK1,sK3)
| ~ object(sK3) ),
inference(paramod,[status(thm)],[c_130,c_136]) ).
cnf(c_138,negated_conjecture,
exemplifies_property(sK1,sK3),
inference(resolve,[status(thm)],[c_44,c_137]) ).
cnf(c_132,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_92,c_138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI010+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.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 04:39:30 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3366131 was started by sandbox on n009,
% 0.09/0.37 % Sat Sep 26 04:39:30 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 20.
% 0.09/0.40 % Level of proof is 6.
% 0.09/0.40 % Maximum clause weight is 19.000.
% 0.09/0.40 % Given clauses 38.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------