%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PHI009+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 : 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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 280 ( 24 equ)
% Maximal formula atoms : 74 ( 6 avg)
% Number of connectives : 409 ( 172 ~; 182 |; 43 &)
% ( 1 <=>; 11 =>; 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 : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 107 ( 0 sgn 59 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(description_axiom_schema_instance,axiom,
! [F,G,X] :
( ( object(X)
& property(G)
& property(F) )
=> ( ( exemplifies_property(G,X)
& is_the(X,F) )
<=> ? [Y] :
( exemplifies_property(G,Y)
& ! [Z] :
( object(Z)
=> ( exemplifies_property(F,Z)
=> Z = Y ) )
& exemplifies_property(F,Y)
& object(Y) ) ) ),
file('theBenchmark.p',description_axiom_schema_instance) ).
fof(description_theorem_1,conjecture,
! [F] :
( property(F)
=> ( ? [Y] :
( ! [Z] :
( object(Z)
=> ( exemplifies_property(F,Z)
=> Z = Y ) )
& exemplifies_property(F,Y)
& object(Y) )
=> ? [U] :
( is_the(U,F)
& object(U) ) ) ),
file('theBenchmark.p',description_theorem_1) ).
fof(description_theorem_1_neg,negated_conjecture,
~ ! [F] :
( property(F)
=> ( ? [Y] :
( ! [Z] :
( object(Z)
=> ( exemplifies_property(F,Z)
=> Z = Y ) )
& exemplifies_property(F,Y)
& object(Y) )
=> ? [U] :
( is_the(U,F)
& object(U) ) ) ),
inference(assume_negation,[status(cth)],[description_theorem_1]) ).
fof(nnf_1,plain,
! [F,G,X] :
( ( ( ! [Y] :
( ~ exemplifies_property(G,Y)
| ? [Z] :
( Z != Y
& exemplifies_property(F,Z)
& object(Z) )
| ~ exemplifies_property(F,Y)
| ~ object(Y) )
| ( exemplifies_property(G,X)
& is_the(X,F) ) )
& ( ? [X0] :
( exemplifies_property(G,X0)
& ! [X1] :
( X1 = X0
| ~ exemplifies_property(F,X1)
| ~ object(X1) )
& exemplifies_property(F,X0)
& object(X0) )
| ~ exemplifies_property(G,X)
| ~ is_the(X,F) ) )
| ~ object(X)
| ~ property(G)
| ~ property(F) ),
inference(fof_nnf,[status(thm)],[description_axiom_schema_instance]) ).
fof(sk_description_axiom_schema_instance_sk,plain,
! [F,G,X] :
( ( ( ! [Y] :
( ~ exemplifies_property(G,Y)
| ( sK0(F,G,X,Y) != Y
& exemplifies_property(F,sK0(F,G,X,Y))
& object(sK0(F,G,X,Y)) )
| ~ exemplifies_property(F,Y)
| ~ object(Y) )
| ( exemplifies_property(G,X)
& is_the(X,F) ) )
& ( ( exemplifies_property(G,sK3(F,G,X))
& ! [X1] :
( X1 = sK3(F,G,X)
| ~ exemplifies_property(F,X1)
| ~ object(X1) )
& exemplifies_property(F,sK3(F,G,X))
& object(sK3(F,G,X)) )
| ~ exemplifies_property(G,X)
| ~ is_the(X,F) ) )
| ~ object(X)
| ~ property(G)
| ~ property(F) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK0]),skolemize(X0,sK3(F,G,X)),skolemize(Z,sK0(F,G,X,Y))],[nnf_1]) ).
fof(sk_description_axiom_schema_instance,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ exemplifies_property(VAR_1,VAR_3)
| sK0(VAR_0,VAR_1,VAR_2,VAR_3) != VAR_3
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| exemplifies_property(VAR_1,VAR_2)
| ~ object(VAR_2)
| ~ property(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ exemplifies_property(VAR_1,VAR_3)
| exemplifies_property(VAR_0,sK0(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| exemplifies_property(VAR_1,VAR_2)
| ~ object(VAR_2)
| ~ property(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ exemplifies_property(VAR_1,VAR_3)
| object(sK0(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| exemplifies_property(VAR_1,VAR_2)
| ~ object(VAR_2)
| ~ property(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ exemplifies_property(VAR_1,VAR_3)
| sK0(VAR_0,VAR_1,VAR_2,VAR_3) != VAR_3
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| is_the(VAR_2,VAR_0)
| ~ object(VAR_2)
| ~ property(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ exemplifies_property(VAR_1,VAR_3)
| exemplifies_property(VAR_0,sK0(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| is_the(VAR_2,VAR_0)
| ~ object(VAR_2)
| ~ property(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ exemplifies_property(VAR_1,VAR_3)
| object(sK0(VAR_0,VAR_1,VAR_2,VAR_3))
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| is_the(VAR_2,VAR_0)
| ~ object(VAR_2)
| ~ property(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( exemplifies_property(VAR_1,sK3(VAR_0,VAR_1,VAR_2))
| ~ exemplifies_property(VAR_1,VAR_2)
| ~ is_the(VAR_2,VAR_0)
| ~ object(VAR_2)
| ~ property(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = sK3(VAR_0,VAR_1,VAR_2)
| ~ exemplifies_property(VAR_0,VAR_3)
| ~ object(VAR_3)
| ~ exemplifies_property(VAR_1,VAR_2)
| ~ is_the(VAR_2,VAR_0)
| ~ object(VAR_2)
| ~ property(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( exemplifies_property(VAR_0,sK3(VAR_0,VAR_1,VAR_2))
| ~ exemplifies_property(VAR_1,VAR_2)
| ~ is_the(VAR_2,VAR_0)
| ~ object(VAR_2)
| ~ property(VAR_1)
| ~ property(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( object(sK3(VAR_0,VAR_1,VAR_2))
| ~ exemplifies_property(VAR_1,VAR_2)
| ~ is_the(VAR_2,VAR_0)
| ~ object(VAR_2)
| ~ property(VAR_1)
| ~ property(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_description_axiom_schema_instance_sk]) ).
cnf(c_8,plain,
( ~ exemplifies_property(B,D)
| object(sK0(A,B,C,D))
| ~ exemplifies_property(A,D)
| ~ object(D)
| is_the(C,A)
| ~ object(C)
| ~ property(B)
| ~ property(A) ),
inference(split_conjunct,[status(thm)],[sk_description_axiom_schema_instance]) ).
cnf(c_9,plain,
( ~ exemplifies_property(B,D)
| exemplifies_property(A,sK0(A,B,C,D))
| ~ exemplifies_property(A,D)
| ~ object(D)
| is_the(C,A)
| ~ object(C)
| ~ property(B)
| ~ property(A) ),
inference(split_conjunct,[status(thm)],[sk_description_axiom_schema_instance]) ).
cnf(c_10,plain,
( ~ exemplifies_property(B,D)
| sK0(A,B,C,D) != D
| ~ exemplifies_property(A,D)
| ~ object(D)
| is_the(C,A)
| ~ object(C)
| ~ property(B)
| ~ property(A) ),
inference(split_conjunct,[status(thm)],[sk_description_axiom_schema_instance]) ).
fof(nnf_2,plain,
? [F] :
( ! [U] :
( ~ is_the(U,F)
| ~ object(U) )
& ? [Y] :
( ! [Z] :
( Z = Y
| ~ exemplifies_property(F,Z)
| ~ object(Z) )
& exemplifies_property(F,Y)
& object(Y) )
& property(F) ),
inference(fof_nnf,[status(thm)],[description_theorem_1_neg]) ).
fof(sk_description_theorem_1_neg,plain,
( ! [U] :
( ~ is_the(U,sK1)
| ~ object(U) )
& ! [Z] :
( Z = sK2
| ~ exemplifies_property(sK1,Z)
| ~ object(Z) )
& exemplifies_property(sK1,sK2)
& object(sK2)
& property(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(F,sK1),skolemize(Y,sK2)],[nnf_2]) ).
cnf(c_14,negated_conjecture,
property(sK1),
inference(split_conjunct,[status(thm)],[sk_description_theorem_1_neg]) ).
cnf(c_15,negated_conjecture,
object(sK2),
inference(split_conjunct,[status(thm)],[sk_description_theorem_1_neg]) ).
cnf(c_16,negated_conjecture,
exemplifies_property(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_description_theorem_1_neg]) ).
cnf(c_17,negated_conjecture,
( A = sK2
| ~ exemplifies_property(sK1,A)
| ~ object(A) ),
inference(split_conjunct,[status(thm)],[sk_description_theorem_1_neg]) ).
cnf(c_18,negated_conjecture,
( sK2 = A
| ~ exemplifies_property(sK1,A)
| ~ object(A) ),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_19,negated_conjecture,
( ~ is_the(A,sK1)
| ~ object(A) ),
inference(split_conjunct,[status(thm)],[sk_description_theorem_1_neg]) ).
cnf(c_67,plain,
( ~ exemplifies_property(A,C)
| object(sK0(A,A,B,C))
| ~ exemplifies_property(A,C)
| ~ object(C)
| is_the(B,A)
| ~ object(B)
| ~ property(A) ),
inference(factor,[status(thm)],[c_8]) ).
cnf(c_25,plain,
( object(sK0(A,A,B,C))
| ~ exemplifies_property(A,C)
| ~ object(C)
| is_the(B,A)
| ~ object(B)
| ~ property(A) ),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_68,plain,
( ~ exemplifies_property(A,C)
| exemplifies_property(A,sK0(A,A,B,C))
| ~ exemplifies_property(A,C)
| ~ object(C)
| is_the(B,A)
| ~ object(B)
| ~ property(A) ),
inference(factor,[status(thm)],[c_9]) ).
cnf(c_27,plain,
( exemplifies_property(A,sK0(A,A,B,C))
| ~ exemplifies_property(A,C)
| ~ object(C)
| is_the(B,A)
| ~ object(B)
| ~ property(A) ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_69,plain,
( ~ exemplifies_property(A,C)
| sK0(A,A,B,C) != C
| ~ exemplifies_property(A,C)
| ~ object(C)
| is_the(B,A)
| ~ object(B)
| ~ property(A) ),
inference(factor,[status(thm)],[c_10]) ).
cnf(c_29,plain,
( sK0(A,A,B,C) != C
| ~ exemplifies_property(A,C)
| ~ object(C)
| is_the(B,A)
| ~ object(B)
| ~ property(A) ),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_34,plain,
( object(sK0(A,A,B,B))
| ~ exemplifies_property(A,B)
| is_the(B,A)
| ~ object(B)
| ~ property(A) ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_35,plain,
( exemplifies_property(A,sK0(A,A,B,B))
| ~ exemplifies_property(A,B)
| is_the(B,A)
| ~ object(B)
| ~ property(A) ),
inference(factor,[status(thm)],[c_27]) ).
cnf(c_36,plain,
( sK0(A,A,B,B) != B
| ~ exemplifies_property(A,B)
| is_the(B,A)
| ~ object(B)
| ~ property(A) ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_49,negated_conjecture,
~ is_the(sK2,sK1),
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_70,negated_conjecture,
( object(sK0(sK1,sK1,sK2,sK2))
| is_the(sK2,sK1)
| ~ object(sK2)
| ~ property(sK1) ),
inference(resolve,[status(thm)],[c_34,c_16]) ).
cnf(c_71,negated_conjecture,
( object(sK0(sK1,sK1,sK2,sK2))
| is_the(sK2,sK1)
| ~ object(sK2) ),
inference(resolve,[status(thm)],[c_14,c_70]) ).
cnf(c_72,negated_conjecture,
( object(sK0(sK1,sK1,sK2,sK2))
| is_the(sK2,sK1) ),
inference(resolve,[status(thm)],[c_15,c_71]) ).
cnf(c_62,negated_conjecture,
object(sK0(sK1,sK1,sK2,sK2)),
inference(resolve,[status(thm)],[c_49,c_72]) ).
cnf(c_73,negated_conjecture,
( exemplifies_property(sK1,sK0(sK1,sK1,sK2,sK2))
| is_the(sK2,sK1)
| ~ object(sK2)
| ~ property(sK1) ),
inference(resolve,[status(thm)],[c_35,c_16]) ).
cnf(c_74,negated_conjecture,
( exemplifies_property(sK1,sK0(sK1,sK1,sK2,sK2))
| is_the(sK2,sK1)
| ~ object(sK2) ),
inference(resolve,[status(thm)],[c_14,c_73]) ).
cnf(c_75,negated_conjecture,
( exemplifies_property(sK1,sK0(sK1,sK1,sK2,sK2))
| is_the(sK2,sK1) ),
inference(resolve,[status(thm)],[c_15,c_74]) ).
cnf(c_63,negated_conjecture,
exemplifies_property(sK1,sK0(sK1,sK1,sK2,sK2)),
inference(resolve,[status(thm)],[c_49,c_75]) ).
cnf(c_76,negated_conjecture,
( sK0(sK1,sK1,sK2,sK2) != sK2
| is_the(sK2,sK1)
| ~ object(sK2)
| ~ property(sK1) ),
inference(resolve,[status(thm)],[c_36,c_16]) ).
cnf(c_77,negated_conjecture,
( sK0(sK1,sK1,sK2,sK2) != sK2
| is_the(sK2,sK1)
| ~ object(sK2) ),
inference(resolve,[status(thm)],[c_14,c_76]) ).
cnf(c_78,negated_conjecture,
( sK0(sK1,sK1,sK2,sK2) != sK2
| is_the(sK2,sK1) ),
inference(resolve,[status(thm)],[c_15,c_77]) ).
cnf(c_64,negated_conjecture,
sK0(sK1,sK1,sK2,sK2) != sK2,
inference(resolve,[status(thm)],[c_49,c_78]) ).
cnf(c_79,negated_conjecture,
( sK2 = sK0(sK1,sK1,sK2,sK2)
| ~ exemplifies_property(sK1,sK0(sK1,sK1,sK2,sK2)) ),
inference(resolve,[status(thm)],[c_18,c_62]) ).
cnf(c_80,plain,
sK2 != sK0(sK1,sK1,sK2,sK2),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_81,negated_conjecture,
~ exemplifies_property(sK1,sK0(sK1,sK1,sK2,sK2)),
inference(resolve,[status(thm)],[c_79,c_80]) ).
cnf(c_66,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_63,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI009+1 : TPTP v9.3.1. Released v7.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n009.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 04:39:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3366141 was started by sandbox2 on n009,
% 0.10/0.36 % Sat Sep 26 04:39:30 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 22.
% 0.13/0.38 % Level of proof is 5.
% 0.13/0.38 % Maximum clause weight is 34.000.
% 0.13/0.38 % Given clauses 38.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------