%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU219+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 08:45:27 AM UTC 2026
% Result : Theorem 23.35s 8.85s
% Output : CNFRefutation 23.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 74 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 68 ( 26 ~; 19 |; 14 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn 6 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d9_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ),
file('theBenchmark.p',d9_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('theBenchmark.p',dt_k2_funct_1) ).
fof(involutiveness_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ),
file('theBenchmark.p',involutiveness_k4_relat_1) ).
fof(t37_relat_1,axiom,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('theBenchmark.p',t37_relat_1) ).
fof(t55_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('theBenchmark.p',t55_funct_1) ).
fof(t55_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
inference(assume_negation,[status(cth)],[t55_funct_1]) ).
cnf(c_439,plain,
( function_inverse(A) = relation_inverse(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d9_funct_1]) ).
cnf(c_440,plain,
( relation_inverse(A) = function_inverse(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(copy,[status(thm)],[c_439]) ).
cnf(c_441,plain,
( relation(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_481,plain,
( relation_inverse(relation_inverse(A)) = A
| ~ relation(A) ),
inference(clausify,[status(thm)],[involutiveness_k4_relat_1]) ).
cnf(c_562,plain,
( relation_rng(A) = relation_dom(relation_inverse(A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t37_relat_1]) ).
fof(nnf_229,plain,
? [A] :
( ( relation_rng(function_inverse(A)) != relation_dom(A)
| relation_rng(A) != relation_dom(function_inverse(A)) )
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t55_funct_1_neg]) ).
fof(sk_t55_funct_1_neg,plain,
( ( relation_rng(function_inverse(sK0)) != relation_dom(sK0)
| relation_rng(sK0) != relation_dom(function_inverse(sK0)) )
& one_to_one(sK0)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_229]) ).
cnf(c_643,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t55_funct_1_neg]) ).
cnf(c_644,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t55_funct_1_neg]) ).
cnf(c_645,negated_conjecture,
one_to_one(sK0),
inference(split_conjunct,[status(thm)],[sk_t55_funct_1_neg]) ).
cnf(c_646,negated_conjecture,
( relation_rng(function_inverse(sK0)) != relation_dom(sK0)
| relation_rng(sK0) != relation_dom(function_inverse(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_t55_funct_1_neg]) ).
cnf(c_16001,negated_conjecture,
( relation(function_inverse(sK0))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_441,c_643]) ).
cnf(c_2042,negated_conjecture,
relation(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_644,c_16001]) ).
cnf(c_16002,negated_conjecture,
( relation_inverse(sK0) = function_inverse(sK0)
| ~ one_to_one(sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_440,c_643]) ).
cnf(c_16003,negated_conjecture,
( relation_inverse(sK0) = function_inverse(sK0)
| ~ one_to_one(sK0) ),
inference(resolve,[status(thm)],[c_644,c_16002]) ).
cnf(c_6254,negated_conjecture,
relation_inverse(sK0) = function_inverse(sK0),
inference(resolve,[status(thm)],[c_645,c_16003]) ).
cnf(c_16004,negated_conjecture,
relation_inverse(relation_inverse(sK0)) = sK0,
inference(resolve,[status(thm)],[c_481,c_643]) ).
cnf(c_10534,negated_conjecture,
relation_inverse(function_inverse(sK0)) = sK0,
inference(paramod,[status(thm)],[c_6254,c_16004]) ).
cnf(c_16005,plain,
relation_rng(function_inverse(sK0)) = relation_dom(relation_inverse(function_inverse(sK0))),
inference(resolve,[status(thm)],[c_562,c_2042]) ).
cnf(c_15766,plain,
relation_rng(function_inverse(sK0)) = relation_dom(sK0),
inference(paramod,[status(thm)],[c_10534,c_16005]) ).
cnf(c_16006,negated_conjecture,
relation_rng(sK0) = relation_dom(relation_inverse(sK0)),
inference(resolve,[status(thm)],[c_562,c_643]) ).
cnf(c_15771,negated_conjecture,
relation_rng(sK0) = relation_dom(function_inverse(sK0)),
inference(paramod,[status(thm)],[c_6254,c_16006]) ).
cnf(c_16007,negated_conjecture,
( relation_rng(function_inverse(sK0)) != relation_dom(sK0)
| relation_dom(function_inverse(sK0)) != relation_dom(function_inverse(sK0)) ),
inference(paramod,[status(thm)],[c_15771,c_646]) ).
cnf(c_16008,negated_conjecture,
( relation_dom(sK0) != relation_dom(sK0)
| relation_dom(function_inverse(sK0)) != relation_dom(function_inverse(sK0)) ),
inference(paramod,[status(thm)],[c_15766,c_16007]) ).
cnf(c_16009,negated_conjecture,
relation_dom(sK0) != relation_dom(sK0),
inference(copy,[status(thm)],[c_16008]) ).
cnf(c_16000,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_16009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU219+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n010.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 26 08:52:37 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 2954598 was started by sandbox2 on n010,
% 0.09/5.38 % Sat Sep 26 08:52:37 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/5.44
% 0.15/5.44 % From the command line: assign(max_seconds, 300).
% 0.15/5.44
% 0.15/5.44 % SInE: 175 to sos, 55 to usable, of 230 axioms (tolerance 2.00, depth 0 fixpoint).
% 23.35/8.85
% 23.35/8.85 % given #500 (F,wt=21): 6916 -in(A,set_difference(B,powerset(A))). [resolve(6396,a,4228,b)].
% 23.35/8.85
% 23.35/8.85 % SZS status Theorem for theBenchmark
% 23.35/8.85
% 23.35/8.85 % Proof 1 at 2.74 (+ 0.55) seconds.
% 23.35/8.85 % Length of proof is 20.
% 23.35/8.85 % Level of proof is 6.
% 23.35/8.85 % Maximum clause weight is 127.000.
% 23.35/8.85 % Given clauses 807.
% 23.35/8.85
% 23.35/8.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------