%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 67 ( 35 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 69 ( 30 ~; 20 |; 12 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 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 : 10 ( 0 sgn 4 !; 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(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_15,plain,
( relation_inverse(A) = function_inverse(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d9_funct_1]) ).
fof(nnf_11,plain,
? [A] :
( ( relation_dom(A) != relation_rng(function_inverse(A))
| relation_dom(function_inverse(A)) != relation_rng(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_dom(sK0) != relation_rng(function_inverse(sK0))
| relation_dom(function_inverse(sK0)) != relation_rng(sK0) )
& one_to_one(sK0)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_11]) ).
cnf(c_16,negated_conjecture,
one_to_one(sK0),
inference(split_conjunct,[status(thm)],[sk_t55_funct_1_neg]) ).
cnf(c_17,negated_conjecture,
( relation_inverse(sK0) = function_inverse(sK0)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_16,c_15]) ).
cnf(c_18,negated_conjecture,
( function_inverse(sK0) = relation_inverse(sK0)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(copy,[status(thm)],[c_17]) ).
cnf(c_25,negated_conjecture,
( relation_dom(sK0) != relation_rng(function_inverse(sK0))
| relation_dom(function_inverse(sK0)) != relation_rng(sK0) ),
inference(split_conjunct,[status(thm)],[sk_t55_funct_1_neg]) ).
cnf(c_51,negated_conjecture,
( relation_dom(sK0) != relation_rng(function_inverse(sK0))
| relation_rng(sK0) != relation_dom(function_inverse(sK0)) ),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_26,negated_conjecture,
( relation_rng(function_inverse(sK0)) != relation_dom(sK0)
| relation_rng(sK0) != relation_dom(function_inverse(sK0)) ),
inference(copy,[status(thm)],[c_51]) ).
cnf(c_27,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t55_funct_1_neg]) ).
cnf(c_28,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t55_funct_1_neg]) ).
cnf(c_29,plain,
( relation_dom(A) = relation_rng(relation_inverse(A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t37_relat_1]) ).
cnf(c_30,plain,
( relation_rng(relation_inverse(A)) = relation_dom(A)
| ~ relation(A) ),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_31,plain,
( relation_dom(relation_inverse(A)) = relation_rng(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t37_relat_1]) ).
cnf(c_32,plain,
( relation_rng(A) = relation_dom(relation_inverse(A))
| ~ relation(A) ),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_52,negated_conjecture,
( function_inverse(sK0) = relation_inverse(sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_28,c_18]) ).
cnf(c_43,negated_conjecture,
function_inverse(sK0) = relation_inverse(sK0),
inference(resolve,[status(thm)],[c_27,c_52]) ).
cnf(c_53,negated_conjecture,
( relation_rng(function_inverse(sK0)) != relation_dom(sK0)
| relation_rng(sK0) != relation_dom(relation_inverse(sK0)) ),
inference(paramod,[status(thm)],[c_43,c_26]) ).
cnf(c_47,negated_conjecture,
( relation_rng(relation_inverse(sK0)) != relation_dom(sK0)
| relation_rng(sK0) != relation_dom(relation_inverse(sK0)) ),
inference(paramod,[status(thm)],[c_43,c_53]) ).
cnf(c_48,negated_conjecture,
relation_rng(relation_inverse(sK0)) = relation_dom(sK0),
inference(resolve,[status(thm)],[c_30,c_28]) ).
cnf(c_54,negated_conjecture,
( relation_dom(sK0) != relation_dom(sK0)
| relation_rng(sK0) != relation_dom(relation_inverse(sK0)) ),
inference(paramod,[status(thm)],[c_48,c_47]) ).
cnf(c_49,negated_conjecture,
relation_rng(sK0) != relation_dom(relation_inverse(sK0)),
inference(copy,[status(thm)],[c_54]) ).
cnf(c_55,negated_conjecture,
relation_rng(sK0) = relation_dom(relation_inverse(sK0)),
inference(resolve,[status(thm)],[c_32,c_28]) ).
cnf(c_50,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_49,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU219+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:52:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.13/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.37 % Process 1300449 was started by sandbox on n004,
% 0.13/0.37 % Sat Sep 26 08:52:07 2026
% 0.13/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.38
% 0.13/0.38 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 20.
% 0.13/0.39 % Level of proof is 7.
% 0.13/0.39 % Maximum clause weight is 12.000.
% 0.13/0.39 % Given clauses 4.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------