%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU219+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 : Fri Sep 25 02:51:23 PM UTC 2026
% Result : Theorem 24.09s 4.23s
% Output : Proof 24.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 7 unt; 0 def)
% Number of atoms : 63 ( 25 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 62 ( 23 ~; 16 |; 17 &)
% ( 0 <=>; 6 =>; 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 : 12 ( 0 sgn 8 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [A] :
( relation(A)
=> ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f32_nnf,plain,
! [A] :
( ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [A] :
( ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) )
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c53,plain,
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f5_nnf,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c7,plain,
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f35,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f35_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(negated_conjecture,[status(cth)],[f35]) ).
fof(f35_nnf,plain,
? [A] :
( ( relation_dom(A) != relation_rng(function_inverse(A))
| relation_rng(A) != relation_dom(function_inverse(A)) )
& one_to_one(A)
& function(A)
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f35_neg]) ).
fof(f35_sk,plain,
( ( relation_dom(sk11) != relation_rng(function_inverse(sk11))
| relation_rng(sk11) != relation_dom(function_inverse(sk11)) )
& one_to_one(sk11)
& function(sk11)
& relation(sk11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f35_nnf]) ).
cnf(c57,plain,
relation(sk11),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p87,plain,
( relation(function_inverse(sk11))
| ~ function(sk11) ),
inference(resolution,[status(thm)],[c7,c57]) ).
cnf(c58,plain,
function(sk11),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p93,plain,
relation(function_inverse(sk11)),
inference(resolution,[status(thm)],[p87,c58]) ).
cnf(p667,plain,
relation_dom(function_inverse(sk11)) = relation_rng(sk11),
inference(resolution,[status(thm)],[c53,p93]) ).
cnf(c52,plain,
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p646,plain,
relation_rng(function_inverse(sk11)) = relation_dom(sk11),
inference(resolution,[status(thm)],[c52,p93]) ).
cnf(c60,plain,
( relation_dom(sk11) != relation_rng(function_inverse(sk11))
| relation_rng(sk11) != relation_dom(function_inverse(sk11)) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p647,plain,
( relation_dom(sk11) != relation_dom(sk11)
| relation_rng(sk11) != relation_dom(function_inverse(sk11)) ),
inference(demodulation,[status(thm)],[p646,c60]) ).
cnf(p669,plain,
( relation_dom(sk11) != relation_dom(sk11)
| relation_rng(sk11) != relation_rng(sk11) ),
inference(demodulation,[status(thm)],[p667,p647]) ).
cnf(p683,plain,
relation_dom(sk11) != relation_dom(sk11),
inference(equality_resolution,[status(thm)],[p669]) ).
cnf(p685,plain,
$false,
inference(equality_resolution,[status(thm)],[p683]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU219+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 13:10:00 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.09/4.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.09/4.23 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------