%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU034+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 08:44:56 AM UTC 2026
% Result : Theorem 0.21s 5.52s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 18 unt; 0 def)
% Number of atoms : 134 ( 47 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 158 ( 72 ~; 67 |; 11 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 46 ( 5 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(fc2_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_funct_1) ).
fof(t44_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( relation_composition(A,B) = A
& relation_rng(A) = relation_dom(B) )
=> B = identity_relation(relation_dom(B)) ) ) ),
file('theBenchmark.p',t44_funct_1) ).
fof(t52_funct_1,axiom,
! [A] : one_to_one(identity_relation(A)),
file('theBenchmark.p',t52_funct_1) ).
fof(t55_funct_1,axiom,
! [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(t61_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A))
& relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A)) ) ) ),
file('theBenchmark.p',t61_funct_1) ).
fof(t71_relat_1,axiom,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_1) ).
fof(t67_funct_1,conjecture,
! [A] : function_inverse(identity_relation(A)) = identity_relation(A),
file('theBenchmark.p',t67_funct_1) ).
fof(t67_funct_1_neg,negated_conjecture,
~ ! [A] : function_inverse(identity_relation(A)) = identity_relation(A),
inference(assume_negation,[status(cth)],[t67_funct_1]) ).
cnf(c_45,plain,
( relation_rng(A) = relation_dom(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t55_funct_1]) ).
cnf(c_46,plain,
one_to_one(identity_relation(A)),
inference(clausify,[status(thm)],[t52_funct_1]) ).
cnf(c_50,plain,
( identity_relation(relation_dom(A)) = relation_composition(A,function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t61_funct_1]) ).
cnf(c_66,plain,
( identity_relation(relation_dom(identity_relation(A))) = relation_composition(identity_relation(A),function_inverse(identity_relation(A)))
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_50,c_46]) ).
cnf(c_67,plain,
( relation_composition(identity_relation(A),function_inverse(identity_relation(A))) = identity_relation(relation_dom(identity_relation(A)))
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_76,plain,
( relation_rng(identity_relation(A)) = relation_dom(function_inverse(identity_relation(A)))
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_45,c_46]) ).
cnf(c_77,plain,
( relation_dom(function_inverse(identity_relation(A))) = relation_rng(identity_relation(A))
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(copy,[status(thm)],[c_76]) ).
fof(nnf_44,plain,
? [A] : identity_relation(A) != function_inverse(identity_relation(A)),
inference(fof_nnf,[status(thm)],[t67_funct_1_neg]) ).
fof(sk_t67_funct_1_neg,plain,
identity_relation(sK0) != function_inverse(identity_relation(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_44]) ).
cnf(c_78,negated_conjecture,
identity_relation(sK0) != function_inverse(identity_relation(sK0)),
inference(split_conjunct,[status(thm)],[sk_t67_funct_1_neg]) ).
cnf(c_79,negated_conjecture,
function_inverse(identity_relation(sK0)) != identity_relation(sK0),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_82,plain,
relation_rng(identity_relation(A)) = A,
inference(clausify,[status(thm)],[t71_relat_1]) ).
cnf(c_83,plain,
relation_dom(identity_relation(A)) = A,
inference(clausify,[status(thm)],[t71_relat_1]) ).
cnf(c_87,plain,
( identity_relation(relation_dom(B)) = B
| relation_composition(A,B) != A
| relation_rng(A) != relation_dom(B)
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t44_funct_1]) ).
cnf(c_118,plain,
function(identity_relation(A)),
inference(clausify,[status(thm)],[fc2_funct_1]) ).
cnf(c_119,plain,
relation(identity_relation(A)),
inference(clausify,[status(thm)],[fc2_funct_1]) ).
cnf(c_127,plain,
( function(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_128,plain,
( relation(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_292,plain,
( relation_dom(function_inverse(identity_relation(A))) = A
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(paramod,[status(thm)],[c_82,c_77]) ).
cnf(c_293,plain,
( relation_dom(function_inverse(identity_relation(A))) = A
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_119,c_292]) ).
cnf(c_132,plain,
relation_dom(function_inverse(identity_relation(A))) = A,
inference(resolve,[status(thm)],[c_118,c_293]) ).
cnf(c_294,plain,
( relation_composition(identity_relation(A),function_inverse(identity_relation(A))) = identity_relation(A)
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(paramod,[status(thm)],[c_83,c_67]) ).
cnf(c_295,plain,
( relation_composition(identity_relation(A),function_inverse(identity_relation(A))) = identity_relation(A)
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_119,c_294]) ).
cnf(c_135,plain,
relation_composition(identity_relation(A),function_inverse(identity_relation(A))) = identity_relation(A),
inference(resolve,[status(thm)],[c_118,c_295]) ).
cnf(c_296,plain,
( function(function_inverse(identity_relation(A)))
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_127,c_119]) ).
cnf(c_276,plain,
function(function_inverse(identity_relation(A))),
inference(resolve,[status(thm)],[c_118,c_296]) ).
cnf(c_297,plain,
( relation(function_inverse(identity_relation(A)))
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_128,c_119]) ).
cnf(c_282,plain,
relation(function_inverse(identity_relation(A))),
inference(resolve,[status(thm)],[c_118,c_297]) ).
cnf(c_298,plain,
( identity_relation(relation_dom(function_inverse(identity_relation(A)))) = function_inverse(identity_relation(A))
| relation_rng(identity_relation(A)) != relation_dom(function_inverse(identity_relation(A)))
| ~ function(function_inverse(identity_relation(A)))
| ~ relation(function_inverse(identity_relation(A)))
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_135,c_87]) ).
cnf(c_299,plain,
( identity_relation(relation_dom(function_inverse(identity_relation(A)))) = function_inverse(identity_relation(A))
| A != relation_dom(function_inverse(identity_relation(A)))
| ~ function(function_inverse(identity_relation(A)))
| ~ relation(function_inverse(identity_relation(A)))
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(paramod,[status(thm)],[c_82,c_298]) ).
cnf(c_300,plain,
( identity_relation(relation_dom(function_inverse(identity_relation(A)))) = function_inverse(identity_relation(A))
| A != A
| ~ function(function_inverse(identity_relation(A)))
| ~ relation(function_inverse(identity_relation(A)))
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(paramod,[status(thm)],[c_132,c_299]) ).
cnf(c_301,plain,
( identity_relation(A) = function_inverse(identity_relation(A))
| A != A
| ~ function(function_inverse(identity_relation(A)))
| ~ relation(function_inverse(identity_relation(A)))
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(paramod,[status(thm)],[c_132,c_300]) ).
cnf(c_302,plain,
( function_inverse(identity_relation(A)) = identity_relation(A)
| A != A
| ~ function(function_inverse(identity_relation(A)))
| ~ relation(function_inverse(identity_relation(A)))
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(copy,[status(thm)],[c_301]) ).
cnf(c_303,plain,
( function_inverse(identity_relation(A)) = identity_relation(A)
| ~ function(function_inverse(identity_relation(A)))
| ~ relation(function_inverse(identity_relation(A)))
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(copy,[status(thm)],[c_302]) ).
cnf(c_304,plain,
( function_inverse(identity_relation(A)) = identity_relation(A)
| ~ function(function_inverse(identity_relation(A)))
| ~ relation(function_inverse(identity_relation(A)))
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_119,c_303]) ).
cnf(c_305,plain,
( function_inverse(identity_relation(A)) = identity_relation(A)
| ~ function(function_inverse(identity_relation(A)))
| ~ relation(function_inverse(identity_relation(A))) ),
inference(resolve,[status(thm)],[c_118,c_304]) ).
cnf(c_306,plain,
( function_inverse(identity_relation(A)) = identity_relation(A)
| ~ function(function_inverse(identity_relation(A))) ),
inference(resolve,[status(thm)],[c_282,c_305]) ).
cnf(c_290,plain,
function_inverse(identity_relation(A)) = identity_relation(A),
inference(resolve,[status(thm)],[c_276,c_306]) ).
cnf(c_291,plain,
$false,
inference(resolve,[status(thm)],[c_290,c_79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU034+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.45 % Computer : n014.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Sat Sep 26 08:32:07 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.45 % Process 2653702 was started by sandbox2 on n014,
% 0.17/5.45 % Sat Sep 26 08:32:07 2026
% 0.17/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.47
% 0.17/5.47 % From the command line: assign(max_seconds, 300).
% 0.21/5.52
% 0.21/5.52 % SZS status Theorem for theBenchmark
% 0.21/5.52
% 0.21/5.52 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.21/5.52 % Length of proof is 30.
% 0.21/5.52 % Level of proof is 6.
% 0.21/5.52 % Maximum clause weight is 38.000.
% 0.21/5.52 % Given clauses 59.
% 0.21/5.52
% 0.21/5.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------