%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU032+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 : 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 : Sun Sep 27 08:44:55 AM UTC 2026
% Result : Theorem 2.53s 0.74s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 13 unt; 0 def)
% Number of atoms : 146 ( 48 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 169 ( 70 ~; 66 |; 19 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 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 : 19 ( 0 sgn 8 !; 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(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(t62_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('theBenchmark.p',t62_funct_1) ).
fof(t63_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( relation_composition(A,B) = identity_relation(relation_dom(A))
& relation_rng(A) = relation_dom(B)
& one_to_one(A) )
=> B = function_inverse(A) ) ) ),
file('theBenchmark.p',t63_funct_1) ).
fof(t65_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(function_inverse(A)) = A ) ),
file('theBenchmark.p',t65_funct_1) ).
fof(t65_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> function_inverse(function_inverse(A)) = A ) ),
inference(assume_negation,[status(cth)],[t65_funct_1]) ).
cnf(c_52,plain,
( relation(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_53,plain,
( function(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_94,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_95,plain,
( relation_rng(function_inverse(A)) = relation_dom(A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t55_funct_1]) ).
cnf(c_98,plain,
( identity_relation(relation_rng(A)) = relation_composition(function_inverse(A),A)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t61_funct_1]) ).
cnf(c_99,plain,
( one_to_one(function_inverse(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t62_funct_1]) ).
cnf(c_100,plain,
( function_inverse(A) = B
| identity_relation(relation_dom(A)) != relation_composition(A,B)
| relation_rng(A) != relation_dom(B)
| ~ one_to_one(A)
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t63_funct_1]) ).
fof(nnf_43,plain,
? [A] :
( function_inverse(function_inverse(A)) != A
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t65_funct_1_neg]) ).
fof(sk_t65_funct_1_neg,plain,
( function_inverse(function_inverse(sK0)) != sK0
& one_to_one(sK0)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_43]) ).
cnf(c_104,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t65_funct_1_neg]) ).
cnf(c_105,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t65_funct_1_neg]) ).
cnf(c_106,negated_conjecture,
one_to_one(sK0),
inference(split_conjunct,[status(thm)],[sk_t65_funct_1_neg]) ).
cnf(c_107,negated_conjecture,
function_inverse(function_inverse(sK0)) != sK0,
inference(split_conjunct,[status(thm)],[sk_t65_funct_1_neg]) ).
cnf(c_4485,negated_conjecture,
( function_inverse(A) = sK0
| identity_relation(relation_dom(A)) != relation_composition(A,sK0)
| relation_rng(A) != relation_dom(sK0)
| ~ one_to_one(A)
| ~ function(sK0)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_104,c_100]) ).
cnf(c_359,negated_conjecture,
( function_inverse(A) = sK0
| identity_relation(relation_dom(A)) != relation_composition(A,sK0)
| relation_rng(A) != relation_dom(sK0)
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_105,c_4485]) ).
cnf(c_4486,negated_conjecture,
( one_to_one(function_inverse(sK0))
| ~ one_to_one(sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_104,c_99]) ).
cnf(c_4487,negated_conjecture,
( one_to_one(function_inverse(sK0))
| ~ one_to_one(sK0) ),
inference(resolve,[status(thm)],[c_105,c_4486]) ).
cnf(c_361,negated_conjecture,
one_to_one(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_106,c_4487]) ).
cnf(c_4488,negated_conjecture,
( identity_relation(relation_rng(sK0)) = relation_composition(function_inverse(sK0),sK0)
| ~ one_to_one(sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_104,c_98]) ).
cnf(c_4489,negated_conjecture,
( identity_relation(relation_rng(sK0)) = relation_composition(function_inverse(sK0),sK0)
| ~ one_to_one(sK0) ),
inference(resolve,[status(thm)],[c_105,c_4488]) ).
cnf(c_362,negated_conjecture,
identity_relation(relation_rng(sK0)) = relation_composition(function_inverse(sK0),sK0),
inference(resolve,[status(thm)],[c_106,c_4489]) ).
cnf(c_4490,negated_conjecture,
( relation_rng(function_inverse(sK0)) = relation_dom(sK0)
| ~ one_to_one(sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_104,c_95]) ).
cnf(c_4491,negated_conjecture,
( relation_rng(function_inverse(sK0)) = relation_dom(sK0)
| ~ one_to_one(sK0) ),
inference(resolve,[status(thm)],[c_105,c_4490]) ).
cnf(c_364,negated_conjecture,
relation_rng(function_inverse(sK0)) = relation_dom(sK0),
inference(resolve,[status(thm)],[c_106,c_4491]) ).
cnf(c_4492,negated_conjecture,
( relation_rng(sK0) = relation_dom(function_inverse(sK0))
| ~ one_to_one(sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_104,c_94]) ).
cnf(c_4493,negated_conjecture,
( relation_rng(sK0) = relation_dom(function_inverse(sK0))
| ~ one_to_one(sK0) ),
inference(resolve,[status(thm)],[c_105,c_4492]) ).
cnf(c_365,negated_conjecture,
relation_rng(sK0) = relation_dom(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_106,c_4493]) ).
cnf(c_4494,negated_conjecture,
( function(function_inverse(sK0))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_104,c_53]) ).
cnf(c_376,negated_conjecture,
function(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_105,c_4494]) ).
cnf(c_4495,negated_conjecture,
( relation(function_inverse(sK0))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_104,c_52]) ).
cnf(c_377,negated_conjecture,
relation(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_105,c_4495]) ).
cnf(c_379,negated_conjecture,
identity_relation(relation_dom(function_inverse(sK0))) = relation_composition(function_inverse(sK0),sK0),
inference(paramod,[status(thm)],[c_365,c_362]) ).
cnf(c_4496,plain,
( function_inverse(function_inverse(sK0)) = sK0
| identity_relation(relation_dom(function_inverse(sK0))) != relation_composition(function_inverse(sK0),sK0)
| relation_rng(function_inverse(sK0)) != relation_dom(sK0)
| ~ one_to_one(function_inverse(sK0))
| ~ function(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_359,c_377]) ).
cnf(c_4497,plain,
( function_inverse(function_inverse(sK0)) = sK0
| identity_relation(relation_dom(function_inverse(sK0))) != relation_composition(function_inverse(sK0),sK0)
| relation_dom(sK0) != relation_dom(sK0)
| ~ one_to_one(function_inverse(sK0))
| ~ function(function_inverse(sK0)) ),
inference(paramod,[status(thm)],[c_364,c_4496]) ).
cnf(c_4498,plain,
( function_inverse(function_inverse(sK0)) = sK0
| relation_composition(function_inverse(sK0),sK0) != relation_composition(function_inverse(sK0),sK0)
| relation_dom(sK0) != relation_dom(sK0)
| ~ one_to_one(function_inverse(sK0))
| ~ function(function_inverse(sK0)) ),
inference(paramod,[status(thm)],[c_379,c_4497]) ).
cnf(c_4499,plain,
( function_inverse(function_inverse(sK0)) = sK0
| relation_composition(function_inverse(sK0),sK0) != relation_composition(function_inverse(sK0),sK0)
| ~ one_to_one(function_inverse(sK0))
| ~ function(function_inverse(sK0)) ),
inference(copy,[status(thm)],[c_4498]) ).
cnf(c_4500,plain,
( function_inverse(function_inverse(sK0)) = sK0
| ~ one_to_one(function_inverse(sK0))
| ~ function(function_inverse(sK0)) ),
inference(copy,[status(thm)],[c_4499]) ).
cnf(c_4501,plain,
( function_inverse(function_inverse(sK0)) = sK0
| ~ one_to_one(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_376,c_4500]) ).
cnf(c_4502,plain,
function_inverse(function_inverse(sK0)) = sK0,
inference(resolve,[status(thm)],[c_361,c_4501]) ).
cnf(c_4484,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_107,c_4502]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU032+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:27:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 274717 was started by sandbox2 on n017,
% 0.09/0.35 % Sat Sep 26 08:27:04 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 2.53/0.74
% 2.53/0.74 % SZS status Theorem for theBenchmark
% 2.53/0.74
% 2.53/0.74 % Proof 1 at 0.29 (+ 0.08) seconds.
% 2.53/0.74 % Length of proof is 26.
% 2.53/0.74 % Level of proof is 4.
% 2.53/0.74 % Maximum clause weight is 41.000.
% 2.53/0.74 % Given clauses 470.
% 2.53/0.74
% 2.53/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------