%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU031+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.88s 0.61s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 17 unt; 0 def)
% Number of atoms : 161 ( 70 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 189 ( 74 ~; 67 |; 33 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 11 !; 2 ?)
% 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(l72_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ! [D] :
( ( function(D)
& relation(D) )
=> ( ( relation_composition(C,D) = identity_relation(A)
& relation_composition(B,C) = identity_relation(relation_dom(D))
& relation_rng(B) = A )
=> D = B ) ) ) ),
file('theBenchmark.p',l72_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(t64_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( relation_composition(B,A) = identity_relation(relation_rng(A))
& relation_rng(B) = relation_dom(A)
& one_to_one(A) )
=> B = function_inverse(A) ) ) ),
file('theBenchmark.p',t64_funct_1) ).
fof(t64_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( relation_composition(B,A) = identity_relation(relation_rng(A))
& relation_rng(B) = relation_dom(A)
& one_to_one(A) )
=> B = function_inverse(A) ) ) ),
inference(assume_negation,[status(cth)],[t64_funct_1]) ).
cnf(c_43,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_47,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]) ).
fof(nnf_42,plain,
? [A] :
( ? [B] :
( function_inverse(A) != B
& identity_relation(relation_rng(A)) = relation_composition(B,A)
& relation_rng(B) = relation_dom(A)
& one_to_one(A)
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t64_funct_1_neg]) ).
fof(sk_t64_funct_1_neg,plain,
( function_inverse(sK0) != sK1
& identity_relation(relation_rng(sK0)) = relation_composition(sK1,sK0)
& relation_rng(sK1) = relation_dom(sK0)
& one_to_one(sK0)
& function(sK1)
& relation(sK1)
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_42]) ).
cnf(c_49,negated_conjecture,
one_to_one(sK0),
inference(split_conjunct,[status(thm)],[sk_t64_funct_1_neg]) ).
cnf(c_54,negated_conjecture,
( relation_rng(sK0) = relation_dom(function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_49,c_43]) ).
cnf(c_55,negated_conjecture,
( relation_dom(function_inverse(sK0)) = relation_rng(sK0)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(copy,[status(thm)],[c_54]) ).
cnf(c_58,negated_conjecture,
( identity_relation(relation_dom(sK0)) = relation_composition(sK0,function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_49,c_47]) ).
cnf(c_74,negated_conjecture,
function_inverse(sK0) != sK1,
inference(split_conjunct,[status(thm)],[sk_t64_funct_1_neg]) ).
cnf(c_75,negated_conjecture,
identity_relation(relation_rng(sK0)) = relation_composition(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t64_funct_1_neg]) ).
cnf(c_76,negated_conjecture,
relation_rng(sK1) = relation_dom(sK0),
inference(split_conjunct,[status(thm)],[sk_t64_funct_1_neg]) ).
cnf(c_77,negated_conjecture,
relation_dom(sK0) = relation_rng(sK1),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_78,negated_conjecture,
function(sK1),
inference(split_conjunct,[status(thm)],[sk_t64_funct_1_neg]) ).
cnf(c_79,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t64_funct_1_neg]) ).
cnf(c_80,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t64_funct_1_neg]) ).
cnf(c_81,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t64_funct_1_neg]) ).
cnf(c_107,plain,
( C = A
| identity_relation(D) != relation_composition(B,C)
| identity_relation(relation_dom(C)) != relation_composition(A,B)
| relation_rng(A) != D
| ~ function(C)
| ~ relation(C)
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[l72_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_409,negated_conjecture,
( identity_relation(relation_rng(sK1)) = relation_composition(sK0,function_inverse(sK0))
| ~ function(sK0)
| ~ relation(sK0) ),
inference(paramod,[status(thm)],[c_77,c_58]) ).
cnf(c_410,negated_conjecture,
( identity_relation(relation_rng(sK1)) = relation_composition(sK0,function_inverse(sK0))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_81,c_409]) ).
cnf(c_133,negated_conjecture,
identity_relation(relation_rng(sK1)) = relation_composition(sK0,function_inverse(sK0)),
inference(resolve,[status(thm)],[c_80,c_410]) ).
cnf(c_411,negated_conjecture,
( relation_dom(function_inverse(sK0)) = relation_rng(sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_81,c_55]) ).
cnf(c_135,negated_conjecture,
relation_dom(function_inverse(sK0)) = relation_rng(sK0),
inference(resolve,[status(thm)],[c_80,c_411]) ).
cnf(c_412,negated_conjecture,
( function(function_inverse(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_127,c_80]) ).
cnf(c_245,negated_conjecture,
function(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_81,c_412]) ).
cnf(c_413,negated_conjecture,
( relation(function_inverse(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_128,c_80]) ).
cnf(c_250,negated_conjecture,
relation(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_81,c_413]) ).
cnf(c_414,negated_conjecture,
( B = sK1
| identity_relation(C) != relation_composition(A,B)
| identity_relation(relation_dom(B)) != relation_composition(sK1,A)
| relation_rng(sK1) != C
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A)
| ~ function(sK1) ),
inference(resolve,[status(thm)],[c_107,c_79]) ).
cnf(c_415,negated_conjecture,
( B = sK1
| identity_relation(C) != relation_composition(A,B)
| identity_relation(relation_dom(B)) != relation_composition(sK1,A)
| relation_rng(sK1) != C
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_414,c_78]) ).
cnf(c_416,negated_conjecture,
( A = sK1
| identity_relation(B) != relation_composition(sK0,A)
| identity_relation(relation_dom(A)) != relation_composition(sK1,sK0)
| relation_rng(sK1) != B
| ~ function(A)
| ~ relation(A)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_415,c_81]) ).
cnf(c_417,negated_conjecture,
( A = sK1
| identity_relation(B) != relation_composition(sK0,A)
| identity_relation(relation_dom(A)) != relation_composition(sK1,sK0)
| relation_rng(sK1) != B
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_416,c_80]) ).
cnf(c_418,negated_conjecture,
( function_inverse(sK0) = sK1
| identity_relation(A) != relation_composition(sK0,function_inverse(sK0))
| identity_relation(relation_dom(function_inverse(sK0))) != relation_composition(sK1,sK0)
| relation_rng(sK1) != A
| ~ function(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_417,c_250]) ).
cnf(c_419,negated_conjecture,
( function_inverse(sK0) = sK1
| identity_relation(A) != relation_composition(sK0,function_inverse(sK0))
| identity_relation(relation_dom(function_inverse(sK0))) != relation_composition(sK1,sK0)
| relation_rng(sK1) != A ),
inference(resolve,[status(thm)],[c_418,c_245]) ).
cnf(c_420,plain,
( function_inverse(sK0) = sK1
| identity_relation(relation_rng(sK1)) != relation_composition(sK0,function_inverse(sK0))
| identity_relation(relation_dom(function_inverse(sK0))) != relation_composition(sK1,sK0) ),
inference(xxres,[status(thm)],[c_419]) ).
cnf(c_421,negated_conjecture,
( function_inverse(sK0) = sK1
| identity_relation(relation_dom(function_inverse(sK0))) != relation_composition(sK1,sK0) ),
inference(resolve,[status(thm)],[c_420,c_133]) ).
cnf(c_422,negated_conjecture,
identity_relation(relation_dom(function_inverse(sK0))) != relation_composition(sK1,sK0),
inference(resolve,[status(thm)],[c_421,c_74]) ).
cnf(c_423,negated_conjecture,
identity_relation(relation_rng(sK0)) != relation_composition(sK1,sK0),
inference(paramod,[status(thm)],[c_135,c_422]) ).
cnf(c_424,negated_conjecture,
relation_composition(sK1,sK0) != relation_composition(sK1,sK0),
inference(paramod,[status(thm)],[c_75,c_423]) ).
cnf(c_408,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_424]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU031+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.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 : Sat Sep 26 08:36:14 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 438739 was started by sandbox on n016,
% 0.11/0.38 % Sat Sep 26 08:36:14 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 0.88/0.61
% 0.88/0.61 % SZS status Theorem for theBenchmark
% 0.88/0.61
% 0.88/0.61 % Proof 1 at 0.20 (+ 0.01) seconds.
% 0.88/0.61 % Length of proof is 27.
% 0.88/0.61 % Level of proof is 5.
% 0.88/0.61 % Maximum clause weight is 32.000.
% 0.88/0.61 % Given clauses 99.
% 0.88/0.61
% 0.88/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------