%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU030+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 : 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 08:44:55 AM UTC 2026
% Result : Theorem 0.19s 15.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 15 unt; 0 def)
% Number of atoms : 156 ( 63 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 184 ( 71 ~; 65 |; 33 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 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 : 30 ( 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(t63_funct_1,conjecture,
! [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(t63_funct_1_neg,negated_conjecture,
~ ! [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) ) ) ),
inference(assume_negation,[status(cth)],[t63_funct_1]) ).
cnf(c_46,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_48,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]) ).
fof(nnf_42,plain,
? [A] :
( ? [B] :
( 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(fof_nnf,[status(thm)],[t63_funct_1_neg]) ).
fof(sk_t63_funct_1_neg,plain,
( function_inverse(sK0) != sK1
& identity_relation(relation_dom(sK0)) = relation_composition(sK0,sK1)
& relation_rng(sK0) = relation_dom(sK1)
& 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_t63_funct_1_neg]) ).
cnf(c_55,negated_conjecture,
( relation_rng(function_inverse(sK0)) = relation_dom(sK0)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_49,c_46]) ).
cnf(c_57,negated_conjecture,
( identity_relation(relation_rng(sK0)) = relation_composition(function_inverse(sK0),sK0)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_49,c_48]) ).
cnf(c_70,negated_conjecture,
function_inverse(sK0) != sK1,
inference(split_conjunct,[status(thm)],[sk_t63_funct_1_neg]) ).
cnf(c_71,negated_conjecture,
identity_relation(relation_dom(sK0)) = relation_composition(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t63_funct_1_neg]) ).
cnf(c_72,negated_conjecture,
relation_rng(sK0) = relation_dom(sK1),
inference(split_conjunct,[status(thm)],[sk_t63_funct_1_neg]) ).
cnf(c_73,negated_conjecture,
function(sK1),
inference(split_conjunct,[status(thm)],[sk_t63_funct_1_neg]) ).
cnf(c_74,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t63_funct_1_neg]) ).
cnf(c_75,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t63_funct_1_neg]) ).
cnf(c_76,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t63_funct_1_neg]) ).
cnf(c_102,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_122,plain,
( function(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_123,plain,
( relation(function_inverse(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_funct_1]) ).
cnf(c_447,negated_conjecture,
( identity_relation(relation_dom(sK1)) = relation_composition(function_inverse(sK0),sK0)
| ~ function(sK0)
| ~ relation(sK0) ),
inference(paramod,[status(thm)],[c_72,c_57]) ).
cnf(c_448,negated_conjecture,
( identity_relation(relation_dom(sK1)) = relation_composition(function_inverse(sK0),sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_76,c_447]) ).
cnf(c_128,negated_conjecture,
identity_relation(relation_dom(sK1)) = relation_composition(function_inverse(sK0),sK0),
inference(resolve,[status(thm)],[c_75,c_448]) ).
cnf(c_449,negated_conjecture,
( relation_rng(function_inverse(sK0)) = relation_dom(sK0)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_76,c_55]) ).
cnf(c_130,negated_conjecture,
relation_rng(function_inverse(sK0)) = relation_dom(sK0),
inference(resolve,[status(thm)],[c_75,c_449]) ).
cnf(c_450,negated_conjecture,
( function(function_inverse(sK0))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_122,c_76]) ).
cnf(c_313,negated_conjecture,
function(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_75,c_450]) ).
cnf(c_451,negated_conjecture,
( relation(function_inverse(sK0))
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_123,c_76]) ).
cnf(c_321,negated_conjecture,
relation(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_75,c_451]) ).
cnf(c_452,plain,
( B = function_inverse(sK0)
| identity_relation(C) != relation_composition(A,B)
| identity_relation(relation_dom(B)) != relation_composition(function_inverse(sK0),A)
| relation_rng(function_inverse(sK0)) != C
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A)
| ~ relation(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_102,c_313]) ).
cnf(c_453,negated_conjecture,
( A = function_inverse(sK0)
| identity_relation(B) != relation_composition(sK0,A)
| identity_relation(relation_dom(A)) != relation_composition(function_inverse(sK0),sK0)
| relation_rng(function_inverse(sK0)) != B
| ~ function(A)
| ~ relation(A)
| ~ function(sK0)
| ~ relation(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_452,c_76]) ).
cnf(c_454,negated_conjecture,
( A = function_inverse(sK0)
| identity_relation(B) != relation_composition(sK0,A)
| identity_relation(relation_dom(A)) != relation_composition(function_inverse(sK0),sK0)
| relation_rng(function_inverse(sK0)) != B
| ~ function(A)
| ~ relation(A)
| ~ relation(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_453,c_75]) ).
cnf(c_455,negated_conjecture,
( sK1 = function_inverse(sK0)
| identity_relation(A) != relation_composition(sK0,sK1)
| identity_relation(relation_dom(sK1)) != relation_composition(function_inverse(sK0),sK0)
| relation_rng(function_inverse(sK0)) != A
| ~ function(sK1)
| ~ relation(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_454,c_74]) ).
cnf(c_456,negated_conjecture,
( sK1 = function_inverse(sK0)
| identity_relation(A) != relation_composition(sK0,sK1)
| identity_relation(relation_dom(sK1)) != relation_composition(function_inverse(sK0),sK0)
| relation_rng(function_inverse(sK0)) != A
| ~ relation(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_455,c_73]) ).
cnf(c_457,negated_conjecture,
( sK1 = function_inverse(sK0)
| identity_relation(relation_dom(sK0)) != relation_composition(sK0,sK1)
| identity_relation(relation_dom(sK1)) != relation_composition(function_inverse(sK0),sK0)
| ~ relation(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_456,c_130]) ).
cnf(c_458,negated_conjecture,
( sK1 = function_inverse(sK0)
| identity_relation(relation_dom(sK0)) != relation_composition(sK0,sK1)
| ~ relation(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_457,c_128]) ).
cnf(c_459,negated_conjecture,
( sK1 = function_inverse(sK0)
| ~ relation(function_inverse(sK0)) ),
inference(resolve,[status(thm)],[c_458,c_71]) ).
cnf(c_460,negated_conjecture,
sK1 != function_inverse(sK0),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_461,negated_conjecture,
~ relation(function_inverse(sK0)),
inference(resolve,[status(thm)],[c_459,c_460]) ).
cnf(c_446,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_321,c_461]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU030+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/15.44 % Computer : n004.cluster.edu
% 0.17/15.44 % Model : x86_64 x86_64
% 0.17/15.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/15.44 % Memory : 8046.5625MB
% 0.17/15.44 % OS : Linux 6.8.0-71-generic
% 0.17/15.44 % CPULimit : 300
% 0.17/15.44 % WCLimit : 300
% 0.17/15.44 % DateTime : Sat Sep 26 08:31:52 UTC 2026
% 0.17/15.44 % CPUTime :
% 0.17/15.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/15.44 % Process 1249948 was started by sandbox2 on n004,
% 0.17/15.44 % Sat Sep 26 08:31:52 2026
% 0.17/15.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/15.45
% 0.17/15.45 % From the command line: assign(max_seconds, 300).
% 0.19/15.52
% 0.19/15.52 % SZS status Theorem for theBenchmark
% 0.19/15.52
% 0.19/15.52 % Proof 1 at 0.06 (+ 0.00) seconds.
% 0.19/15.52 % Length of proof is 25.
% 0.19/15.52 % Level of proof is 4.
% 0.19/15.52 % Maximum clause weight is 38.000.
% 0.19/15.52 % Given clauses 94.
% 0.19/15.52
% 0.19/15.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------