%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU031+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 03:44:23 PM UTC 2025
% Result : Theorem 15.93s 2.39s
% Output : CNFRefutation 15.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 26 unt; 0 def)
% Number of atoms : 114 ( 32 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 113 ( 41 ~; 38 |; 19 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 19 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t64_funct_1,plain,
! [A] :
( ( relation(A)
& function(A) )
=> ! [B] :
( ( relation(B)
& function(B) )
=> ( ( one_to_one(A)
& relation_rng(B) = relation_dom(A)
& relation_composition(B,A) = identity_relation(relation_rng(A)) )
=> B = function_inverse(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_funct_1) ).
fof(t64_funct_1_negated,plain,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ! [B] :
( ( relation(B)
& function(B) )
=> ( ( one_to_one(A)
& relation_rng(B) = relation_dom(A)
& relation_composition(B,A) = identity_relation(relation_rng(A)) )
=> B = function_inverse(A) ) ) ),
inference(negate_conjecture,[status(cth)],[t64_funct_1]) ).
cnf(68,plain,
relation_composition(sK13,sK12) = identity_relation(relation_rng(sK12)),
inference(cnf,[status(esa)],[t64_funct_1_negated]) ).
cnf(l0,plain,
relation_composition(sK13,sK12) = identity_relation(relation_rng(sK12)),
inference(instantiation,[status(thm)],[68]) ).
fof(t55_funct_1,plain,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> ( relation_rng(A) = relation_dom(function_inverse(A))
& relation_dom(A) = relation_rng(function_inverse(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
cnf(57,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(cnf,[status(esa)],[t55_funct_1]) ).
cnf(l83,plain,
( ~ function(sK12)
| ~ relation(sK12)
| ~ one_to_one(sK12)
| relation_rng(sK12) = relation_dom(function_inverse(sK12)) ),
inference(instantiation,[status(thm)],[57]) ).
cnf(63,plain,
function(sK12),
inference(cnf,[status(esa)],[t64_funct_1_negated]) ).
cnf(l84,plain,
function(sK12),
inference(instantiation,[status(thm)],[63]) ).
cnf(66,plain,
one_to_one(sK12),
inference(cnf,[status(esa)],[t64_funct_1_negated]) ).
cnf(l222,plain,
one_to_one(sK12),
inference(instantiation,[status(thm)],[66]) ).
cnf(62,plain,
relation(sK12),
inference(cnf,[status(esa)],[t64_funct_1_negated]) ).
cnf(l86,plain,
relation(sK12),
inference(instantiation,[status(thm)],[62]) ).
fof(l72_funct_1,plain,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ! [D] :
( ( relation(D)
& function(D) )
=> ( ( relation_rng(B) = A
& relation_composition(B,C) = identity_relation(relation_dom(D))
& relation_composition(C,D) = identity_relation(A) )
=> D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l72_funct_1) ).
cnf(30,plain,
( ~ function(X0)
| ~ function(X1)
| ~ function(X2)
| ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| relation_composition(X0,X1) != identity_relation(relation_dom(X2))
| relation_composition(X1,X2) != identity_relation(X3)
| relation_rng(X0) != X3
| X2 = X0 ),
inference(cnf,[status(esa)],[l72_funct_1]) ).
cnf(l3,plain,
( ~ function(sK13)
| ~ function(sK12)
| ~ function(function_inverse(sK12))
| ~ relation(sK13)
| ~ relation(sK12)
| ~ relation(function_inverse(sK12))
| relation_composition(sK13,sK12) != identity_relation(relation_dom(function_inverse(sK12)))
| relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12))
| relation_rng(sK13) != relation_dom(sK12)
| function_inverse(sK12) = sK13 ),
inference(instantiation,[status(thm)],[30]) ).
fof(t61_funct_1,plain,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> ( relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A))
& relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
cnf(60,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ),
inference(cnf,[status(esa)],[t61_funct_1]) ).
cnf(l30,plain,
( ~ function(sK12)
| ~ relation(sK12)
| ~ one_to_one(sK12)
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
inference(instantiation,[status(thm)],[60]) ).
fof(dt_k2_funct_1,plain,
! [A] :
( ( relation(A)
& function(A) )
=> ( relation(function_inverse(A))
& function(function_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
cnf(4,plain,
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf,[status(esa)],[dt_k2_funct_1]) ).
cnf(l70,plain,
( ~ function(sK12)
| ~ relation(sK12)
| relation(function_inverse(sK12)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l57,plain,
one_to_one(sK12),
inference(instantiation,[status(thm)],[66]) ).
cnf(5,plain,
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf,[status(esa)],[dt_k2_funct_1]) ).
cnf(l31,plain,
( ~ function(sK12)
| ~ relation(sK12)
| function(function_inverse(sK12)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l35,plain,
relation(sK12),
inference(instantiation,[status(thm)],[62]) ).
cnf(l32,plain,
relation(sK12),
inference(instantiation,[status(thm)],[62]) ).
cnf(65,plain,
function(sK13),
inference(cnf,[status(esa)],[t64_funct_1_negated]) ).
cnf(l4,plain,
function(sK13),
inference(instantiation,[status(thm)],[65]) ).
cnf(l36,plain,
function(sK12),
inference(instantiation,[status(thm)],[63]) ).
cnf(l6,plain,
function(sK12),
inference(instantiation,[status(thm)],[63]) ).
cnf(64,plain,
relation(sK13),
inference(cnf,[status(esa)],[t64_funct_1_negated]) ).
cnf(l23,plain,
relation(sK13),
inference(instantiation,[status(thm)],[64]) ).
cnf(l108,plain,
relation(sK12),
inference(instantiation,[status(thm)],[62]) ).
cnf(l41,plain,
function(sK12),
inference(instantiation,[status(thm)],[63]) ).
cnf(l71,plain,
function(sK12),
inference(instantiation,[status(thm)],[63]) ).
cnf(l11,plain,
relation(sK12),
inference(instantiation,[status(thm)],[62]) ).
cnf(69,plain,
sK13 != function_inverse(sK12),
inference(cnf,[status(esa)],[t64_funct_1_negated]) ).
cnf(l58,plain,
sK13 != function_inverse(sK12),
inference(instantiation,[status(thm)],[69]) ).
cnf(67,plain,
relation_rng(sK13) = relation_dom(sK12),
inference(cnf,[status(esa)],[t64_funct_1_negated]) ).
cnf(l34,plain,
relation_rng(sK13) = relation_dom(sK12),
inference(instantiation,[status(thm)],[67]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l83,l84,l222,l86,l3,l30,l70,l57,l31,l35,l32,l4,l36,l6,l23,l108,l41,l71,l11,l58,l34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU031+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 23:16:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.35 % launching worker at depth: 10
% 0.18/0.49 % launching worker at depth: 11
% 15.93/2.39 % SZS status Theorem for theBenchmark
% 15.93/2.39 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------