%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU028+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 02:55:05 PM UTC 2026
% Result : Theorem 3.81s 11.22s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 125 ( 32 unt; 9 def)
% Number of atoms : 588 ( 148 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 533 ( 226 ~; 229 |; 58 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 102 !; 5 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f11,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1)
& function(X0)
& relation(X0) )
=> ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f34,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f37,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_dom(X1))
& one_to_one(X1) )
=> ( X0 = apply(relation_composition(X1,function_inverse(X1)),X0)
& X0 = apply(function_inverse(X1),apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_1) ).
fof(f38,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( in(X0,relation_rng(X1))
& one_to_one(X1) )
=> ( X0 = apply(relation_composition(function_inverse(X1),X1),X0)
& X0 = apply(X1,apply(function_inverse(X1),X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f39,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_rng(relation_composition(X0,function_inverse(X0))) = relation_dom(X0)
& relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funct_1) ).
fof(f40,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_rng(relation_composition(function_inverse(X0),X0)) = relation_rng(X0)
& relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_1) ).
fof(f42,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
& relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
fof(f43,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0))
& relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f56,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f57,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(flattening,[],[f58]) ).
fof(f62,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f63,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ( function(relation_composition(X0,X1))
& relation(relation_composition(X0,X1)) ) ),
inference(flattening,[],[f62]) ).
fof(f76,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f77,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(flattening,[],[f76]) ).
fof(f81,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| ~ one_to_one(X1)
| ( X0 = apply(relation_composition(X1,function_inverse(X1)),X0)
& X0 = apply(function_inverse(X1),apply(X1,X0)) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f82,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| ~ one_to_one(X1)
| ( X0 = apply(relation_composition(X1,function_inverse(X1)),X0)
& X0 = apply(function_inverse(X1),apply(X1,X0)) ) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ( X0 = apply(relation_composition(function_inverse(X1),X1),X0)
& X0 = apply(X1,apply(function_inverse(X1),X0)) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f84,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| ( X0 = apply(relation_composition(function_inverse(X1),X1),X0)
& X0 = apply(X1,apply(function_inverse(X1),X0)) ) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_rng(relation_composition(X0,function_inverse(X0))) = relation_dom(X0)
& relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f86,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_rng(relation_composition(X0,function_inverse(X0))) = relation_dom(X0)
& relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) ) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_rng(relation_composition(function_inverse(X0),X0)) = relation_rng(X0)
& relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f88,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ( relation_rng(relation_composition(function_inverse(X0),X0)) = relation_rng(X0)
& relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) ) ),
inference(flattening,[],[f87]) ).
fof(f90,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ( relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0))
| relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0)) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f91,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ( relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0))
| relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0)) ) ),
inference(flattening,[],[f90]) ).
fof(f106,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f77]) ).
fof(f107,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK11(X0,X1),X0)
& sK11(X0,X1) != apply(X1,sK11(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f108]) ).
fof(f110,plain,
( function(sK12)
& relation(sK12)
& one_to_one(sK12)
& ( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
| relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f91]) ).
fof(f117,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f118,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f119,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f126,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f166,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK11(X0,X1),X0)
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f109]) ).
fof(f167,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| sK11(X0,X1) != apply(X1,sK11(X0,X1))
| relation_dom(X1) != X0
| identity_relation(X0) = X1 ),
inference(cnf_transformation,[],[f109]) ).
fof(f170,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1))
| ~ one_to_one(X1)
| apply(relation_composition(X1,function_inverse(X1)),X0) = X0 ),
inference(cnf_transformation,[],[f82]) ).
fof(f172,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| apply(relation_composition(function_inverse(X1),X1),X0) = X0 ),
inference(cnf_transformation,[],[f84]) ).
fof(f175,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0))) ),
inference(cnf_transformation,[],[f86]) ).
fof(f177,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f179,plain,
function(sK12),
inference(cnf_transformation,[],[f110]) ).
fof(f180,plain,
relation(sK12),
inference(cnf_transformation,[],[f110]) ).
fof(f181,plain,
one_to_one(sK12),
inference(cnf_transformation,[],[f110]) ).
fof(f182,plain,
( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
| relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f186,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| sK11(relation_dom(X1),X1) != apply(X1,sK11(relation_dom(X1),X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f167]) ).
fof(f187,plain,
! [X1] :
( ~ function(X1)
| ~ relation(X1)
| in(sK11(relation_dom(X1),X1),relation_dom(X1))
| identity_relation(relation_dom(X1)) = X1 ),
inference(equality_resolution,[],[f166]) ).
tcf(c_53,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_54,plain,
! [X0: $i] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( function(relation_composition(X1,X0))
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_100,plain,
! [X0: $i] :
( ( identity_relation(relation_dom(X0)) = X0 )
| ~ relation(X0)
| ~ function(X0)
| ( apply(X0,sK11(relation_dom(X0),X0)) != sK11(relation_dom(X0),X0) ) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_101,plain,
! [X0: $i] :
( in(sK11(relation_dom(X0),X0),relation_dom(X0))
| ( identity_relation(relation_dom(X0)) = X0 )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(X1,function_inverse(X1)),X0) = X0 )
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0 )
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_110,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_112,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_115,negated_conjecture,
( ( relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12)) )
| ( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12)) ) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_116,negated_conjecture,
one_to_one(sK12),
inference(cnf_transformation,[],[f181]) ).
tcf(c_117,negated_conjecture,
relation(sK12),
inference(cnf_transformation,[],[f180]) ).
tcf(c_118,negated_conjecture,
function(sK12),
inference(cnf_transformation,[],[f179]) ).
tcf(c_153,plain,
( ( relation_dom(relation_composition(function_inverse(sK12),sK12)) = relation_rng(sK12) )
| ~ one_to_one(sK12)
| ~ relation(sK12)
| ~ function(sK12) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_155,plain,
( ( relation_dom(relation_composition(sK12,function_inverse(sK12))) = relation_dom(sK12) )
| ~ one_to_one(sK12)
| ~ relation(sK12)
| ~ function(sK12) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_896,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(function_inverse(X0),X0),X1) = X1 )
| ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_rng(X0))
| ( X0 != sK12 ) ),
inference(resolution_lifted,[status(thm)],[c_109,c_116]) ).
tcf(c_897,plain,
! [X0: $i] :
( ( apply(relation_composition(function_inverse(sK12),sK12),X0) = X0 )
| ~ relation(sK12)
| ~ function(sK12)
| ~ in(X0,relation_rng(sK12)) ),
inference(unflattening,[status(thm)],[c_896]) ).
tcf(c_899,plain,
! [X0: $i] :
( ( apply(relation_composition(function_inverse(sK12),sK12),X0) = X0 )
| ~ in(X0,relation_rng(sK12)) ),
inference(global_subsumption_just,[status(thm)],[c_897,c_118,c_117,c_897]) ).
tcf(c_920,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(X0,function_inverse(X0)),X1) = X1 )
| ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ( X0 != sK12 ) ),
inference(resolution_lifted,[status(thm)],[c_107,c_116]) ).
tcf(c_921,plain,
! [X0: $i] :
( ( apply(relation_composition(sK12,function_inverse(sK12)),X0) = X0 )
| ~ relation(sK12)
| ~ function(sK12)
| ~ in(X0,relation_dom(sK12)) ),
inference(unflattening,[status(thm)],[c_920]) ).
tcf(c_923,plain,
! [X0: $i] :
( ( apply(relation_composition(sK12,function_inverse(sK12)),X0) = X0 )
| ~ in(X0,relation_dom(sK12)) ),
inference(global_subsumption_just,[status(thm)],[c_921,c_118,c_117,c_921]) ).
tcf(c_979,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) )
| ~ relation(X0)
| ~ function(X0)
| ( X0 != sK12 ) ),
inference(resolution_lifted,[status(thm)],[c_112,c_116]) ).
tcf(c_980,plain,
( ( relation_dom(relation_composition(function_inverse(sK12),sK12)) = relation_rng(sK12) )
| ~ relation(sK12)
| ~ function(sK12) ),
inference(unflattening,[status(thm)],[c_979]) ).
tcf(c_981,plain,
relation_dom(relation_composition(function_inverse(sK12),sK12)) = relation_rng(sK12),
inference(global_subsumption_just,[status(thm)],[c_980,c_118,c_117,c_116,c_153]) ).
tcf(c_993,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) )
| ~ relation(X0)
| ~ function(X0)
| ( X0 != sK12 ) ),
inference(resolution_lifted,[status(thm)],[c_110,c_116]) ).
tcf(c_994,plain,
( ( relation_dom(relation_composition(sK12,function_inverse(sK12))) = relation_dom(sK12) )
| ~ relation(sK12)
| ~ function(sK12) ),
inference(unflattening,[status(thm)],[c_993]) ).
tcf(c_995,plain,
relation_dom(relation_composition(sK12,function_inverse(sK12))) = relation_dom(sK12),
inference(global_subsumption_just,[status(thm)],[c_994,c_118,c_117,c_116,c_155]) ).
tcf(c_1044,definition,
iPr_def_10 = function_inverse(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1045,definition,
iPr_def_11 = relation_composition(sK12,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1046,definition,
iPr_def_12 = relation_dom(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1047,definition,
iPr_def_13 = relation_dom(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1049,definition,
iPr_def_15 = relation_composition(iPr_def_10,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_1050,definition,
iPr_def_16 = relation_dom(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_1051,definition,
iPr_def_17 = relation_rng(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_1053,definition,
iPr_def_19 = identity_relation(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_1054,definition,
iPr_def_20 = identity_relation(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_1055,plain,
iPr_def_12 = iPr_def_13,
inference(demodulation,[status(thm)],[c_995,c_1047,c_1044,c_1045,c_1046]) ).
tcf(c_1057,plain,
iPr_def_16 = iPr_def_17,
inference(demodulation,[status(thm)],[c_981,c_1051,c_1049,c_1050]) ).
tcf(c_1060,plain,
! [X0: $i] :
( ( apply(iPr_def_11,X0) = X0 )
| ~ in(X0,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_923]) ).
tcf(c_1062,plain,
! [X0: $i] :
( ( apply(iPr_def_15,X0) = X0 )
| ~ in(X0,iPr_def_17) ),
inference(demodulation,[status(thm)],[c_899]) ).
tcf(c_1063,negated_conjecture,
function(sK12),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_1064,negated_conjecture,
relation(sK12),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_1065,negated_conjecture,
( ( iPr_def_15 != iPr_def_19 )
| ( iPr_def_11 != iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_115,c_1054,c_1053]) ).
tcf(c_1892,plain,
! [X0: $i] :
( ( apply(iPr_def_11,X0) = X0 )
| ~ in(X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_1060,c_1055]) ).
tcf(c_1899,plain,
! [X0: $i] :
( ( apply(iPr_def_15,X0) = X0 )
| ~ in(X0,iPr_def_16) ),
inference(light_normalisation,[status(thm)],[c_1062,c_1057]) ).
tcf(c_1944,plain,
identity_relation(iPr_def_16) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_1053,c_1057]) ).
tcf(c_1948,plain,
identity_relation(iPr_def_12) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_1054,c_1055]) ).
tcf(c_2264,plain,
( relation(iPr_def_10)
| ~ relation(sK12)
| ~ function(sK12) ),
inference(superposition,[status(thm)],[c_1044,c_53]) ).
tcf(c_2265,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2264,c_1064,c_1063]) ).
tcf(c_2272,plain,
( function(iPr_def_10)
| ~ relation(sK12)
| ~ function(sK12) ),
inference(superposition,[status(thm)],[c_1044,c_54]) ).
tcf(c_2273,plain,
function(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2272,c_1064,c_1063]) ).
tcf(c_2358,plain,
( relation(iPr_def_11)
| ~ relation(iPr_def_10)
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_1045,c_55]) ).
tcf(c_2359,plain,
( relation(iPr_def_15)
| ~ relation(iPr_def_10)
| ~ relation(sK12) ),
inference(superposition,[status(thm)],[c_1049,c_55]) ).
tcf(c_2360,plain,
relation(iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_2359,c_2265,c_1064]) ).
tcf(c_2361,plain,
relation(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_2358,c_2265,c_1064]) ).
tcf(c_2781,plain,
( function(iPr_def_11)
| ~ relation(iPr_def_10)
| ~ relation(sK12)
| ~ function(iPr_def_10)
| ~ function(sK12) ),
inference(superposition,[status(thm)],[c_1045,c_63]) ).
tcf(c_2782,plain,
( function(iPr_def_15)
| ~ relation(iPr_def_10)
| ~ relation(sK12)
| ~ function(iPr_def_10)
| ~ function(sK12) ),
inference(superposition,[status(thm)],[c_1049,c_63]) ).
tcf(c_2783,plain,
function(iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_2782,c_2265,c_1064,c_2273,c_1063]) ).
tcf(c_2784,plain,
function(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_2781,c_2265,c_1064,c_2273,c_1063]) ).
tcf(c_3092,plain,
( in(sK11(iPr_def_12,iPr_def_11),iPr_def_12)
| ( identity_relation(relation_dom(iPr_def_11)) = iPr_def_11 )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11) ),
inference(superposition,[status(thm)],[c_1046,c_101]) ).
tcf(c_3093,plain,
( in(sK11(iPr_def_16,iPr_def_15),iPr_def_16)
| ( identity_relation(relation_dom(iPr_def_15)) = iPr_def_15 )
| ~ relation(iPr_def_15)
| ~ function(iPr_def_15) ),
inference(superposition,[status(thm)],[c_1050,c_101]) ).
tcf(c_3111,plain,
( in(sK11(iPr_def_16,iPr_def_15),iPr_def_16)
| ( iPr_def_15 = iPr_def_19 )
| ~ relation(iPr_def_15)
| ~ function(iPr_def_15) ),
inference(light_normalisation,[status(thm)],[c_3093,c_1050,c_1944]) ).
tcf(c_3112,plain,
( in(sK11(iPr_def_16,iPr_def_15),iPr_def_16)
| ( iPr_def_15 = iPr_def_19 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3111,c_2360,c_2783]) ).
tcf(c_3115,plain,
( in(sK11(iPr_def_12,iPr_def_11),iPr_def_12)
| ( iPr_def_11 = iPr_def_20 )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_3092,c_1046,c_1948]) ).
tcf(c_3116,plain,
( in(sK11(iPr_def_12,iPr_def_11),iPr_def_12)
| ( iPr_def_11 = iPr_def_20 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3115,c_2361,c_2784]) ).
tcf(c_3172,plain,
( ( identity_relation(relation_dom(iPr_def_11)) = iPr_def_11 )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11)
| ( apply(iPr_def_11,sK11(iPr_def_12,iPr_def_11)) != sK11(iPr_def_12,iPr_def_11) ) ),
inference(superposition,[status(thm)],[c_1046,c_100]) ).
tcf(c_3173,plain,
( ( identity_relation(relation_dom(iPr_def_15)) = iPr_def_15 )
| ~ relation(iPr_def_15)
| ~ function(iPr_def_15)
| ( apply(iPr_def_15,sK11(iPr_def_16,iPr_def_15)) != sK11(iPr_def_16,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_1050,c_100]) ).
tcf(c_3183,plain,
( ( iPr_def_15 = iPr_def_19 )
| ~ relation(iPr_def_15)
| ~ function(iPr_def_15)
| ( apply(iPr_def_15,sK11(iPr_def_16,iPr_def_15)) != sK11(iPr_def_16,iPr_def_15) ) ),
inference(light_normalisation,[status(thm)],[c_3173,c_1050,c_1944]) ).
tcf(c_3184,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( apply(iPr_def_15,sK11(iPr_def_16,iPr_def_15)) != sK11(iPr_def_16,iPr_def_15) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3183,c_2360,c_2783]) ).
tcf(c_3187,plain,
( ( iPr_def_11 = iPr_def_20 )
| ~ relation(iPr_def_11)
| ~ function(iPr_def_11)
| ( apply(iPr_def_11,sK11(iPr_def_12,iPr_def_11)) != sK11(iPr_def_12,iPr_def_11) ) ),
inference(light_normalisation,[status(thm)],[c_3172,c_1046,c_1948]) ).
tcf(c_3188,plain,
( ( iPr_def_11 = iPr_def_20 )
| ( apply(iPr_def_11,sK11(iPr_def_12,iPr_def_11)) != sK11(iPr_def_12,iPr_def_11) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3187,c_2361,c_2784]) ).
tcf(c_3379,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( apply(iPr_def_15,sK11(iPr_def_16,iPr_def_15)) = sK11(iPr_def_16,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_3112,c_1899]) ).
tcf(c_3398,plain,
in(sK11(iPr_def_12,iPr_def_11),iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_3116,c_1065,c_3116,c_3184,c_3379]) ).
tcf(c_3405,plain,
apply(iPr_def_11,sK11(iPr_def_12,iPr_def_11)) = sK11(iPr_def_12,iPr_def_11),
inference(superposition,[status(thm)],[c_3398,c_1892]) ).
tcf(c_3418,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3405,c_3379,c_3184,c_3188,c_1065]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU028+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.38 % Computer : n004.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Thu Sep 24 12:35:48 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.42 Running first-order theorem proving
% 0.14/10.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/10.44
% 0.14/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.44
% 0.14/10.44 % Detected problem language: tptp
% 0.14/10.45 % Proving...
% 3.81/11.22 % SZS status Started for theBenchmark.p
% 3.81/11.22 % SZS status Theorem for theBenchmark.p
% 3.81/11.22
% 3.81/11.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.81/11.22
% 3.81/11.22 % ------ iProver source info
% 3.81/11.22
% 3.81/11.22 % git: date: 2026-07-19 20:42:38 +0200
% 3.81/11.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.81/11.22 % git: non_committed_changes: false
% 3.81/11.22
% 3.81/11.22 % ------ Parsing...
% 3.81/11.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.81/11.22
% 3.81/11.22 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 3.81/11.22
% 3.81/11.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.81/11.22
% 3.81/11.22 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.81/11.22 % ------ Proving...
% 3.81/11.22 % ------ Problem Properties
% 3.81/11.22
% 3.81/11.22 %
% 3.81/11.22 % clauses 91
% 3.81/11.22 % conjectures 3
% 3.81/11.22 % EPR 31
% 3.81/11.22 % Horn 88
% 3.81/11.22 % unary 45
% 3.81/11.22 % binary 26
% 3.81/11.22 % lits 161
% 3.81/11.22 % lits eq 44
% 3.81/11.22 % fd_pure 0
% 3.81/11.22 % fd_pseudo 0
% 3.81/11.22 % fd_cond 1
% 3.81/11.22 % fd_pseudo_cond 1
% 3.81/11.22 % AC symbols 0
% 3.81/11.22
% 3.81/11.22 % ------ Schedule dynamic 5 is on
% 3.81/11.22
% 3.81/11.22 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.81/11.22
% 3.81/11.22
% 3.81/11.22 % ------
% 3.81/11.22 % Current options:
% 3.81/11.22 % ------
% 3.81/11.22
% 3.81/11.22
% 3.81/11.22 %
% 3.81/11.22
% 3.81/11.22 % ------ Proving...
% 3.81/11.22 %
% 3.81/11.22
% 3.81/11.22 % SZS status Theorem for theBenchmark.p
% 3.81/11.22
% 3.81/11.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.81/11.23
% 3.81/11.23
%------------------------------------------------------------------------------