%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU027+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 17.80s 3.73s
% Output : CNFRefutation 17.80s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f76ERROR: Could not build tree for root c_46130ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f33,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2,X3] :
( ( in(X3,relation_dom(X1))
& in(X2,relation_dom(X0)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0) )
=> X1 = function_inverse(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2,X3] :
( ( in(X3,relation_dom(X1))
& in(X2,relation_dom(X0)) )
=> ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0) )
=> X1 = function_inverse(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f38,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( ( ! [X2] :
( in(X2,relation_dom(X0))
=> apply(X0,X2) = apply(X1,X2) )
& relation_dom(X0) = relation_dom(X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_1) ).
fof(f48,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f51,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f50]) ).
fof(f68,plain,
? [X0] :
( function(X0)
& relation(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ! [X2,X3] :
( ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0))
| ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function_inverse(X0) != X1 ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f69,plain,
? [X0] :
( function(X0)
& relation(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ! [X2,X3] :
( ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0))
| ( apply(X0,X2) = X3
<=> apply(X1,X3) = X2 ) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function_inverse(X0) != X1 ) ),
inference(flattening,[],[f68]) ).
fof(f73,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ? [X2] :
( in(X2,relation_dom(X0))
& apply(X1,X2) != apply(X0,X2) )
| relation_dom(X0) != relation_dom(X1)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f74,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ? [X2] :
( in(X2,relation_dom(X0))
& apply(X1,X2) != apply(X0,X2) )
| relation_dom(X0) != relation_dom(X1)
| X0 = X1 ) ),
inference(flattening,[],[f73]) ).
fof(f77,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f78,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK3(X0,X5)) = X5
& in(sK3(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| ( sK1(X0,X1) = apply(X0,sK2(X0,X1))
& in(sK2(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK1(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK1(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f78]) ).
fof(f94,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X2,X3] :
( sP0(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f95,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X2,X3] :
( sP0(X0,X2,X3,X1)
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X4,X5] :
( sP0(X0,X4,X5,X1)
& ( apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| ( apply(X0,X5) = X4
& in(X5,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ? [X2,X3] :
( ~ sP0(X0,X2,X3,X1)
| ( apply(X1,X2) = X3
& in(X2,relation_rng(X0))
& ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( function_inverse(X0) != X1
| ( ! [X4,X5] :
( sP0(X0,X4,X5,X1)
& ( apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| ( apply(X0,X5) = X4
& in(X5,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) )
& ( ~ sP0(X0,sK15(X0,X1),sK16(X0,X1),X1)
| ( sK16(X0,X1) = apply(X1,sK15(X0,X1))
& in(sK15(X0,X1),relation_rng(X0))
& ( sK15(X0,X1) != apply(X0,sK16(X0,X1))
| ~ in(sK16(X0,X1),relation_dom(X0)) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X2,sK15(X0,X1)),skolemize(X3,sK16(X0,X1))],[f96]) ).
fof(f98,plain,
? [X0] :
( function(X0)
& relation(X0)
& ? [X1] :
( function(X1)
& relation(X1)
& ! [X2,X3] :
( ~ in(X3,relation_dom(X1))
| ~ in(X2,relation_dom(X0))
| ( ( apply(X0,X2) != X3
| apply(X1,X3) = X2 )
& ( apply(X1,X3) != X2
| apply(X0,X2) = X3 ) ) )
& relation_rng(X0) = relation_dom(X1)
& relation_dom(X0) = relation_rng(X1)
& one_to_one(X0)
& function_inverse(X0) != X1 ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f99,plain,
( function(sK17)
& relation(sK17)
& function(sK18)
& relation(sK18)
& ! [X2,X3] :
( ~ in(X3,relation_dom(sK18))
| ~ in(X2,relation_dom(sK17))
| ( ( apply(sK17,X2) != X3
| apply(sK18,X3) = X2 )
& ( apply(sK18,X3) != X2
| apply(sK17,X2) = X3 ) ) )
& relation_rng(sK17) = relation_dom(sK18)
& relation_dom(sK17) = relation_rng(sK18)
& one_to_one(sK17)
& sK18 != function_inverse(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X0,sK17),skolemize(X1,sK18)],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( in(sK19(X0,X1),relation_dom(X0))
& apply(X1,sK19(X0,X1)) != apply(X0,sK19(X0,X1)) )
| relation_dom(X0) != relation_dom(X1)
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X2,sK19(X0,X1))],[f74]) ).
fof(f109,plain,
! [X0,X1,X6,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| in(X5,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f113,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f114,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f158,plain,
! [X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| apply(X0,X5) = X4 ),
inference(cnf_transformation,[],[f97]) ).
fof(f159,plain,
! [X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| apply(X1,X4) != X5
| ~ in(X4,relation_rng(X0))
| in(X5,relation_dom(X0)) ),
inference(cnf_transformation,[],[f97]) ).
fof(f160,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| relation_rng(X0) = relation_dom(X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f165,plain,
function(sK17),
inference(cnf_transformation,[],[f99]) ).
fof(f166,plain,
relation(sK17),
inference(cnf_transformation,[],[f99]) ).
fof(f167,plain,
function(sK18),
inference(cnf_transformation,[],[f99]) ).
fof(f168,plain,
relation(sK18),
inference(cnf_transformation,[],[f99]) ).
fof(f169,plain,
! [X2,X3] :
( ~ in(X3,relation_dom(sK18))
| ~ in(X2,relation_dom(sK17))
| apply(sK17,X2) != X3
| apply(sK18,X3) = X2 ),
inference(cnf_transformation,[],[f99]) ).
fof(f171,plain,
relation_rng(sK17) = relation_dom(sK18),
inference(cnf_transformation,[],[f99]) ).
fof(f173,plain,
one_to_one(sK17),
inference(cnf_transformation,[],[f99]) ).
fof(f174,plain,
sK18 != function_inverse(sK17),
inference(cnf_transformation,[],[f99]) ).
fof(f178,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1)
| in(sK19(X0,X1),relation_dom(X0))
| relation_dom(X0) != relation_dom(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f100]) ).
fof(f179,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(X1)
| ~ relation(X1)
| apply(X1,sK19(X0,X1)) != apply(X0,sK19(X0,X1))
| relation_dom(X0) != relation_dom(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f100]) ).
fof(f180,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),X1) ),
inference(equality_resolution,[],[f109]) ).
fof(f181,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f180]) ).
fof(f187,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(equality_resolution,[],[f160]) ).
fof(f188,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| ~ in(X4,relation_rng(X0))
| in(apply(X1,X4),relation_dom(X0)) ),
inference(equality_resolution,[],[f159]) ).
fof(f189,plain,
! [X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ in(X4,relation_rng(X0))
| in(apply(function_inverse(X0),X4),relation_dom(X0)) ),
inference(equality_resolution,[],[f188]) ).
fof(f190,plain,
! [X0,X1,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| ~ in(X4,relation_rng(X0))
| apply(X0,apply(X1,X4)) = X4 ),
inference(equality_resolution,[],[f158]) ).
fof(f191,plain,
! [X0,X4] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ in(X4,relation_rng(X0))
| apply(X0,apply(function_inverse(X0),X4)) = X4 ),
inference(equality_resolution,[],[f190]) ).
fof(f194,plain,
! [X2] :
( ~ in(apply(sK17,X2),relation_dom(sK18))
| ~ in(X2,relation_dom(sK17))
| apply(sK18,apply(sK17,X2)) = X2 ),
inference(equality_resolution,[],[f169]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_59,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_60,plain,
! [X0: $i] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_106,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(X0)) = relation_rng(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(function_inverse(X0))
| ~ function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( in(apply(function_inverse(X1),X0),relation_dom(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(function_inverse(X1))
| ~ function(function_inverse(X1))
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(function_inverse(X1))
| ~ function(function_inverse(X1))
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_111,negated_conjecture,
function_inverse(sK17) != sK18,
inference(cnf_transformation,[],[f174]) ).
tcf(c_112,negated_conjecture,
one_to_one(sK17),
inference(cnf_transformation,[],[f173]) ).
tcf(c_114,negated_conjecture,
relation_rng(sK17) = relation_dom(sK18),
inference(cnf_transformation,[],[f171]) ).
tcf(c_116,negated_conjecture,
! [X0: $i] :
( ( apply(sK18,apply(sK17,X0)) = X0 )
| ~ in(X0,relation_dom(sK17))
| ~ in(apply(sK17,X0),relation_dom(sK18)) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_117,negated_conjecture,
relation(sK18),
inference(cnf_transformation,[],[f168]) ).
tcf(c_118,negated_conjecture,
function(sK18),
inference(cnf_transformation,[],[f167]) ).
tcf(c_119,negated_conjecture,
relation(sK17),
inference(cnf_transformation,[],[f166]) ).
tcf(c_120,negated_conjecture,
function(sK17),
inference(cnf_transformation,[],[f165]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0)
| ( relation_dom(X0) != relation_dom(X1) )
| ( apply(X0,sK19(X0,X1)) != apply(X1,sK19(X0,X1)) ) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( in(sK19(X0,X1),relation_dom(X0))
| ( X0 = X1 )
| ~ relation(X1)
| ~ relation(X0)
| ~ function(X1)
| ~ function(X0)
| ( relation_dom(X0) != relation_dom(X1) ) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_175,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(X0)) = relation_rng(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(global_subsumption_just,[status(thm)],[c_106,c_60,c_59,c_106]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i] :
( in(apply(function_inverse(X1),X0),relation_dom(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ function(function_inverse(X1))
| ~ in(X0,relation_rng(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_107,c_59]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ function(function_inverse(X1))
| ~ in(X0,relation_rng(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_108,c_59]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i] :
( in(apply(function_inverse(X1),X0),relation_dom(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_312,c_60]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,apply(function_inverse(X1),X0)) = X0 )
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_313,c_60]) ).
tcf(c_3005,definition,
iPr_def_10 = relation_dom(sK18),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3006,definition,
iPr_def_11 = relation_dom(sK17),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3007,definition,
iPr_def_12 = relation_rng(sK17),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_3009,definition,
iPr_def_14 = function_inverse(sK17),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_3010,negated_conjecture,
function(sK17),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_3011,negated_conjecture,
relation(sK17),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_3012,negated_conjecture,
function(sK18),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_3013,negated_conjecture,
relation(sK18),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_3014,negated_conjecture,
! [X0: $i] :
( ( apply(sK18,apply(sK17,X0)) = X0 )
| ~ in(X0,iPr_def_11)
| ~ in(apply(sK17,X0),iPr_def_10) ),
inference(demodulation,[status(thm)],[c_116,c_3006,c_3005]) ).
tcf(c_3016,negated_conjecture,
iPr_def_12 = iPr_def_10,
inference(demodulation,[status(thm)],[c_114,c_3007]) ).
tcf(c_3018,negated_conjecture,
one_to_one(sK17),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_3019,negated_conjecture,
iPr_def_14 != sK18,
inference(demodulation,[status(thm)],[c_111,c_3009]) ).
tcf(c_3020,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3022,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3989,plain,
relation_rng(sK17) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_3007,c_3016]) ).
tcf(c_4078,plain,
( ( relation_dom(function_inverse(sK17)) = relation_rng(sK17) )
| ~ relation(sK17)
| ~ function(sK17) ),
inference(superposition,[status(thm)],[c_3018,c_175]) ).
tcf(c_4088,plain,
( ( relation_dom(iPr_def_14) = iPr_def_10 )
| ~ relation(sK17)
| ~ function(sK17) ),
inference(light_normalisation,[status(thm)],[c_4078,c_3009,c_3989]) ).
tcf(c_4089,plain,
relation_dom(iPr_def_14) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_4088,c_3011,c_3010]) ).
tcf(c_4252,plain,
( relation(iPr_def_14)
| ~ relation(sK17)
| ~ function(sK17) ),
inference(superposition,[status(thm)],[c_3009,c_59]) ).
tcf(c_4253,plain,
relation(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_4252,c_3011,c_3010]) ).
tcf(c_4303,plain,
( function(iPr_def_14)
| ~ relation(sK17)
| ~ function(sK17) ),
inference(superposition,[status(thm)],[c_3009,c_60]) ).
tcf(c_4304,plain,
function(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_4303,c_3011,c_3010]) ).
tcf(c_4572,plain,
! [X0: $i] :
( in(apply(sK17,X0),iPr_def_10)
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(X0,relation_dom(sK17)) ),
inference(superposition,[status(thm)],[c_3989,c_56]) ).
tcf(c_4580,plain,
! [X0: $i] :
( in(apply(sK17,X0),iPr_def_10)
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_4572,c_3006]) ).
tcf(c_4581,plain,
! [X0: $i] :
( in(apply(sK17,X0),iPr_def_10)
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4580,c_3011,c_3010]) ).
tcf(c_4617,plain,
! [X0: $i] :
( ( apply(sK18,apply(sK17,X0)) = X0 )
| ~ in(X0,iPr_def_11) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3014,c_4581]) ).
tcf(c_4687,plain,
! [X0: $i] :
( ( iPr_def_14 = sK18 )
| ( iPr_def_14 != X0 )
| ( sK18 != X0 ) ),
inference(instantiation,[status(thm)],[c_3022]) ).
tcf(c_5745,plain,
! [X0: $i] :
( in(sK19(sK18,X0),relation_dom(sK18))
| ( X0 = sK18 )
| ~ relation(sK18)
| ~ function(sK18)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3005,c_125]) ).
tcf(c_5780,plain,
! [X0: $i] :
( in(sK19(sK18,X0),iPr_def_10)
| ( X0 = sK18 )
| ~ relation(sK18)
| ~ function(sK18)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_5745,c_3005]) ).
tcf(c_5781,plain,
! [X0: $i] :
( in(sK19(sK18,X0),iPr_def_10)
| ( X0 = sK18 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5780,c_3013,c_3012]) ).
tcf(c_6082,plain,
( in(sK19(sK18,iPr_def_14),iPr_def_10)
| ( sK18 = iPr_def_14 )
| ~ relation(iPr_def_14)
| ~ function(iPr_def_14) ),
inference(superposition,[status(thm)],[c_4089,c_5781]) ).
tcf(c_6084,plain,
( in(sK19(sK18,iPr_def_14),iPr_def_10)
| ( sK18 = iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6082,c_4253,c_4304]) ).
tcf(c_11348,plain,
( ( iPr_def_14 = sK18 )
| ( iPr_def_14 != iPr_def_14 )
| ( sK18 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_4687]) ).
tcf(c_11349,plain,
iPr_def_14 = iPr_def_14,
inference(instantiation,[status(thm)],[c_3020]) ).
tcf(c_34495,negated_conjecture,
! [X0: $i] :
( ( apply(sK18,apply(sK17,X0)) = X0 )
| ~ in(X0,iPr_def_11) ),
inference(global_subsumption_just,[status(thm)],[c_3014,c_4617]) ).
tcf(c_34532,plain,
relation_rng(sK17) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_3007,c_3016]) ).
tcf(c_34712,plain,
( relation(iPr_def_14)
| ~ relation(sK17)
| ~ function(sK17) ),
inference(superposition,[status(thm)],[c_3009,c_59]) ).
tcf(c_34713,plain,
relation(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_34712,c_3011,c_3010]) ).
tcf(c_34720,plain,
( function(iPr_def_14)
| ~ relation(sK17)
| ~ function(sK17) ),
inference(superposition,[status(thm)],[c_3009,c_60]) ).
tcf(c_34721,plain,
function(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_34720,c_3011,c_3010]) ).
tcf(c_34997,plain,
( ( relation_dom(function_inverse(sK17)) = relation_rng(sK17) )
| ~ relation(sK17)
| ~ function(sK17) ),
inference(superposition,[status(thm)],[c_3018,c_175]) ).
tcf(c_35003,plain,
( ( relation_dom(iPr_def_14) = iPr_def_10 )
| ~ relation(sK17)
| ~ function(sK17) ),
inference(light_normalisation,[status(thm)],[c_34997,c_3009,c_34532]) ).
tcf(c_35004,plain,
relation_dom(iPr_def_14) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_35003,c_3011,c_3010]) ).
tcf(c_35471,plain,
! [X0: $i] :
( in(apply(function_inverse(sK17),X0),iPr_def_11)
| ~ one_to_one(sK17)
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(X0,relation_rng(sK17)) ),
inference(superposition,[status(thm)],[c_3006,c_322]) ).
tcf(c_35489,plain,
! [X0: $i] :
( in(apply(iPr_def_14,X0),iPr_def_11)
| ~ one_to_one(sK17)
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_35471,c_3009,c_34532]) ).
tcf(c_35490,plain,
! [X0: $i] :
( in(apply(iPr_def_14,X0),iPr_def_11)
| ~ in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35489,c_3018,c_3011,c_3010]) ).
tcf(c_35650,plain,
! [X0: $i] :
( ( apply(sK17,apply(function_inverse(sK17),X0)) = X0 )
| ~ one_to_one(sK17)
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_34532,c_323]) ).
tcf(c_35652,plain,
! [X0: $i] :
( ( apply(sK17,apply(iPr_def_14,X0)) = X0 )
| ~ one_to_one(sK17)
| ~ relation(sK17)
| ~ function(sK17)
| ~ in(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_35650,c_3009]) ).
tcf(c_35653,plain,
! [X0: $i] :
( ( apply(sK17,apply(iPr_def_14,X0)) = X0 )
| ~ in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35652,c_3018,c_3011,c_3010]) ).
tcf(c_35710,plain,
! [X0: $i] :
( ( apply(sK18,apply(sK17,apply(iPr_def_14,X0))) = apply(iPr_def_14,X0) )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_35490,c_34495]) ).
tcf(c_36100,plain,
! [X0: $i] :
( in(sK19(sK18,X0),relation_dom(sK18))
| ( X0 = sK18 )
| ~ relation(sK18)
| ~ function(sK18)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_3005,c_125]) ).
tcf(c_36147,plain,
! [X0: $i] :
( in(sK19(sK18,X0),iPr_def_10)
| ( X0 = sK18 )
| ~ relation(sK18)
| ~ function(sK18)
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_36100,c_3005]) ).
tcf(c_36148,plain,
! [X0: $i] :
( in(sK19(sK18,X0),iPr_def_10)
| ( X0 = sK18 )
| ~ relation(X0)
| ~ function(X0)
| ( relation_dom(X0) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36147,c_3013,c_3012]) ).
tcf(c_36982,plain,
( in(sK19(sK18,iPr_def_14),iPr_def_10)
| ( sK18 = iPr_def_14 )
| ~ relation(iPr_def_14)
| ~ function(iPr_def_14) ),
inference(superposition,[status(thm)],[c_35004,c_36148]) ).
tcf(c_36984,plain,
( in(sK19(sK18,iPr_def_14),iPr_def_10)
| ( sK18 = iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36982,c_34713,c_34721]) ).
tcf(c_37121,plain,
in(sK19(sK18,iPr_def_14),iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_36984,c_3019,c_6084,c_11348,c_11349]) ).
tcf(c_37126,plain,
apply(sK18,apply(sK17,apply(iPr_def_14,sK19(sK18,iPr_def_14)))) = apply(iPr_def_14,sK19(sK18,iPr_def_14)),
inference(superposition,[status(thm)],[c_37121,c_35710]) ).
tcf(c_37129,plain,
apply(sK17,apply(iPr_def_14,sK19(sK18,iPr_def_14))) = sK19(sK18,iPr_def_14),
inference(superposition,[status(thm)],[c_37121,c_35653]) ).
tcf(c_45958,plain,
apply(sK18,sK19(sK18,iPr_def_14)) = apply(iPr_def_14,sK19(sK18,iPr_def_14)),
inference(light_normalisation,[status(thm)],[c_37126,c_37129]) ).
tcf(c_45968,plain,
( ( sK18 = iPr_def_14 )
| ~ relation(iPr_def_14)
| ~ relation(sK18)
| ~ function(iPr_def_14)
| ~ function(sK18)
| ( relation_dom(sK18) != relation_dom(iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_45958,c_124]) ).
tcf(c_45976,plain,
( ( sK18 = iPr_def_14 )
| ~ relation(iPr_def_14)
| ~ relation(sK18)
| ~ function(iPr_def_14)
| ~ function(sK18) ),
inference(ground_joinability,[status(thm)],[c_45968,c_3005,c_35004]) ).
tcf(c_45977,plain,
sK18 = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_45976,c_34713,c_3013,c_34721,c_3012]) ).
tcf(c_46127,plain,
iPr_def_14 != iPr_def_14,
inference(demodulation,[status(thm)],[c_3019,c_45977]) ).
tcf(c_46130,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_46127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU027+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:36:18 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 17.80/3.73 % SZS status Started for theBenchmark.p
% 17.80/3.73 % SZS status Theorem for theBenchmark.p
% 17.80/3.73
% 17.80/3.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.80/3.73
% 17.80/3.73 % ------ iProver source info
% 17.80/3.73
% 17.80/3.73 % git: date: 2026-07-19 20:42:38 +0200
% 17.80/3.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.80/3.73 % git: non_committed_changes: false
% 17.80/3.73
% 17.80/3.73 % ------ Parsing...
% 17.80/3.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.80/3.73
% 17.80/3.73 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 17.80/3.73
% 17.80/3.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.80/3.73
% 17.80/3.73 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.80/3.73 % ------ Proving...
% 17.80/3.73 % ------ Problem Properties
% 17.80/3.73
% 17.80/3.73 %
% 17.80/3.73 % clauses 78
% 17.80/3.73 % conjectures 10
% 17.80/3.73 % EPR 34
% 17.80/3.73 % Horn 69
% 17.80/3.73 % unary 35
% 17.80/3.73 % binary 16
% 17.80/3.73 % lits 191
% 17.80/3.73 % lits eq 35
% 17.80/3.73 % fd_pure 0
% 17.80/3.73 % fd_pseudo 0
% 17.80/3.73 % fd_cond 1
% 17.80/3.73 % fd_pseudo_cond 10
% 17.80/3.73 % AC symbols 0
% 17.80/3.73
% 17.80/3.73 % ------ Schedule dynamic 5 is on
% 17.80/3.73
% 17.80/3.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.80/3.73
% 17.80/3.73
% 17.80/3.73 % ------
% 17.80/3.73 % Current options:
% 17.80/3.73 % ------
% 17.80/3.73
% 17.80/3.73
% 17.80/3.73 %
% 17.80/3.73
% 17.80/3.73 % ------ Proving...
% 17.80/3.73 %
% 17.80/3.73
% 17.80/3.73 % SZS status Theorem for theBenchmark.p
% 17.80/3.73
% 17.80/3.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.80/3.73
%------------------------------------------------------------------------------