%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU023+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 : n018.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 2.82s 1.18s
% Output : CNFRefutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 116 ( 32 unt; 7 def)
% Number of atoms : 615 ( 143 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 723 ( 317 ~; 308 |; 80 &)
% ( 5 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 175 ( 0 sgn 165 !; 10 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(f31,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f35,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( ( ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) )
=> ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) )
=> ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f36,conjecture,
! [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/sandbox2/benchmark/theBenchmark.p',t56_funct_1) ).
fof(f37,negated_conjecture,
~ ! [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(negated_conjecture,[status(cth)],[f36]) ).
fof(f51,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f51]) ).
fof(f69,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f70,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(flattening,[],[f69]) ).
fof(f76,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f77,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = function_inverse(X0)
<=> ( ! [X2,X3] :
( ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0))
| ( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) )
& relation_dom(X1) = relation_rng(X0) ) ) ) ),
inference(flattening,[],[f76]) ).
fof(f78,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
| apply(function_inverse(X1),apply(X1,X0)) != X0 ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f79,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
| apply(function_inverse(X1),apply(X1,X0)) != X0 ) ),
inference(flattening,[],[f78]) ).
fof(f100,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,[],[f85]) ).
fof(f101,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,[],[f100]) ).
fof(f102,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,[],[f101]) ).
fof(f103,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,sK12(X0,X1),sK13(X0,X1),X1)
| ( sK13(X0,X1) = apply(X1,sK12(X0,X1))
& in(sK12(X0,X1),relation_rng(X0))
& ( sK12(X0,X1) != apply(X0,sK13(X0,X1))
| ~ in(sK13(X0,X1),relation_dom(X0)) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X2,sK12(X0,X1)),skolemize(X3,sK13(X0,X1))],[f102]) ).
fof(f104,plain,
( function(sK15)
& relation(sK15)
& in(sK14,relation_dom(sK15))
& one_to_one(sK15)
& ( sK14 != apply(relation_composition(sK15,function_inverse(sK15)),sK14)
| sK14 != apply(function_inverse(sK15),apply(sK15,sK14)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f79]) ).
fof(f111,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f112,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f154,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f163,plain,
! [X0,X1,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(X1)
| ~ relation(X1)
| function_inverse(X0) != X1
| sP0(X0,X4,X5,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f164,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,[],[f103]) ).
fof(f165,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,[],[f103]) ).
fof(f166,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,[],[f103]) ).
fof(f170,plain,
function(sK15),
inference(cnf_transformation,[],[f104]) ).
fof(f171,plain,
relation(sK15),
inference(cnf_transformation,[],[f104]) ).
fof(f172,plain,
in(sK14,relation_dom(sK15)),
inference(cnf_transformation,[],[f104]) ).
fof(f173,plain,
one_to_one(sK15),
inference(cnf_transformation,[],[f104]) ).
fof(f174,plain,
( sK14 != apply(relation_composition(sK15,function_inverse(sK15)),sK14)
| sK14 != apply(function_inverse(sK15),apply(sK15,sK14)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f182,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,[],[f166]) ).
fof(f183,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,[],[f165]) ).
fof(f184,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,[],[f183]) ).
fof(f185,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,[],[f164]) ).
fof(f186,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,[],[f185]) ).
fof(f187,plain,
! [X0,X4,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| sP0(X0,X4,X5,function_inverse(X0)) ),
inference(equality_resolution,[],[f163]) ).
tcf(c_53,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_54,plain,
! [X0: $i] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) )
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_108,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,[],[f182]) ).
tcf(c_109,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,[],[f184]) ).
tcf(c_110,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,[],[f186]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2,function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ~ relation(function_inverse(X0))
| ~ function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_112,negated_conjecture,
( ( apply(function_inverse(sK15),apply(sK15,sK14)) != sK14 )
| ( apply(relation_composition(sK15,function_inverse(sK15)),sK14) != sK14 ) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_113,negated_conjecture,
one_to_one(sK15),
inference(cnf_transformation,[],[f173]) ).
tcf(c_114,negated_conjecture,
in(sK14,relation_dom(sK15)),
inference(cnf_transformation,[],[f172]) ).
tcf(c_115,negated_conjecture,
relation(sK15),
inference(cnf_transformation,[],[f171]) ).
tcf(c_116,negated_conjecture,
function(sK15),
inference(cnf_transformation,[],[f170]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X0,X1,X2,function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(global_subsumption_just,[status(thm)],[c_111,c_54,c_53,c_111]) ).
tcf(c_168,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_108,c_54,c_53,c_108]) ).
tcf(c_301,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_109,c_53]) ).
tcf(c_302,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_110,c_53]) ).
tcf(c_311,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_302,c_54]) ).
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)
| ~ in(X0,relation_rng(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_301,c_54]) ).
tcf(c_2865,definition,
iPr_def_10 = relation_dom(sK15),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2866,definition,
iPr_def_11 = function_inverse(sK15),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2867,definition,
iPr_def_12 = relation_composition(sK15,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2868,definition,
iPr_def_13 = apply(iPr_def_12,sK14),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2869,definition,
iPr_def_14 = apply(sK15,sK14),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2870,definition,
iPr_def_15 = apply(iPr_def_11,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_2871,negated_conjecture,
function(sK15),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_2872,negated_conjecture,
relation(sK15),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_2873,negated_conjecture,
in(sK14,iPr_def_10),
inference(demodulation,[status(thm)],[c_114,c_2865]) ).
tcf(c_2874,negated_conjecture,
one_to_one(sK15),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_2875,negated_conjecture,
( ( iPr_def_15 != sK14 )
| ( iPr_def_13 != sK14 ) ),
inference(demodulation,[status(thm)],[c_112,c_2869,c_2870,c_2866,c_2867,c_2868]) ).
tcf(c_3845,plain,
( ( relation_dom(function_inverse(sK15)) = relation_rng(sK15) )
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[status(thm)],[c_2874,c_168]) ).
tcf(c_3857,plain,
( ( relation_dom(iPr_def_11) = relation_rng(sK15) )
| ~ relation(sK15)
| ~ function(sK15) ),
inference(light_normalisation,[status(thm)],[c_3845,c_2866]) ).
tcf(c_3858,plain,
relation_dom(iPr_def_11) = relation_rng(sK15),
inference(forward_subsumption_resolution,[status(thm)],[c_3857,c_2872,c_2871]) ).
tcf(c_3945,plain,
( relation(iPr_def_11)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[status(thm)],[c_2866,c_53]) ).
tcf(c_3946,plain,
relation(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_3945,c_2872,c_2871]) ).
tcf(c_3953,plain,
( function(iPr_def_11)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[status(thm)],[c_2866,c_54]) ).
tcf(c_3954,plain,
function(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_3953,c_2872,c_2871]) ).
tcf(c_4274,plain,
! [X0: $i] :
( ( apply(sK15,apply(function_inverse(sK15),X0)) = X0 )
| ~ one_to_one(sK15)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,relation_dom(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_3858,c_311]) ).
tcf(c_4280,plain,
! [X0: $i] :
( ( apply(sK15,apply(iPr_def_11,X0)) = X0 )
| ~ one_to_one(sK15)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,relation_dom(iPr_def_11)) ),
inference(light_normalisation,[status(thm)],[c_4274,c_2866]) ).
tcf(c_4281,plain,
! [X0: $i] :
( ( apply(sK15,apply(iPr_def_11,X0)) = X0 )
| ~ in(X0,relation_dom(iPr_def_11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4280,c_2874,c_2872,c_2871]) ).
tcf(c_4519,plain,
! [X0: $i,X1: $i] :
( sP0(sK15,X0,X1,iPr_def_11)
| ~ one_to_one(sK15)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(superposition,[status(thm)],[c_2866,c_165]) ).
tcf(c_4522,plain,
! [X0: $i,X1: $i] : sP0(sK15,X0,X1,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_4519,c_2874,c_2872,c_2871]) ).
tcf(c_4751,plain,
! [X0: $i] :
( in(apply(function_inverse(sK15),X0),iPr_def_10)
| ~ one_to_one(sK15)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,relation_rng(sK15)) ),
inference(superposition,[status(thm)],[c_2865,c_312]) ).
tcf(c_4764,plain,
! [X0: $i] :
( in(apply(iPr_def_11,X0),iPr_def_10)
| ~ one_to_one(sK15)
| ~ relation(sK15)
| ~ function(sK15)
| ~ in(X0,relation_dom(iPr_def_11)) ),
inference(light_normalisation,[status(thm)],[c_4751,c_2866,c_3858]) ).
tcf(c_4765,plain,
! [X0: $i] :
( in(apply(iPr_def_11,X0),iPr_def_10)
| ~ in(X0,relation_dom(iPr_def_11)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4764,c_2874,c_2872,c_2871]) ).
tcf(c_4824,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(sK15,X1),X0) = apply(X1,apply(sK15,X0)) )
| ~ relation(sK15)
| ~ function(sK15)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2865,c_96]) ).
tcf(c_4832,plain,
! [X0: $i,X1: $i] :
( ( apply(relation_composition(sK15,X1),X0) = apply(X1,apply(sK15,X0)) )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4824,c_2872,c_2871]) ).
tcf(c_4993,plain,
( in(iPr_def_15,iPr_def_10)
| ~ in(iPr_def_14,relation_dom(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_2870,c_4765]) ).
fof(f84,definition,
! [X0,X2,X3,X1] :
( sP0(X0,X2,X3,X1)
<=> ( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f85,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| ! [X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = function_inverse(X0)
<=> ( ! [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) ) ) ) ),
inference(definition_folding,[],[f77,f84]) ).
fof(f97,plain,
! [X0,X2,X3,X1] :
( ( ~ sP0(X0,X2,X3,X1)
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0))
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
| sP0(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f84]) ).
fof(f98,plain,
! [X0,X2,X3,X1] :
( ( ~ sP0(X0,X2,X3,X1)
| apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0))
| ( X3 = apply(X1,X2)
& in(X2,relation_rng(X0)) ) )
& ( ( apply(X0,X3) = X2
& in(X3,relation_dom(X0))
& ( apply(X1,X2) != X3
| ~ in(X2,relation_rng(X0)) ) )
| sP0(X0,X2,X3,X1) ) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( ( ~ sP0(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| ( apply(X3,X1) = X2
& in(X1,relation_rng(X0)) ) )
& ( ( apply(X0,X2) = X1
& in(X2,relation_dom(X0))
& ( apply(X3,X1) != X2
| ~ in(X1,relation_rng(X0)) ) )
| sP0(X0,X1,X2,X3) ) ),
inference(rectify,[],[f98]) ).
fof(f158,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| apply(X3,X1) = X2 ),
inference(cnf_transformation,[],[f99]) ).
fof(f159,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| apply(X0,X2) != X1
| ~ in(X2,relation_dom(X0))
| in(X1,relation_rng(X0)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f180,plain,
! [X2,X3,X0] :
( ~ sP0(X0,apply(X0,X2),X2,X3)
| ~ in(X2,relation_dom(X0))
| in(apply(X0,X2),relation_rng(X0)) ),
inference(equality_resolution,[],[f159]) ).
fof(f181,plain,
! [X2,X3,X0] :
( ~ sP0(X0,apply(X0,X2),X2,X3)
| ~ in(X2,relation_dom(X0))
| apply(X3,apply(X0,X2)) = X2 ),
inference(equality_resolution,[],[f158]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(apply(X0,X1),relation_rng(X0))
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,apply(X0,X1),X1,X2) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(X2,apply(X0,X1)) = X1 )
| ~ in(X1,relation_dom(X0))
| ~ sP0(X0,apply(X0,X1),X1,X2) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_4551,plain,
! [X0: $i] :
( in(apply(sK15,sK14),relation_rng(sK15))
| ~ in(sK14,relation_dom(sK15))
| ~ sP0(sK15,iPr_def_14,sK14,X0) ),
inference(superposition,[status(thm)],[c_2869,c_103]) ).
tcf(c_4563,plain,
! [X0: $i] :
( in(iPr_def_14,relation_dom(iPr_def_11))
| ~ in(sK14,iPr_def_10)
| ~ sP0(sK15,iPr_def_14,sK14,X0) ),
inference(light_normalisation,[status(thm)],[c_4551,c_2865,c_2869,c_3858]) ).
tcf(c_4564,plain,
! [X0: $i] :
( in(iPr_def_14,relation_dom(iPr_def_11))
| ~ sP0(sK15,iPr_def_14,sK14,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4563,c_2873]) ).
tcf(c_4610,plain,
in(iPr_def_14,relation_dom(iPr_def_11)),
inference(superposition,[status(thm)],[c_4522,c_4564]) ).
tcf(c_4614,plain,
apply(sK15,apply(iPr_def_11,iPr_def_14)) = iPr_def_14,
inference(superposition,[status(thm)],[c_4610,c_4281]) ).
tcf(c_4615,plain,
apply(sK15,iPr_def_15) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_4614,c_2870]) ).
tcf(c_4682,plain,
! [X0: $i] :
( ( apply(X0,apply(sK15,sK14)) = sK14 )
| ~ in(sK14,relation_dom(sK15))
| ~ sP0(sK15,iPr_def_14,sK14,X0) ),
inference(superposition,[status(thm)],[c_2869,c_104]) ).
tcf(c_4704,plain,
! [X0: $i] :
( ( apply(X0,iPr_def_14) = sK14 )
| ~ in(sK14,iPr_def_10)
| ~ sP0(sK15,iPr_def_14,sK14,X0) ),
inference(light_normalisation,[status(thm)],[c_4682,c_2865,c_2869]) ).
tcf(c_4705,plain,
! [X0: $i] :
( ( apply(X0,iPr_def_14) = sK14 )
| ~ sP0(sK15,iPr_def_14,sK14,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4704,c_2873]) ).
tcf(c_4998,plain,
in(iPr_def_15,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_4993,c_4610]) ).
tcf(c_5015,plain,
apply(iPr_def_11,iPr_def_14) = sK14,
inference(superposition,[status(thm)],[c_4522,c_4705]) ).
tcf(c_5016,plain,
sK14 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_5015,c_2870]) ).
tcf(c_5022,plain,
! [X0: $i] :
( ( apply(X0,iPr_def_14) = iPr_def_15 )
| ~ sP0(sK15,iPr_def_14,iPr_def_15,X0) ),
inference(demodulation,[status(thm)],[c_4705,c_5016]) ).
tcf(c_5026,plain,
apply(iPr_def_12,iPr_def_15) = iPr_def_13,
inference(demodulation,[status(thm)],[c_2868,c_5016]) ).
tcf(c_5027,plain,
( ( iPr_def_15 != iPr_def_15 )
| ( iPr_def_13 != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_2875,c_5016]) ).
tcf(c_5029,plain,
iPr_def_13 != iPr_def_15,
inference(equality_resolution_simp,[status(thm)],[c_5027]) ).
tcf(c_5195,plain,
! [X0: $i] :
( ( apply(relation_composition(sK15,X0),iPr_def_15) = apply(X0,apply(sK15,iPr_def_15)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_4998,c_4832]) ).
tcf(c_5198,plain,
! [X0: $i] :
( ( apply(relation_composition(sK15,X0),iPr_def_15) = apply(X0,iPr_def_14) )
| ~ relation(X0)
| ~ function(X0) ),
inference(light_normalisation,[status(thm)],[c_5195,c_4615]) ).
tcf(c_5308,plain,
apply(iPr_def_11,iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_4522,c_5022]) ).
tcf(c_14454,plain,
( ( apply(relation_composition(sK15,iPr_def_11),iPr_def_15) = apply(iPr_def_11,iPr_def_14) )
| ~ relation(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3954,c_5198]) ).
tcf(c_14462,plain,
( ( iPr_def_13 = iPr_def_15 )
| ~ relation(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_14454,c_2867,c_5026,c_5308]) ).
tcf(c_14463,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14462,c_5029,c_3946]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU023+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n018.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 : Thu Sep 24 12:37:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 2.82/1.18 % SZS status Started for theBenchmark.p
% 2.82/1.18 % SZS status Theorem for theBenchmark.p
% 2.82/1.18
% 2.82/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.82/1.18
% 2.82/1.18 % ------ iProver source info
% 2.82/1.18
% 2.82/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.82/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.82/1.18 % git: non_committed_changes: false
% 2.82/1.18
% 2.82/1.18 % ------ Parsing...
% 2.82/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.82/1.18
% 2.82/1.18 % ------ 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 %
% 2.82/1.18
% 2.82/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.82/1.18
% 2.82/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.82/1.18 % ------ Proving...
% 2.82/1.18 % ------ Problem Properties
% 2.82/1.18
% 2.82/1.18 %
% 2.82/1.18 % clauses 73
% 2.82/1.18 % conjectures 5
% 2.82/1.18 % EPR 31
% 2.82/1.18 % Horn 67
% 2.82/1.18 % unary 32
% 2.82/1.18 % binary 17
% 2.82/1.18 % lits 168
% 2.82/1.18 % lits eq 23
% 2.82/1.18 % fd_pure 0
% 2.82/1.18 % fd_pseudo 0
% 2.82/1.18 % fd_cond 1
% 2.82/1.18 % fd_pseudo_cond 5
% 2.82/1.18 % AC symbols 0
% 2.82/1.18
% 2.82/1.18 % ------ Schedule dynamic 5 is on
% 2.82/1.18
% 2.82/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.82/1.18
% 2.82/1.18
% 2.82/1.18 % ------
% 2.82/1.18 % Current options:
% 2.82/1.18 % ------
% 2.82/1.18
% 2.82/1.18
% 2.82/1.18 %
% 2.82/1.18
% 2.82/1.18 % ------ Proving...
% 2.82/1.18 %
% 2.82/1.18
% 2.82/1.18 % SZS status Theorem for theBenchmark.p
% 2.82/1.18
% 2.82/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.82/1.18
% 2.82/1.18
%------------------------------------------------------------------------------