%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU219+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 02:56:09 PM UTC 2026
% Result : Theorem 15.58s 3.96s
% Output : CNFRefutation 15.58s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f439ERROR: Could not build tree for root c_37144ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> function_inverse(X0) = relation_inverse(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_funct_1) ).
fof(f50,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(f99,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f174,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f202,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f203,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(X0) = relation_rng(function_inverse(X0))
& relation_rng(X0) = relation_dom(function_inverse(X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f202]) ).
fof(f274,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f275,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(flattening,[],[f274]) ).
fof(f276,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f277,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( function(function_inverse(X0))
& relation(function_inverse(X0)) ) ),
inference(flattening,[],[f276]) ).
fof(f313,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(ennf_transformation,[],[f99]) ).
fof(f381,plain,
! [X0] :
( ~ relation(X0)
| ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
inference(ennf_transformation,[],[f174]) ).
fof(f408,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ( relation_dom(X0) != relation_rng(function_inverse(X0))
| relation_rng(X0) != relation_dom(function_inverse(X0)) ) ),
inference(ennf_transformation,[],[f203]) ).
fof(f409,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ( relation_dom(X0) != relation_rng(function_inverse(X0))
| relation_rng(X0) != relation_dom(function_inverse(X0)) ) ),
inference(flattening,[],[f408]) ).
fof(f575,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,[],[f439]) ).
fof(f576,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,[],[f575]) ).
fof(f577,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,[],[f576]) ).
fof(f578,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,sK71(X0,X1),sK72(X0,X1),X1)
| ( sK72(X0,X1) = apply(X1,sK71(X0,X1))
& in(sK71(X0,X1),relation_rng(X0))
& ( sK71(X0,X1) != apply(X0,sK72(X0,X1))
| ~ in(sK72(X0,X1),relation_dom(X0)) ) )
| relation_rng(X0) != relation_dom(X1)
| X1 = function_inverse(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71,sK72]),skolemize(X2,sK71(X0,X1)),skolemize(X3,sK72(X0,X1))],[f577]) ).
fof(f579,plain,
( function(sK73)
& relation(sK73)
& one_to_one(sK73)
& ( relation_dom(sK73) != relation_rng(function_inverse(sK73))
| relation_rng(sK73) != relation_dom(function_inverse(sK73)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(X0,sK73)],[f409]) ).
fof(f741,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_inverse(X0) = function_inverse(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f742,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[],[f277]) ).
fof(f743,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f277]) ).
fof(f791,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(cnf_transformation,[],[f313]) ).
fof(f906,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) ),
inference(cnf_transformation,[],[f381]) ).
fof(f951,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,[],[f578]) ).
fof(f956,plain,
function(sK73),
inference(cnf_transformation,[],[f579]) ).
fof(f957,plain,
relation(sK73),
inference(cnf_transformation,[],[f579]) ).
fof(f958,plain,
one_to_one(sK73),
inference(cnf_transformation,[],[f579]) ).
fof(f959,plain,
( relation_dom(sK73) != relation_rng(function_inverse(sK73))
| relation_rng(sK73) != relation_dom(function_inverse(sK73)) ),
inference(cnf_transformation,[],[f579]) ).
fof(f1216,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,[],[f951]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( relation_inverse(X0) = function_inverse(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f741]) ).
tcf(c_197,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f743]) ).
tcf(c_198,plain,
! [X0: $i] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f742]) ).
tcf(c_246,plain,
! [X0: $i] :
( ( relation_inverse(relation_inverse(X0)) = X0 )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f791]) ).
tcf(c_360,plain,
! [X0: $i] :
( ( relation_dom(relation_inverse(X0)) = relation_rng(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f906]) ).
tcf(c_405,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,[],[f1216]) ).
tcf(c_410,negated_conjecture,
( ( relation_rng(function_inverse(sK73)) != relation_dom(sK73) )
| ( relation_dom(function_inverse(sK73)) != relation_rng(sK73) ) ),
inference(cnf_transformation,[],[f959]) ).
tcf(c_411,negated_conjecture,
one_to_one(sK73),
inference(cnf_transformation,[],[f958]) ).
tcf(c_412,negated_conjecture,
relation(sK73),
inference(cnf_transformation,[],[f957]) ).
tcf(c_413,negated_conjecture,
function(sK73),
inference(cnf_transformation,[],[f956]) ).
tcf(c_715,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_405,c_198,c_197,c_405]) ).
tcf(c_996,plain,
( ( relation_dom(function_inverse(sK73)) != relation_rng(sK73) )
| ( relation_rng(function_inverse(sK73)) != relation_dom(sK73) ) ),
inference(prop_impl_just,[status(thm)],[c_410]) ).
tcf(c_997,plain,
( ( relation_rng(function_inverse(sK73)) != relation_dom(sK73) )
| ( relation_dom(function_inverse(sK73)) != relation_rng(sK73) ) ),
inference(renaming,[status(thm)],[c_996]) ).
tcf(c_6237,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(X0)) = relation_rng(X0) )
| ~ relation(X0)
| ~ function(X0)
| ( X0 != sK73 ) ),
inference(resolution_lifted,[status(thm)],[c_715,c_411]) ).
tcf(c_6238,plain,
( ( relation_dom(function_inverse(sK73)) = relation_rng(sK73) )
| ~ relation(sK73)
| ~ function(sK73) ),
inference(unflattening,[status(thm)],[c_6237]) ).
tcf(c_6239,plain,
relation_dom(function_inverse(sK73)) = relation_rng(sK73),
inference(global_subsumption_just,[status(thm)],[c_6238,c_413,c_412,c_6238]) ).
tcf(c_6374,plain,
relation_rng(function_inverse(sK73)) != relation_dom(sK73),
inference(backward_subsumption_resolution,[status(thm)],[c_997,c_6239]) ).
tcf(c_12275,definition,
iPr_def_10 = function_inverse(sK73),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_12276,definition,
iPr_def_11 = relation_rng(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_12277,definition,
iPr_def_12 = relation_dom(sK73),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_12278,plain,
iPr_def_11 != iPr_def_12,
inference(demodulation,[status(thm)],[c_6374,c_12277,c_12275,c_12276]) ).
tcf(c_12279,negated_conjecture,
function(sK73),
inference(demodulation,[status(thm)],[c_413]) ).
tcf(c_12280,negated_conjecture,
relation(sK73),
inference(demodulation,[status(thm)],[c_412]) ).
tcf(c_12281,negated_conjecture,
one_to_one(sK73),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_19907,plain,
( relation(iPr_def_10)
| ~ relation(sK73)
| ~ function(sK73) ),
inference(superposition,[status(thm)],[c_12275,c_197]) ).
tcf(c_19908,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_19907,c_12280,c_12279]) ).
tcf(c_20083,plain,
relation_inverse(relation_inverse(sK73)) = sK73,
inference(superposition,[status(thm)],[c_12280,c_246]) ).
tcf(c_21085,plain,
relation_dom(relation_inverse(iPr_def_10)) = relation_rng(iPr_def_10),
inference(superposition,[status(thm)],[c_19908,c_360]) ).
tcf(c_21086,plain,
relation_dom(relation_inverse(iPr_def_10)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_21085,c_12276]) ).
tcf(c_37094,plain,
( ( relation_inverse(sK73) = function_inverse(sK73) )
| ~ relation(sK73)
| ~ function(sK73) ),
inference(superposition,[status(thm)],[c_12281,c_196]) ).
tcf(c_37103,plain,
( ( relation_inverse(sK73) = iPr_def_10 )
| ~ relation(sK73)
| ~ function(sK73) ),
inference(light_normalisation,[status(thm)],[c_37094,c_12275]) ).
tcf(c_37104,plain,
relation_inverse(sK73) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_37103,c_12280,c_12279]) ).
tcf(c_37138,plain,
relation_inverse(iPr_def_10) = sK73,
inference(demodulation,[status(thm)],[c_20083,c_37104]) ).
tcf(c_37141,plain,
relation_dom(sK73) = iPr_def_11,
inference(demodulation,[status(thm)],[c_21086,c_37138]) ).
tcf(c_37143,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_12277,c_37141]) ).
tcf(c_37144,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_37143,c_12278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU219+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.43 % Computer : n014.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Thu Sep 24 13:14:04 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.49 Running first-order theorem proving
% 0.18/0.49 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
% 0.18/0.50
% 0.18/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.18/0.50
% 0.18/0.50 % Detected problem language: tptp
% 0.25/0.52 % Proving...
% 15.58/3.96 % SZS status Started for theBenchmark.p
% 15.58/3.96 % SZS status Theorem for theBenchmark.p
% 15.58/3.96
% 15.58/3.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.58/3.96
% 15.58/3.96 % ------ iProver source info
% 15.58/3.96
% 15.58/3.96 % git: date: 2026-07-19 20:42:38 +0200
% 15.58/3.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.58/3.96 % git: non_committed_changes: false
% 15.58/3.96
% 15.58/3.96 % ------ Parsing...
% 15.58/3.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.58/3.96
% 15.58/3.96 % ------ Preprocessing... sup_sim: 41 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 15.58/3.96
% 15.58/3.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.58/3.96
% 15.58/3.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.58/3.96 % ------ Proving...
% 15.58/3.96 % ------ Problem Properties
% 15.58/3.96
% 15.58/3.96 %
% 15.58/3.96 % clauses 363
% 15.58/3.96 % conjectures 3
% 15.58/3.96 % EPR 48
% 15.58/3.96 % Horn 294
% 15.58/3.96 % unary 61
% 15.58/3.96 % binary 114
% 15.58/3.96 % lits 992
% 15.58/3.96 % lits eq 192
% 15.58/3.96 % fd_pure 0
% 15.58/3.96 % fd_pseudo 0
% 15.58/3.96 % fd_cond 14
% 15.58/3.96 % fd_pseudo_cond 73
% 15.58/3.96 % AC symbols 0
% 15.58/3.96
% 15.58/3.96 % ------ Schedule dynamic 5 is on
% 15.58/3.96
% 15.58/3.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.58/3.96
% 15.58/3.96
% 15.58/3.96 % ------
% 15.58/3.96 % Current options:
% 15.58/3.96 % ------
% 15.58/3.96
% 15.58/3.96
% 15.58/3.96 %
% 15.58/3.96
% 15.58/3.96 % ------ Proving...
% 15.58/3.96 %
% 15.58/3.96
% 15.58/3.96 % SZS status Theorem for theBenchmark.p
% 15.58/3.96
% 15.58/3.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.58/3.96
% 15.58/3.96
%------------------------------------------------------------------------------