%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU026+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 : n019.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 2.25s 1.18s
% Output : CNFRefutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 77 ( 30 unt; 8 def)
% Number of atoms : 267 ( 71 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 235 ( 105 ~; 96 |; 21 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn 46 !; 2 ?; 15 :)
% 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(f29,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f33,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f34,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_dom(X0),relation_rng(X1))
=> relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_relat_1) ).
fof(f36,axiom,
! [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/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f37,conjecture,
! [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(f38,negated_conjecture,
~ ! [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(negated_conjecture,[status(cth)],[f37]) ).
fof(f43,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f29]) ).
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(f71,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f72,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f74,plain,
! [X0] :
( ~ relation(X0)
| ! [X1] :
( ~ relation(X1)
| ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(relation_composition(X1,X0)) = relation_rng(X0) ) ),
inference(flattening,[],[f73]) ).
fof(f77,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,[],[f36]) ).
fof(f78,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,[],[f77]) ).
fof(f79,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ( relation_rng(X0) != relation_rng(relation_composition(function_inverse(X0),X0))
| relation_rng(X0) != relation_dom(relation_composition(function_inverse(X0),X0)) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f80,plain,
? [X0] :
( function(X0)
& relation(X0)
& one_to_one(X0)
& ( relation_rng(X0) != relation_rng(relation_composition(function_inverse(X0),X0))
| relation_rng(X0) != relation_dom(relation_composition(function_inverse(X0),X0)) ) ),
inference(flattening,[],[f79]) ).
fof(f97,plain,
( function(sK11)
& relation(sK11)
& one_to_one(sK11)
& ( relation_rng(sK11) != relation_rng(relation_composition(function_inverse(sK11),sK11))
| relation_rng(sK11) != relation_dom(relation_composition(function_inverse(sK11),sK11)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f80]) ).
fof(f105,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f145,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f43]) ).
fof(f150,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f151,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(relation_dom(X0),relation_rng(X1))
| relation_rng(X0) = relation_rng(relation_composition(X1,X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f153,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f154,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f155,plain,
function(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f156,plain,
relation(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f157,plain,
one_to_one(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f158,plain,
( relation_rng(sK11) != relation_rng(relation_composition(function_inverse(sK11),sK11))
| relation_rng(sK11) != relation_dom(relation_composition(function_inverse(sK11),sK11)) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_53,plain,
! [X0: $i] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_94,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f145]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( ( relation_dom(relation_composition(X0,X1)) = relation_dom(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_rng(X0),relation_dom(X1)) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( ( relation_rng(relation_composition(X1,X0)) = relation_rng(X0) )
| ~ relation(X1)
| ~ relation(X0)
| ~ subset(relation_dom(X0),relation_rng(X1)) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_102,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(X0)) = relation_rng(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_103,plain,
! [X0: $i] :
( ( relation_rng(function_inverse(X0)) = relation_dom(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_104,negated_conjecture,
( ( relation_rng(relation_composition(function_inverse(sK11),sK11)) != relation_rng(sK11) )
| ( relation_dom(relation_composition(function_inverse(sK11),sK11)) != relation_rng(sK11) ) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_105,negated_conjecture,
one_to_one(sK11),
inference(cnf_transformation,[],[f157]) ).
tcf(c_106,negated_conjecture,
relation(sK11),
inference(cnf_transformation,[],[f156]) ).
tcf(c_107,negated_conjecture,
function(sK11),
inference(cnf_transformation,[],[f155]) ).
tcf(c_137,plain,
( ( relation_rng(function_inverse(sK11)) = relation_dom(sK11) )
| ~ one_to_one(sK11)
| ~ relation(sK11)
| ~ function(sK11) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_138,plain,
( ( relation_dom(function_inverse(sK11)) = relation_rng(sK11) )
| ~ one_to_one(sK11)
| ~ relation(sK11)
| ~ function(sK11) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_751,plain,
! [X0: $i] :
( ( relation_rng(function_inverse(X0)) = relation_dom(X0) )
| ~ relation(X0)
| ~ function(X0)
| ( X0 != sK11 ) ),
inference(resolution_lifted,[status(thm)],[c_103,c_105]) ).
tcf(c_752,plain,
( ( relation_rng(function_inverse(sK11)) = relation_dom(sK11) )
| ~ relation(sK11)
| ~ function(sK11) ),
inference(unflattening,[status(thm)],[c_751]) ).
tcf(c_753,plain,
relation_rng(function_inverse(sK11)) = relation_dom(sK11),
inference(global_subsumption_just,[status(thm)],[c_752,c_107,c_106,c_105,c_137]) ).
tcf(c_758,plain,
! [X0: $i] :
( ( relation_dom(function_inverse(X0)) = relation_rng(X0) )
| ~ relation(X0)
| ~ function(X0)
| ( X0 != sK11 ) ),
inference(resolution_lifted,[status(thm)],[c_102,c_105]) ).
tcf(c_759,plain,
( ( relation_dom(function_inverse(sK11)) = relation_rng(sK11) )
| ~ relation(sK11)
| ~ function(sK11) ),
inference(unflattening,[status(thm)],[c_758]) ).
tcf(c_760,plain,
relation_dom(function_inverse(sK11)) = relation_rng(sK11),
inference(global_subsumption_just,[status(thm)],[c_759,c_107,c_106,c_105,c_138]) ).
tcf(c_1817,definition,
iPr_def_10 = function_inverse(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1818,definition,
iPr_def_11 = relation_dom(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1819,definition,
iPr_def_12 = relation_rng(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1820,definition,
iPr_def_13 = relation_rng(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1821,definition,
iPr_def_14 = relation_dom(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1822,definition,
iPr_def_15 = relation_composition(iPr_def_10,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_1823,definition,
iPr_def_16 = relation_dom(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_1824,definition,
iPr_def_17 = relation_rng(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_1825,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_760,c_1819,c_1817,c_1818]) ).
tcf(c_1826,plain,
iPr_def_13 = iPr_def_14,
inference(demodulation,[status(thm)],[c_753,c_1821,c_1820]) ).
tcf(c_1827,negated_conjecture,
function(sK11),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_1828,negated_conjecture,
relation(sK11),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_1829,negated_conjecture,
( ( iPr_def_17 != iPr_def_12 )
| ( iPr_def_16 != iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_104,c_1824,c_1822,c_1823]) ).
tcf(c_2799,plain,
( ( iPr_def_11 != iPr_def_17 )
| ( iPr_def_11 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1829,c_1825]) ).
tcf(c_2822,plain,
relation_rng(sK11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1819,c_1825]) ).
tcf(c_2823,plain,
relation_dom(sK11) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_1821,c_1826]) ).
tcf(c_3076,plain,
( relation(iPr_def_10)
| ~ relation(sK11)
| ~ function(sK11) ),
inference(superposition,[status(thm)],[c_1817,c_53]) ).
tcf(c_3077,plain,
relation(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_3076,c_1828,c_1827]) ).
tcf(c_3523,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(X0,sK11)) = relation_dom(X0) )
| ~ relation(sK11)
| ~ relation(X0)
| ~ subset(relation_rng(X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_2823,c_99]) ).
tcf(c_3540,plain,
! [X0: $i] :
( ( relation_dom(relation_composition(X0,sK11)) = relation_dom(X0) )
| ~ relation(X0)
| ~ subset(relation_rng(X0),iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3523,c_1828]) ).
tcf(c_3636,plain,
( ( relation_dom(relation_composition(iPr_def_10,sK11)) = relation_dom(iPr_def_10) )
| ~ relation(iPr_def_10)
| ~ subset(iPr_def_13,iPr_def_13) ),
inference(superposition,[status(thm)],[c_1820,c_3540]) ).
tcf(c_3645,plain,
( ( iPr_def_11 = iPr_def_16 )
| ~ relation(iPr_def_10)
| ~ subset(iPr_def_13,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_3636,c_1818,c_1822,c_1823]) ).
tcf(c_3646,plain,
iPr_def_11 = iPr_def_16,
inference(forward_subsumption_resolution,[status(thm)],[c_3645,c_3077,c_94]) ).
tcf(c_3653,plain,
iPr_def_11 != iPr_def_17,
inference(backward_subsumption_resolution,[status(thm)],[c_2799,c_3646]) ).
tcf(c_3753,plain,
! [X0: $i] :
( ( relation_rng(relation_composition(X0,sK11)) = relation_rng(sK11) )
| ~ relation(sK11)
| ~ relation(X0)
| ~ subset(iPr_def_13,relation_rng(X0)) ),
inference(superposition,[status(thm)],[c_2823,c_100]) ).
tcf(c_3789,plain,
! [X0: $i] :
( ( relation_rng(relation_composition(X0,sK11)) = iPr_def_11 )
| ~ relation(sK11)
| ~ relation(X0)
| ~ subset(iPr_def_13,relation_rng(X0)) ),
inference(light_normalisation,[status(thm)],[c_3753,c_2822]) ).
tcf(c_3790,plain,
! [X0: $i] :
( ( relation_rng(relation_composition(X0,sK11)) = iPr_def_11 )
| ~ relation(X0)
| ~ subset(iPr_def_13,relation_rng(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3789,c_1828]) ).
tcf(c_3917,plain,
( ( relation_rng(relation_composition(iPr_def_10,sK11)) = iPr_def_11 )
| ~ relation(iPr_def_10)
| ~ subset(iPr_def_13,iPr_def_13) ),
inference(superposition,[status(thm)],[c_1820,c_3790]) ).
tcf(c_3926,plain,
( ( iPr_def_11 = iPr_def_17 )
| ~ relation(iPr_def_10)
| ~ subset(iPr_def_13,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_3917,c_1822,c_1824]) ).
tcf(c_3927,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3926,c_3653,c_3077,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU026+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 12:35:19 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 2.25/1.18 % SZS status Started for theBenchmark.p
% 2.25/1.18 % SZS status Theorem for theBenchmark.p
% 2.25/1.18
% 2.25/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.25/1.18
% 2.25/1.18 % ------ iProver source info
% 2.25/1.18
% 2.25/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.25/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.25/1.18 % git: non_committed_changes: false
% 2.25/1.18
% 2.25/1.18 % ------ Parsing...
% 2.25/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.25/1.18
% 2.25/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.25/1.18
% 2.25/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.25/1.18
% 2.25/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.25/1.18 % ------ Proving...
% 2.25/1.18 % ------ Problem Properties
% 2.25/1.18
% 2.25/1.18 %
% 2.25/1.18 % clauses 68
% 2.25/1.18 % conjectures 3
% 2.25/1.18 % EPR 32
% 2.25/1.18 % Horn 66
% 2.25/1.18 % unary 35
% 2.25/1.18 % binary 17
% 2.25/1.18 % lits 121
% 2.25/1.18 % lits eq 20
% 2.25/1.18 % fd_pure 0
% 2.25/1.18 % fd_pseudo 0
% 2.25/1.18 % fd_cond 1
% 2.25/1.18 % fd_pseudo_cond 1
% 2.25/1.18 % AC symbols 0
% 2.25/1.18
% 2.25/1.18 % ------ Schedule dynamic 5 is on
% 2.25/1.18
% 2.25/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
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% 2.25/1.18
% 2.25/1.18 % ------
% 2.25/1.18 % Current options:
% 2.25/1.18 % ------
% 2.25/1.18
% 2.25/1.18
% 2.25/1.18 %
% 2.25/1.18
% 2.25/1.18 % ------ Proving...
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% 2.25/1.18 % SZS status Theorem for theBenchmark.p
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% 2.25/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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