%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU368+1 : 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 : n005.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 02:57:14 PM UTC 2026
% Result : Theorem 3.82s 1.28s
% Output : CNFRefutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 60 ( 25 unt; 4 def)
% Number of atoms : 162 ( 60 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 109 ( 50 ~; 41 |; 13 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 17 ( 15 usr; 5 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 72 !; 1 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f33,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ! [X2,X3] :
( rel_str_of(X0,X1) = rel_str_of(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(f34,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(f38,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f47,axiom,
! [X0] :
( relation_of2_as_subset(inclusion_order(X0),X0,X0)
& v1_partfun1(inclusion_order(X0),X0,X0)
& transitive(inclusion_order(X0))
& antisymmetric(inclusion_order(X0))
& reflexive(inclusion_order(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
fof(f48,axiom,
! [X0] :
( rel_str(incl_POSet(X0))
& strict_rel_str(incl_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
fof(f51,axiom,
! [X0] :
( antisymmetric_relstr(incl_POSet(X0))
& transitive_relstr(incl_POSet(X0))
& reflexive_relstr(incl_POSet(X0))
& strict_rel_str(incl_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_yellow_1) ).
fof(f52,axiom,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow_1) ).
fof(f53,conjecture,
! [X0] :
( the_InternalRel(incl_POSet(X0)) = inclusion_order(X0)
& the_carrier(incl_POSet(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_yellow_1) ).
fof(f54,negated_conjecture,
~ ! [X0] :
( the_InternalRel(incl_POSet(X0)) = inclusion_order(X0)
& the_carrier(incl_POSet(X0)) = X0 ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f83,plain,
! [X0,X1] :
( ~ relation_of2(X1,X0,X0)
| ! [X2,X3] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ( X1 = X3
& X0 = X2 ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f84,plain,
! [X0] :
( ~ rel_str(X0)
| ~ strict_rel_str(X0)
| X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f85,plain,
! [X0] :
( ~ rel_str(X0)
| ~ strict_rel_str(X0)
| X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0)) ),
inference(flattening,[],[f84]) ).
fof(f92,plain,
? [X0] :
( inclusion_order(X0) != the_InternalRel(incl_POSet(X0))
| the_carrier(incl_POSet(X0)) != X0 ),
inference(ennf_transformation,[],[f54]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
& ( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f107,plain,
( inclusion_order(sK13) != the_InternalRel(incl_POSet(sK13))
| sK13 != the_carrier(incl_POSet(sK13)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f92]) ).
fof(f151,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X1,X0,X0)
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f83]) ).
fof(f152,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X1,X0,X0)
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f153,plain,
! [X0] :
( ~ rel_str(X0)
| ~ strict_rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ),
inference(cnf_transformation,[],[f85]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f170,plain,
! [X0] : relation_of2_as_subset(inclusion_order(X0),X0,X0),
inference(cnf_transformation,[],[f47]) ).
fof(f175,plain,
! [X0] : rel_str(incl_POSet(X0)),
inference(cnf_transformation,[],[f48]) ).
fof(f181,plain,
! [X0] : strict_rel_str(incl_POSet(X0)),
inference(cnf_transformation,[],[f51]) ).
fof(f182,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
inference(cnf_transformation,[],[f52]) ).
fof(f183,plain,
( inclusion_order(sK13) != the_InternalRel(incl_POSet(sK13))
| sK13 != the_carrier(incl_POSet(sK13)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f190,plain,
! [X0] : rel_str(rel_str_of(X0,inclusion_order(X0))),
inference(definition_unfolding,[],[f175,f182]) ).
fof(f191,plain,
! [X0] : strict_rel_str(rel_str_of(X0,inclusion_order(X0))),
inference(definition_unfolding,[],[f181,f182]) ).
fof(f195,plain,
( inclusion_order(sK13) != the_InternalRel(rel_str_of(sK13,inclusion_order(sK13)))
| sK13 != the_carrier(rel_str_of(sK13,inclusion_order(sK13))) ),
inference(definition_unfolding,[],[f183,f182,f182]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ~ relation_of2(X1,X0,X0)
| ( rel_str_of(X0,X1) != rel_str_of(X2,X3) ) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ relation_of2(X1,X0,X0)
| ( rel_str_of(X0,X1) != rel_str_of(X2,X3) ) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_94,plain,
! [X0: $i] :
( ( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 )
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_114,plain,
! [X0: $i] : relation_of2_as_subset(inclusion_order(X0),X0,X0),
inference(cnf_transformation,[],[f170]) ).
tcf(c_116,plain,
! [X0: $i] : rel_str(rel_str_of(X0,inclusion_order(X0))),
inference(cnf_transformation,[],[f190]) ).
tcf(c_118,plain,
! [X0: $i] : strict_rel_str(rel_str_of(X0,inclusion_order(X0))),
inference(cnf_transformation,[],[f191]) ).
tcf(c_122,negated_conjecture,
( ( the_InternalRel(rel_str_of(sK13,inclusion_order(sK13))) != inclusion_order(sK13) )
| ( the_carrier(rel_str_of(sK13,inclusion_order(sK13))) != sK13 ) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_99]) ).
tcf(c_921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( relation_of2(X1,X2,X3)
| ( X0 != X3 )
| ( X0 != X2 )
| ( inclusion_order(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_185,c_114]) ).
tcf(c_922,plain,
! [X0: $i] : relation_of2(inclusion_order(X0),X0,X0),
inference(unflattening,[status(thm)],[c_921]) ).
tcf(c_2899,definition,
iPr_def_10 = inclusion_order(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2900,definition,
iPr_def_11 = rel_str_of(sK13,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2901,definition,
iPr_def_12 = the_carrier(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2902,definition,
iPr_def_13 = the_InternalRel(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2903,negated_conjecture,
( ( iPr_def_13 != iPr_def_10 )
| ( iPr_def_12 != sK13 ) ),
inference(demodulation,[status(thm)],[c_122,c_2902,c_2899,c_2900,c_2901]) ).
tcf(c_3485,plain,
rel_str(rel_str_of(sK13,iPr_def_10)),
inference(superposition,[status(thm)],[c_2899,c_116]) ).
tcf(c_3486,plain,
rel_str(iPr_def_11),
inference(light_normalisation,[status(thm)],[c_3485,c_2900]) ).
tcf(c_3487,plain,
strict_rel_str(rel_str_of(sK13,iPr_def_10)),
inference(superposition,[status(thm)],[c_2899,c_118]) ).
tcf(c_3488,plain,
strict_rel_str(iPr_def_11),
inference(light_normalisation,[status(thm)],[c_3487,c_2900]) ).
tcf(c_3489,plain,
relation_of2(iPr_def_10,sK13,sK13),
inference(superposition,[status(thm)],[c_2899,c_922]) ).
tcf(c_3771,plain,
( ( rel_str_of(the_carrier(iPr_def_11),the_InternalRel(iPr_def_11)) = iPr_def_11 )
| ~ rel_str(iPr_def_11) ),
inference(superposition,[status(thm)],[c_3488,c_94]) ).
tcf(c_3772,plain,
( ( rel_str_of(iPr_def_12,iPr_def_13) = iPr_def_11 )
| ~ rel_str(iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_3771,c_2901,c_2902]) ).
tcf(c_3773,plain,
rel_str_of(iPr_def_12,iPr_def_13) = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_3772,c_3486]) ).
tcf(c_3787,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK13 )
| ~ relation_of2(iPr_def_10,sK13,sK13)
| ( rel_str_of(X0,X1) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_2900,c_92]) ).
tcf(c_3793,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK13 )
| ( rel_str_of(X0,X1) != iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3787,c_3489]) ).
tcf(c_3802,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_10 )
| ~ relation_of2(iPr_def_10,sK13,sK13)
| ( rel_str_of(X0,X1) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_2900,c_93]) ).
tcf(c_3808,plain,
! [X0: $i,X1: $i] :
( ( X1 = iPr_def_10 )
| ( rel_str_of(X0,X1) != iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3802,c_3489]) ).
tcf(c_4438,plain,
sK13 = iPr_def_12,
inference(superposition,[status(thm)],[c_3773,c_3793]) ).
tcf(c_4459,plain,
( ( iPr_def_12 != iPr_def_12 )
| ( iPr_def_10 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_2903,c_4438]) ).
tcf(c_4460,plain,
iPr_def_10 != iPr_def_13,
inference(equality_resolution_simp,[status(thm)],[c_4459]) ).
tcf(c_4555,plain,
iPr_def_10 = iPr_def_13,
inference(superposition,[status(thm)],[c_3773,c_3808]) ).
tcf(c_4557,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4555,c_4460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU368+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 13:51:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.82/1.28 % SZS status Started for theBenchmark.p
% 3.82/1.28 % SZS status Theorem for theBenchmark.p
% 3.82/1.28
% 3.82/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.82/1.28
% 3.82/1.28 % ------ iProver source info
% 3.82/1.28
% 3.82/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.82/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.82/1.28 % git: non_committed_changes: false
% 3.82/1.28
% 3.82/1.28 % ------ Parsing...
% 3.82/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.82/1.28
% 3.82/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 25 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe_e %
% 3.82/1.28
% 3.82/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.82/1.28
% 3.82/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.82/1.28 % ------ Proving...
% 3.82/1.28 % ------ Problem Properties
% 3.82/1.28
% 3.82/1.28 %
% 3.82/1.28 % clauses 57
% 3.82/1.28 % conjectures 1
% 3.82/1.28 % EPR 17
% 3.82/1.28 % Horn 52
% 3.82/1.28 % unary 29
% 3.82/1.28 % binary 16
% 3.82/1.28 % lits 97
% 3.82/1.28 % lits eq 13
% 3.82/1.28 % fd_pure 0
% 3.82/1.28 % fd_pseudo 0
% 3.82/1.28 % fd_cond 1
% 3.82/1.28 % fd_pseudo_cond 3
% 3.82/1.28 % AC symbols 0
% 3.82/1.28
% 3.82/1.28 % ------ Schedule dynamic 5 is on
% 3.82/1.28
% 3.82/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.82/1.28
% 3.82/1.28
% 3.82/1.28 % ------
% 3.82/1.28 % Current options:
% 3.82/1.28 % ------
% 3.82/1.28
% 3.82/1.28
% 3.82/1.28 %
% 3.82/1.28
% 3.82/1.28 % ------ Proving...
% 3.82/1.28 %
% 3.82/1.28
% 3.82/1.28 % SZS status Theorem for theBenchmark.p
% 3.82/1.28
% 3.82/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.82/1.28
% 3.82/1.28
%------------------------------------------------------------------------------