%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET679+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 02:47:46 PM UTC 2026
% Result : Theorem 3.46s 1.42s
% Output : CNFRefutation 3.46s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f130ERROR: Could not build tree for root c_2208ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ~ member(X0,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( not_equal(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).
fof(f23,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f24,conjecture,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> not_equal(identity_relation_of(X0),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_46) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> not_equal(identity_relation_of(X0),empty_set) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ member(X0,empty_set) ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( not_equal(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f51,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ~ not_equal(identity_relation_of(X0),empty_set) ),
inference(ennf_transformation,[],[f25]) ).
fof(f52,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ empty(X0)
& ~ not_equal(identity_relation_of(X0),empty_set) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ member(X1,X0)
| member(ordered_pair(X1,X1),identity_relation_of(X0)) )
& ( ~ member(ordered_pair(X1,X1),identity_relation_of(X0))
| member(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f60,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ not_equal(X0,X1)
| X0 != X1 )
& ( X0 = X1
| not_equal(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f61,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0) )
| empty(X0) ) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f62,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ? [X1] :
( ilf_type(X1,set_type)
& member(X1,X0) )
| empty(X0) ) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ~ empty(X0)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
& ( ( ilf_type(sK1(X0),set_type)
& member(sK1(X0),X0) )
| empty(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f62]) ).
fof(f77,plain,
( ilf_type(sK9,set_type)
& ~ empty(sK9)
& ~ not_equal(identity_relation_of(sK9),empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f52]) ).
fof(f78,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X1,X0)
| member(ordered_pair(X1,X1),identity_relation_of(X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f80,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ member(X0,empty_set) ),
inference(cnf_transformation,[],[f28]) ).
fof(f92,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| X0 = X1
| not_equal(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f95,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| member(sK1(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f122,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f23]) ).
fof(f124,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f77]) ).
fof(f125,plain,
~ not_equal(identity_relation_of(sK9),empty_set),
inference(cnf_transformation,[],[f77]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_51,plain,
! [X0: $i] :
( ~ ilf_type(X0,set_type)
| ~ member(X0,empty_set) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( not_equal(X1,X0)
| ( X0 = X1 )
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_64,plain,
! [X0: $i] :
( empty(X0)
| member(sK1(X0),X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_92,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f122]) ).
tcf(c_93,negated_conjecture,
~ not_equal(identity_relation_of(sK9),empty_set),
inference(cnf_transformation,[],[f125]) ).
tcf(c_94,negated_conjecture,
~ empty(sK9),
inference(cnf_transformation,[],[f124]) ).
tcf(c_145,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_51,c_92,c_51]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] :
( not_equal(X1,X0)
| ( X0 = X1 )
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_62,c_92,c_62]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] :
( not_equal(X0,X1)
| ( X1 = X0 )
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_187]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( not_equal(X0,X1)
| ( X1 = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_188,c_92,c_188]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( not_equal(X1,X0)
| ( X0 = X1 ) ),
inference(renaming,[status(thm)],[c_189]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_92,c_53]) ).
tcf(c_279,plain,
! [X0: $i,X1: $i] :
( not_equal(X1,X0)
| ( X0 = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_190]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_220,c_92]) ).
tcf(c_652,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( X0 != empty_set )
| ( identity_relation_of(sK9) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_279,c_93]) ).
tcf(c_653,plain,
empty_set = identity_relation_of(sK9),
inference(unflattening,[status(thm)],[c_652]) ).
tcf(c_914,plain,
! [X0: $i,X1: $i] :
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ member(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_365]) ).
tcf(c_938,plain,
! [X0: $i] :
( member(sK1(X0),X0)
| empty(X0) ),
inference(prop_impl_just,[status(thm)],[c_92,c_64]) ).
tcf(c_939,plain,
! [X0: $i] :
( empty(X0)
| member(sK1(X0),X0) ),
inference(renaming,[status(thm)],[c_938]) ).
tcf(c_1469,definition,
iPr_def_10 = identity_relation_of(sK9),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1470,plain,
empty_set = iPr_def_10,
inference(demodulation,[status(thm)],[c_653,c_1469]) ).
tcf(c_1471,negated_conjecture,
~ empty(sK9),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_2096,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_145,c_1470]) ).
tcf(c_2191,plain,
! [X0: $i] :
( member(ordered_pair(X0,X0),iPr_def_10)
| ~ member(X0,sK9) ),
inference(superposition,[status(thm)],[c_1469,c_914]) ).
tcf(c_2195,plain,
! [X0: $i] : ~ member(X0,sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_2191,c_2096]) ).
tcf(c_2205,plain,
empty(sK9),
inference(superposition,[status(thm)],[c_939,c_2195]) ).
tcf(c_2208,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2205,c_1471]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET679+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n016.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 11:43:27 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 0.16/0.43
% 0.16/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.43
% 0.16/0.43 % Detected problem language: tptp
% 0.16/0.45 % Proving...
% 3.46/1.42 % SZS status Started for theBenchmark.p
% 3.46/1.42 % SZS status Theorem for theBenchmark.p
% 3.46/1.42
% 3.46/1.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.46/1.42
% 3.46/1.42 % ------ iProver source info
% 3.46/1.42
% 3.46/1.42 % git: date: 2026-07-19 20:42:38 +0200
% 3.46/1.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.46/1.42 % git: non_committed_changes: false
% 3.46/1.42
% 3.46/1.42 % ------ Parsing...
% 3.46/1.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.46/1.42
% 3.46/1.42 % ------ 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 %
% 3.46/1.42
% 3.46/1.42 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.46/1.42
% 3.46/1.42 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.46/1.42 % ------ Proving...
% 3.46/1.42 % ------ Problem Properties
% 3.46/1.42
% 3.46/1.42 %
% 3.46/1.42 % clauses 32
% 3.46/1.42 % conjectures 1
% 3.46/1.42 % EPR 10
% 3.46/1.42 % Horn 26
% 3.46/1.42 % unary 10
% 3.46/1.42 % binary 17
% 3.46/1.42 % lits 59
% 3.46/1.42 % lits eq 7
% 3.46/1.42 % fd_pure 0
% 3.46/1.42 % fd_pseudo 0
% 3.46/1.42 % fd_cond 0
% 3.46/1.42 % fd_pseudo_cond 3
% 3.46/1.42 % AC symbols 0
% 3.46/1.42
% 3.46/1.42 % ------ Schedule dynamic 5 is on
% 3.46/1.42
% 3.46/1.42 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.46/1.42
% 3.46/1.42
% 3.46/1.42 % ------
% 3.46/1.42 % Current options:
% 3.46/1.42 % ------
% 3.46/1.42
% 3.46/1.42
% 3.46/1.42 %
% 3.46/1.42
% 3.46/1.42 % ------ Proving...
% 3.46/1.42 %
% 3.46/1.42
% 3.46/1.42 % SZS status Theorem for theBenchmark.p
% 3.46/1.42
% 3.46/1.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.46/1.43
% 3.46/1.43
%------------------------------------------------------------------------------