%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET677+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 : n002.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 3.54s 1.27s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 9 unt; 0 def)
% Number of atoms : 150 ( 33 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 184 ( 77 ~; 71 |; 18 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 68 !; 4 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( subset(identity_relation_of(X1),X2)
=> ( subset(X1,range(X1,X0,X2))
& X1 = domain(X1,X0,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( X1 = range(X0,X1,X2)
& subset(X1,domain(X0,X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34) ).
fof(f35,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
=> ( subset(identity_relation_of(X0),X1)
=> ( X0 = range(X0,X0,X1)
& X0 = domain(X0,X0,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_44) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
=> ( subset(identity_relation_of(X0),X1)
=> ( X0 = range(X0,X0,X1)
& X0 = domain(X0,X0,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
& subset(identity_relation_of(X0),X1)
& ( range(X0,X0,X1) != X0
| domain(X0,X0,X1) != X0 ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f38,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,identity_relation_of_type(X0))
& subset(identity_relation_of(X0),X1)
& ( range(X0,X0,X1) != X0
| domain(X0,X0,X1) != X0 ) ) ),
inference(flattening,[],[f37]) ).
fof(f46,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ~ subset(identity_relation_of(X1),X2)
| ( X1 = range(X0,X1,X2)
& subset(X1,domain(X0,X1,X2)) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f47,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ~ subset(identity_relation_of(X1),X2)
| ( X1 = range(X0,X1,X2)
& subset(X1,domain(X0,X1,X2)) ) ) ) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X1,X0))
| ~ subset(identity_relation_of(X1),X2)
| ( subset(X1,range(X1,X0,X2))
& X1 = domain(X1,X0,X2) ) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f49,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X1,X0))
| ~ subset(identity_relation_of(X1),X2)
| ( subset(X1,range(X1,X0,X2))
& X1 = domain(X1,X0,X2) ) ) ) ),
inference(flattening,[],[f48]) ).
fof(f53,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f68,plain,
( ilf_type(sK0,set_type)
& ilf_type(sK1,identity_relation_of_type(sK0))
& subset(identity_relation_of(sK0),sK1)
& ( sK0 != range(sK0,sK0,sK1)
| sK0 != domain(sK0,sK0,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f38]) ).
fof(f77,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ~ ilf_type(X1,identity_relation_of_type(X0))
| ilf_type(X1,relation_type(X0,X0)) )
& ( ~ ilf_type(X1,relation_type(X0,X0))
| ilf_type(X1,identity_relation_of_type(X0)) ) ) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f93,plain,
ilf_type(sK1,identity_relation_of_type(sK0)),
inference(cnf_transformation,[],[f68]) ).
fof(f94,plain,
subset(identity_relation_of(sK0),sK1),
inference(cnf_transformation,[],[f68]) ).
fof(f95,plain,
( sK0 != range(sK0,sK0,sK1)
| sK0 != domain(sK0,sK0,sK1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f99,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ subset(identity_relation_of(X1),X2)
| range(X0,X1,X2) = X1 ),
inference(cnf_transformation,[],[f47]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X1,X0))
| ~ subset(identity_relation_of(X1),X2)
| domain(X1,X0,X2) = X1 ),
inference(cnf_transformation,[],[f49]) ).
fof(f117,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,identity_relation_of_type(X0))
| ilf_type(X1,relation_type(X0,X0)) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_49,negated_conjecture,
( ( range(sK0,sK0,sK1) != sK0 )
| ( domain(sK0,sK0,sK1) != sK0 ) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_50,negated_conjecture,
subset(identity_relation_of(sK0),sK1),
inference(cnf_transformation,[],[f94]) ).
tcf(c_51,negated_conjecture,
ilf_type(sK1,identity_relation_of_type(sK0)),
inference(cnf_transformation,[],[f93]) ).
tcf(c_56,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f99]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = X2 )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(identity_relation_of(X2),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = X1 )
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(identity_relation_of(X1),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,relation_type(X1,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,relation_type(X1,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_75,c_56,c_75]) ).
tcf(c_347,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = X2 )
| ~ ilf_type(X2,set_type)
| ~ subset(identity_relation_of(X2),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_68,c_56]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = X1 )
| ~ ilf_type(X2,set_type)
| ~ subset(identity_relation_of(X1),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_69,c_56]) ).
tcf(c_354,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,relation_type(X1,X1))
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_203,c_56]) ).
tcf(c_598,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( range(X1,X2,X0) = X2 )
| ~ subset(identity_relation_of(X2),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_347,c_56]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( domain(X1,X2,X0) = X1 )
| ~ subset(identity_relation_of(X1),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_351,c_56]) ).
tcf(c_1083,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,relation_type(X1,X1))
| ~ ilf_type(X0,identity_relation_of_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_354]) ).
tcf(c_2668,plain,
! [X0: $i,X1: $i] :
( ( range(X0,X0,X1) = X0 )
| ~ ilf_type(X1,identity_relation_of_type(X0))
| ~ subset(identity_relation_of(X0),X1) ),
inference(superposition,[status(thm)],[c_1083,c_598]) ).
tcf(c_2727,plain,
( ilf_type(sK1,relation_type(sK0,sK0))
| ~ ilf_type(sK1,identity_relation_of_type(sK0)) ),
inference(instantiation,[status(thm)],[c_1083]) ).
tcf(c_3002,plain,
! [X0: $i] :
( ( domain(sK0,X0,sK1) = sK0 )
| ~ subset(identity_relation_of(sK0),sK1)
| ~ ilf_type(sK1,relation_type(sK0,X0)) ),
inference(instantiation,[status(thm)],[c_613]) ).
tcf(c_3049,plain,
( ( range(sK0,sK0,sK1) = sK0 )
| ~ ilf_type(sK1,identity_relation_of_type(sK0)) ),
inference(superposition,[status(thm)],[c_50,c_2668]) ).
tcf(c_3057,plain,
range(sK0,sK0,sK1) = sK0,
inference(forward_subsumption_resolution,[status(thm)],[c_3049,c_51]) ).
tcf(c_3171,plain,
( ( domain(sK0,sK0,sK1) = sK0 )
| ~ subset(identity_relation_of(sK0),sK1)
| ~ ilf_type(sK1,relation_type(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_3002]) ).
tcf(c_3172,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3171,c_3057,c_2727,c_49,c_50,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET677+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 : n002.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 11:41:34 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 3.54/1.27 % SZS status Started for theBenchmark.p
% 3.54/1.27 % SZS status Theorem for theBenchmark.p
% 3.54/1.27
% 3.54/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.54/1.27
% 3.54/1.27 % ------ iProver source info
% 3.54/1.27
% 3.54/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.54/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.54/1.27 % git: non_committed_changes: false
% 3.54/1.27
% 3.54/1.27 % ------ Parsing...
% 3.54/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.54/1.27
% 3.54/1.27 % ------ Preprocessing... sup_sim: 0 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 %
% 3.54/1.27
% 3.54/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.54/1.27
% 3.54/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.54/1.27 % ------ Proving...
% 3.54/1.27 % ------ Problem Properties
% 3.54/1.27
% 3.54/1.27 %
% 3.54/1.27 % clauses 38
% 3.54/1.27 % conjectures 3
% 3.54/1.27 % EPR 9
% 3.54/1.27 % Horn 34
% 3.54/1.27 % unary 9
% 3.54/1.27 % binary 20
% 3.54/1.27 % lits 78
% 3.54/1.27 % lits eq 8
% 3.54/1.27 % fd_pure 0
% 3.54/1.27 % fd_pseudo 0
% 3.54/1.27 % fd_cond 0
% 3.54/1.27 % fd_pseudo_cond 2
% 3.54/1.27 % AC symbols 0
% 3.54/1.27
% 3.54/1.27 % ------ Schedule dynamic 5 is on
% 3.54/1.27
% 3.54/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.54/1.27
% 3.54/1.27
% 3.54/1.27 % ------
% 3.54/1.27 % Current options:
% 3.54/1.27 % ------
% 3.54/1.27
% 3.54/1.27
% 3.54/1.27 %
% 3.54/1.27
% 3.54/1.27 % ------ Proving...
% 3.54/1.27 %
% 3.54/1.27
% 3.54/1.27 % SZS status Theorem for theBenchmark.p
% 3.54/1.27
% 3.54/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.54/1.27
% 3.54/1.27
%------------------------------------------------------------------------------