%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET653+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:47:42 PM UTC 2026
% Result : Theorem 3.58s 1.15s
% Output : CNFRefutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 203 ( 85 ~; 78 |; 18 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 89 !; 8 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/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(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ( subset(domain_of(X3),X1)
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f22,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f23,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ( subset(X0,X1)
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_15) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ( subset(X0,X1)
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f28,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X2))
| ~ subset(domain_of(X3),X1)
| ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X2))
| ~ subset(domain_of(X3),X1)
| ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
inference(flattening,[],[f28]) ).
fof(f54,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X0,X2))
& subset(X0,X1)
& ~ ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f55,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( ilf_type(X3,relation_type(X0,X2))
& subset(X0,X1)
& ~ ilf_type(X3,relation_type(X1,X2)) ) ) ) ),
inference(flattening,[],[f54]) ).
fof(f73,plain,
( ilf_type(sK9,set_type)
& ilf_type(sK10,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK12,relation_type(sK9,sK11))
& subset(sK9,sK10)
& ~ ilf_type(sK12,relation_type(sK10,sK11)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f55]) ).
fof(f74,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| subset(domain_of(X2),X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X2))
| ~ subset(domain_of(X3),X1)
| ilf_type(X3,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f113,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f22]) ).
fof(f117,plain,
ilf_type(sK12,relation_type(sK9,sK11)),
inference(cnf_transformation,[],[f73]) ).
fof(f118,plain,
subset(sK9,sK10),
inference(cnf_transformation,[],[f73]) ).
fof(f119,plain,
~ ilf_type(sK12,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f73]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(domain_of(X0),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(X0,relation_type(X3,X2))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(domain_of(X0),X3)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_88,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f113]) ).
tcf(c_89,negated_conjecture,
~ ilf_type(sK12,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f119]) ).
tcf(c_90,negated_conjecture,
subset(sK9,sK10),
inference(cnf_transformation,[],[f118]) ).
tcf(c_91,negated_conjecture,
ilf_type(sK12,relation_type(sK9,sK11)),
inference(cnf_transformation,[],[f117]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_88,c_49]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(renaming,[status(thm)],[c_216]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_217,c_88]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(domain_of(X0),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_50,c_88]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(X0,relation_type(X3,X2))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(domain_of(X0),X3)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_88]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(domain_of(X0),X1)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_229,c_88]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_228,c_88]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(X0,relation_type(X3,X2))
| ~ subset(domain_of(X0),X3)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_231,c_88,c_88]) ).
tcf(c_612,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(domain_of(X0),X1)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_340]) ).
tcf(c_1691,plain,
( subset(domain_of(sK12),sK9)
| ~ ilf_type(sK12,relation_type(sK9,sK11)) ),
inference(instantiation,[status(thm)],[c_612]) ).
tcf(c_2053,plain,
! [X0: $i] :
( ilf_type(sK12,relation_type(X0,sK11))
| ~ subset(domain_of(sK12),X0) ),
inference(superposition,[status(thm)],[c_91,c_434]) ).
tcf(c_2070,plain,
~ subset(domain_of(sK12),sK10),
inference(superposition,[status(thm)],[c_2053,c_89]) ).
tcf(c_2586,plain,
! [X0: $i] :
( subset(domain_of(sK12),sK10)
| ~ subset(X0,sK10)
| ~ subset(domain_of(sK12),X0) ),
inference(instantiation,[status(thm)],[c_405]) ).
tcf(c_2665,plain,
( subset(domain_of(sK12),sK10)
| ~ subset(sK9,sK10)
| ~ subset(domain_of(sK12),sK9) ),
inference(instantiation,[status(thm)],[c_2586]) ).
tcf(c_2666,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2665,c_2070,c_1691,c_91,c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET653+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n002.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 11:37:34 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.39 % Detected problem language: tptp
% 0.12/0.40 % Proving...
% 3.58/1.15 % SZS status Started for theBenchmark.p
% 3.58/1.15 % SZS status Theorem for theBenchmark.p
% 3.58/1.15
% 3.58/1.15 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.58/1.15
% 3.58/1.15 % ------ iProver source info
% 3.58/1.15
% 3.58/1.15 % git: date: 2026-07-19 20:42:38 +0200
% 3.58/1.15 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.58/1.15 % git: non_committed_changes: false
% 3.58/1.15
% 3.58/1.15 % ------ Parsing...
% 3.58/1.15 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.58/1.15
% 3.58/1.15 % ------ 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 %
% 3.58/1.15
% 3.58/1.15 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.58/1.15
% 3.58/1.15 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.58/1.15 % ------ Proving...
% 3.58/1.15 % ------ Problem Properties
% 3.58/1.15
% 3.58/1.15 %
% 3.58/1.15 % clauses 32
% 3.58/1.15 % conjectures 3
% 3.58/1.15 % EPR 7
% 3.58/1.15 % Horn 26
% 3.58/1.15 % unary 8
% 3.58/1.15 % binary 18
% 3.58/1.15 % lits 62
% 3.58/1.15 % lits eq 2
% 3.58/1.15 % fd_pure 0
% 3.58/1.15 % fd_pseudo 0
% 3.58/1.15 % fd_cond 0
% 3.58/1.15 % fd_pseudo_cond 0
% 3.58/1.15 % AC symbols 0
% 3.58/1.15
% 3.58/1.15 % ------ Input Options Time Limit: Unbounded
% 3.58/1.15
% 3.58/1.15
% 3.58/1.15 % ------
% 3.58/1.15 % Current options:
% 3.58/1.15 % ------
% 3.58/1.15
% 3.58/1.15
% 3.58/1.15 %
% 3.58/1.15
% 3.58/1.15 % ------ Proving...
% 3.58/1.15 %
% 3.58/1.15
% 3.58/1.15 % SZS status Theorem for theBenchmark.p
% 3.58/1.15
% 3.58/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.58/1.15
% 3.58/1.15
%------------------------------------------------------------------------------