%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET642+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 : n018.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 02:47:40 PM UTC 2026
% Result : Theorem 2.59s 1.28s
% Output : CNFRefutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 17 unt; 1 def)
% Number of atoms : 132 ( 1 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 145 ( 59 ~; 52 |; 15 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 68 !; 8 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,cross_product(X1,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,set_type)
=> ( subset(X0,cross_product(X1,X2))
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f20,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(X1,X2))
=> ( subset(X0,X3)
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_4) ).
fof(f21,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(X1,X2))
=> ( subset(X0,X3)
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,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(X1,X2))
| ~ subset(X0,X3)
| subset(X0,cross_product(X1,X2)) ) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f23,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(X1,X2))
| ~ subset(X0,X3)
| subset(X0,cross_product(X1,X2)) ) ) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ subset(X0,cross_product(X1,X2))
| ilf_type(X0,relation_type(X1,X2)) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ subset(X0,cross_product(X1,X2))
| ilf_type(X0,relation_type(X1,X2)) ) ) ),
inference(flattening,[],[f24]) ).
fof(f48,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(X1,X2))
& subset(X0,X3)
& ~ ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f49,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(X1,X2))
& subset(X0,X3)
& ~ ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
inference(flattening,[],[f48]) ).
fof(f67,plain,
( ilf_type(sK9,set_type)
& ilf_type(sK10,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK12,relation_type(sK10,sK11))
& subset(sK9,sK12)
& ~ ilf_type(sK9,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)],[f49]) ).
fof(f68,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(X1,X2))
| ~ subset(X0,X3)
| subset(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,cross_product(X1,X2))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f103,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f107,plain,
ilf_type(sK12,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f67]) ).
fof(f108,plain,
subset(sK9,sK12),
inference(cnf_transformation,[],[f67]) ).
fof(f109,plain,
~ ilf_type(sK9,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f67]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,cross_product(X1,X2))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X3,X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_84,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f103]) ).
tcf(c_85,negated_conjecture,
~ ilf_type(sK9,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f109]) ).
tcf(c_86,negated_conjecture,
subset(sK9,sK12),
inference(cnf_transformation,[],[f108]) ).
tcf(c_87,negated_conjecture,
ilf_type(sK12,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f107]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,cross_product(X1,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_84,c_50]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ subset(X0,cross_product(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_210,c_84]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,cross_product(X1,X2))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X3,X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_84]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_226,c_84]) ).
tcf(c_401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X3,cross_product(X1,X2))
| ~ subset(X3,X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_229,c_84,c_84]) ).
tcf(c_672,plain,
! [X0: $i,X1: $i,X2: $i] :
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_338]) ).
tcf(c_1130,definition,
iPr_def_10 = relation_type(sK10,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1131,negated_conjecture,
ilf_type(sK12,iPr_def_10),
inference(demodulation,[status(thm)],[c_87,c_1130]) ).
tcf(c_1132,negated_conjecture,
subset(sK9,sK12),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_1133,negated_conjecture,
~ ilf_type(sK9,iPr_def_10),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_1849,plain,
! [X0: $i,X1: $i] :
( subset(X0,cross_product(sK10,sK11))
| ~ ilf_type(X1,iPr_def_10)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_1130,c_401]) ).
tcf(c_2648,plain,
( subset(sK9,cross_product(sK10,sK11))
| ~ ilf_type(sK12,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1132,c_1849]) ).
tcf(c_2652,plain,
subset(sK9,cross_product(sK10,sK11)),
inference(forward_subsumption_resolution,[status(thm)],[c_2648,c_1131]) ).
tcf(c_2700,plain,
ilf_type(sK9,relation_type(sK10,sK11)),
inference(superposition,[status(thm)],[c_2652,c_672]) ).
tcf(c_2703,plain,
ilf_type(sK9,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_2700,c_1130]) ).
tcf(c_2704,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2703,c_1133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET642+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 11:34:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 2.59/1.28 % SZS status Started for theBenchmark.p
% 2.59/1.28 % SZS status Theorem for theBenchmark.p
% 2.59/1.28
% 2.59/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.59/1.28
% 2.59/1.28 % ------ iProver source info
% 2.59/1.28
% 2.59/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.59/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.59/1.28 % git: non_committed_changes: false
% 2.59/1.28
% 2.59/1.28 % ------ Parsing...
% 2.59/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.59/1.28
% 2.59/1.28 % ------ 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 %
% 2.59/1.28
% 2.59/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.59/1.28
% 2.59/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.59/1.28 % ------ Proving...
% 2.59/1.28 % ------ Problem Properties
% 2.59/1.28
% 2.59/1.28 %
% 2.59/1.28 % clauses 31
% 2.59/1.28 % conjectures 3
% 2.59/1.28 % EPR 8
% 2.59/1.28 % Horn 25
% 2.59/1.28 % unary 9
% 2.59/1.28 % binary 17
% 2.59/1.28 % lits 58
% 2.59/1.28 % lits eq 3
% 2.59/1.28 % fd_pure 0
% 2.59/1.28 % fd_pseudo 0
% 2.59/1.28 % fd_cond 0
% 2.59/1.28 % fd_pseudo_cond 0
% 2.59/1.28 % AC symbols 0
% 2.59/1.28
% 2.59/1.28 % ------ Schedule dynamic 5 is on
% 2.59/1.28
% 2.59/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.59/1.28
% 2.59/1.28
% 2.59/1.28 % ------
% 2.59/1.28 % Current options:
% 2.59/1.28 % ------
% 2.59/1.28
% 2.59/1.28
% 2.59/1.28 %
% 2.59/1.28
% 2.59/1.28 % ------ Proving...
% 2.59/1.28 %
% 2.59/1.28
% 2.59/1.28 % SZS status Theorem for theBenchmark.p
% 2.59/1.28
% 2.59/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.59/1.28
% 2.59/1.28
%------------------------------------------------------------------------------