%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET643+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 02:47:40 PM UTC 2026
% Result : Theorem 1.58s 6.32s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 65 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 72 ( 32 ~; 27 |; 4 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 42 !; 2 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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',p1) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> subset(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
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)
=> ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_5) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
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)
| ~ subset(X0,cross_product(X1,X2))
| ilf_type(X0,relation_type(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)
| ~ subset(X0,cross_product(X1,X2))
| ilf_type(X0,relation_type(X1,X2)) ) ) ),
inference(flattening,[],[f22]) ).
fof(f33,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| subset(X0,X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f47,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ~ ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f68,plain,
( ilf_type(sK11,set_type)
& ilf_type(sK12,set_type)
& ~ ilf_type(cross_product(sK11,sK12),relation_type(sK11,sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f47]) ).
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,[],[f23]) ).
fof(f88,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| subset(X0,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f109,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f112,plain,
~ ilf_type(cross_product(sK11,sK12),relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f68]) ).
tcf(c_49,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_68,plain,
! [X0: $i] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_89,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f109]) ).
tcf(c_90,negated_conjecture,
~ ilf_type(cross_product(sK11,sK12),relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f112]) ).
tcf(c_129,plain,
! [X0: $i] : subset(X0,X0),
inference(global_subsumption_just,[status(thm)],[c_68,c_89,c_68]) ).
tcf(c_217,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_49,c_89,c_49]) ).
tcf(c_251,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_217,c_89]) ).
tcf(c_351,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_251,c_89]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ilf_type(X3,relation_type(X0,X1))
| ( X2 != X3 )
| ( cross_product(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_351,c_129]) ).
tcf(c_672,plain,
! [X0: $i,X1: $i] : ilf_type(cross_product(X0,X1),relation_type(X0,X1)),
inference(unflattening,[status(thm)],[c_671]) ).
tcf(c_690,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_90,c_672]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET643+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.40 % Computer : n002.cluster.edu
% 0.11/5.40 % Model : x86_64 x86_64
% 0.11/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.40 % Memory : 8046.5625MB
% 0.11/5.40 % OS : Linux 6.8.0-71-generic
% 0.02/5.40 % CPULimit : 300
% 0.02/5.40 % WCLimit : 300
% 0.02/5.40 % DateTime : Thu Sep 24 11:35:54 UTC 2026
% 0.02/5.40 % CPUTime :
% 0.02/5.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/5.44 Running first-order theorem proving
% 0.02/5.44 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
% 0.02/5.45
% 0.02/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.02/5.45
% 0.02/5.46 % Detected problem language: tptp
% 0.02/5.47 % Proving...
% 1.58/6.32 % SZS status Started for theBenchmark.p
% 1.58/6.32 % SZS status Theorem for theBenchmark.p
% 1.58/6.32
% 1.58/6.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.58/6.32
% 1.58/6.32 % ------ iProver source info
% 1.58/6.32
% 1.58/6.32 % git: date: 2026-07-19 20:42:38 +0200
% 1.58/6.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.58/6.32 % git: non_committed_changes: false
% 1.58/6.32
% 1.58/6.32 % ------ Parsing...
% 1.58/6.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.58/6.32
% 1.58/6.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s %
% 1.58/6.32
% 1.58/6.32 % SZS status Theorem for theBenchmark.p
% 1.58/6.32
% 1.58/6.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.58/6.32
% 1.58/6.32
%------------------------------------------------------------------------------