%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET676+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 : 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 02:47:46 PM UTC 2026
% Result : Theorem 3.65s 1.51s
% Output : CNFRefutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 14 unt; 2 def)
% Number of atoms : 77 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 67 ( 31 ~; 25 |; 3 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 39 !; 1 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f4,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',p4) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(f20,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_41) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,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,[],[f1]) ).
fof(f25,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,[],[f4]) ).
fof(f45,plain,
? [X0] :
( ilf_type(X0,set_type)
& ~ ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f49,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,[],[f25]) ).
fof(f65,plain,
( ilf_type(sK11,set_type)
& ~ ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f45]) ).
fof(f66,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f75,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,relation_type(X0,X0))
| ilf_type(X1,identity_relation_of_type(X0)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f104,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f106,plain,
~ ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11)),
inference(cnf_transformation,[],[f65]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,relation_type(X1,X1)) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_87,plain,
! [X0: $i] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f104]) ).
tcf(c_88,negated_conjecture,
~ ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11)),
inference(cnf_transformation,[],[f106]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_87,c_49]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( ilf_type(cross_product(X1,X0),relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(renaming,[status(thm)],[c_175]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i] : ilf_type(cross_product(X1,X0),relation_type(X1,X0)),
inference(global_subsumption_just,[status(thm)],[c_176,c_87,c_176]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] : ilf_type(cross_product(X0,X1),relation_type(X0,X1)),
inference(renaming,[status(thm)],[c_177]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_87,c_57]) ).
tcf(c_246,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X0,relation_type(X1,X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_203,c_87]) ).
tcf(c_690,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_246]) ).
tcf(c_691,plain,
! [X0: $i,X1: $i] :
( ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X0,relation_type(X1,X1)) ),
inference(renaming,[status(thm)],[c_690]) ).
tcf(c_1166,definition,
iPr_def_10 = cross_product(sK11,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1167,definition,
iPr_def_11 = identity_relation_of_type(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1168,negated_conjecture,
~ ilf_type(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_88,c_1167,c_1166]) ).
tcf(c_1851,plain,
ilf_type(iPr_def_10,relation_type(sK11,sK11)),
inference(superposition,[status(thm)],[c_1166,c_178]) ).
tcf(c_1895,plain,
ilf_type(iPr_def_10,identity_relation_of_type(sK11)),
inference(superposition,[status(thm)],[c_1851,c_691]) ).
tcf(c_1896,plain,
ilf_type(iPr_def_10,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_1895,c_1167]) ).
tcf(c_1897,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1896,c_1168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET676+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.44 % Computer : n018.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Thu Sep 24 11:40:34 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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
% 0.26/0.52
% 0.26/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.52
% 0.26/0.52 % Detected problem language: tptp
% 0.26/0.53 % Proving...
% 3.65/1.51 % SZS status Started for theBenchmark.p
% 3.65/1.51 % SZS status Theorem for theBenchmark.p
% 3.65/1.51
% 3.65/1.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.65/1.51
% 3.65/1.51 % ------ iProver source info
% 3.65/1.51
% 3.65/1.51 % git: date: 2026-07-19 20:42:38 +0200
% 3.65/1.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.65/1.51 % git: non_committed_changes: false
% 3.65/1.51
% 3.65/1.51 % ------ Parsing...
% 3.65/1.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.65/1.51
% 3.65/1.51 % ------ 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 %
% 3.65/1.51
% 3.65/1.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.65/1.51
% 3.65/1.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.65/1.51 % ------ Proving...
% 3.65/1.51 % ------ Problem Properties
% 3.65/1.51
% 3.65/1.51 %
% 3.65/1.51 % clauses 32
% 3.65/1.51 % conjectures 1
% 3.65/1.51 % EPR 4
% 3.65/1.51 % Horn 27
% 3.65/1.51 % unary 9
% 3.65/1.51 % binary 19
% 3.65/1.51 % lits 59
% 3.65/1.51 % lits eq 5
% 3.65/1.51 % fd_pure 0
% 3.65/1.51 % fd_pseudo 0
% 3.65/1.51 % fd_cond 0
% 3.65/1.51 % fd_pseudo_cond 0
% 3.65/1.51 % AC symbols 0
% 3.65/1.51
% 3.65/1.51 % ------ Schedule dynamic 5 is on
% 3.65/1.51
% 3.65/1.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.65/1.51
% 3.65/1.51
% 3.65/1.51 % ------
% 3.65/1.51 % Current options:
% 3.65/1.51 % ------
% 3.65/1.51
% 3.65/1.51
% 3.65/1.51 %
% 3.65/1.51
% 3.65/1.51 % ------ Proving...
% 3.65/1.51 %
% 3.65/1.51
% 3.65/1.51 % SZS status Theorem for theBenchmark.p
% 3.65/1.51
% 3.65/1.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.65/1.51
% 3.65/1.51
%------------------------------------------------------------------------------