%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU223+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 02:56:11 PM UTC 2026
% Result : Theorem 0.28s 1.09s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 19 unt; 4 def)
% Number of atoms : 212 ( 56 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 240 ( 99 ~; 92 |; 36 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 83 !; 9 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1] :
( ( relation_empty_yielding(X0)
& relation(X0) )
=> ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_relat_1) ).
fof(f23,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f24,axiom,
! [X0,X1] :
( ( function(X0)
& relation(X0) )
=> ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f38,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).
fof(f39,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f40,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f52,plain,
! [X0,X1] :
( ~ relation_empty_yielding(X0)
| ~ relation(X0)
| ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f53,plain,
! [X0,X1] :
( ~ relation_empty_yielding(X0)
| ~ relation(X0)
| ( relation_empty_yielding(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f52]) ).
fof(f64,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f23]) ).
fof(f65,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f66,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f65]) ).
fof(f72,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,relation_dom(relation_dom_restriction(X2,X0)))
& apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f73,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,relation_dom(relation_dom_restriction(X2,X0)))
& apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f75,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( X1 = relation_dom_restriction(X2,X0)
<=> ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
inference(flattening,[],[f74]) ).
fof(f87,plain,
( function(sK13)
& relation(sK13)
& in(sK12,relation_dom(relation_dom_restriction(sK13,sK11)))
& apply(relation_dom_restriction(sK13,sK11),sK12) != apply(sK13,sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f73]) ).
fof(f88,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(nnf_transformation,[],[f75]) ).
fof(f89,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X3] :
( ~ in(X3,relation_dom(X1))
| apply(X1,X3) = apply(X2,X3) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ? [X3] :
( in(X3,relation_dom(X1))
& apply(X1,X3) != apply(X2,X3) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ( ( relation_dom_restriction(X2,X0) != X1
| ( ! [X4] :
( ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) )
& relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
& ( ( in(sK14(X1,X2),relation_dom(X1))
& apply(X1,sK14(X1,X2)) != apply(X2,sK14(X1,X2)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X3,sK14(X1,X2))],[f90]) ).
fof(f109,plain,
! [X0,X1] :
( ~ relation_empty_yielding(X0)
| ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f120,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f121,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f145,plain,
function(sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f146,plain,
relation(sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f147,plain,
in(sK12,relation_dom(relation_dom_restriction(sK13,sK11))),
inference(cnf_transformation,[],[f87]) ).
fof(f148,plain,
apply(relation_dom_restriction(sK13,sK11),sK12) != apply(sK13,sK12),
inference(cnf_transformation,[],[f87]) ).
fof(f149,plain,
! [X2,X0,X1,X4] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| relation_dom_restriction(X2,X0) != X1
| ~ in(X4,relation_dom(X1))
| apply(X1,X4) = apply(X2,X4) ),
inference(cnf_transformation,[],[f91]) ).
fof(f154,plain,
! [X2,X0,X4] :
( ~ function(relation_dom_restriction(X2,X0))
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(X2)
| ~ relation(X2)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4) ),
inference(equality_resolution,[],[f149]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_100,negated_conjecture,
apply(relation_dom_restriction(sK13,sK11),sK12) != apply(sK13,sK12),
inference(cnf_transformation,[],[f148]) ).
tcf(c_101,negated_conjecture,
in(sK12,relation_dom(relation_dom_restriction(sK13,sK11))),
inference(cnf_transformation,[],[f147]) ).
tcf(c_102,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f146]) ).
tcf(c_103,negated_conjecture,
function(sK13),
inference(cnf_transformation,[],[f145]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_75]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_107,c_135]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) )
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_240,c_77]) ).
tcf(c_820,definition,
iPr_def_10 = relation_dom_restriction(sK13,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_821,definition,
iPr_def_11 = relation_dom(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_822,definition,
iPr_def_12 = apply(iPr_def_10,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_823,definition,
iPr_def_13 = apply(sK13,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_824,negated_conjecture,
function(sK13),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_825,negated_conjecture,
relation(sK13),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_826,negated_conjecture,
in(sK12,iPr_def_11),
inference(demodulation,[status(thm)],[c_101,c_820,c_821]) ).
tcf(c_827,negated_conjecture,
iPr_def_12 != iPr_def_13,
inference(demodulation,[status(thm)],[c_100,c_823,c_822]) ).
tcf(c_1795,plain,
! [X0: $i] :
( ( apply(relation_dom_restriction(sK13,sK11),X0) = apply(sK13,X0) )
| ~ function(sK13)
| ~ relation(sK13)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_820,c_280]) ).
tcf(c_1799,plain,
! [X0: $i] :
( ( apply(sK13,X0) = apply(iPr_def_10,X0) )
| ~ function(sK13)
| ~ relation(sK13)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_1795,c_820,c_821]) ).
tcf(c_1800,plain,
! [X0: $i] :
( ( apply(sK13,X0) = apply(iPr_def_10,X0) )
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1799,c_824,c_825]) ).
tcf(c_2050,plain,
apply(sK13,sK12) = apply(iPr_def_10,sK12),
inference(superposition,[status(thm)],[c_826,c_1800]) ).
tcf(c_2052,plain,
iPr_def_12 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_2050,c_822,c_823]) ).
tcf(c_2053,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2052,c_827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU223+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n017.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 13:11:46 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.44 % Proving...
% 0.28/1.09 % SZS status Started for theBenchmark.p
% 0.28/1.09 % SZS status Theorem for theBenchmark.p
% 0.28/1.09
% 0.28/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.28/1.09
% 0.28/1.09 % ------ iProver source info
% 0.28/1.09
% 0.28/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 0.28/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.28/1.09 % git: non_committed_changes: false
% 0.28/1.09
% 0.28/1.09 % ------ Parsing...
% 0.28/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.28/1.09
% 0.28/1.09 % ------ Preprocessing... sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 0.28/1.09
% 0.28/1.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.28/1.09
% 0.28/1.09 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.28/1.09 % ------ Proving...
% 0.28/1.09 % ------ Problem Properties
% 0.28/1.09
% 0.28/1.09 %
% 0.28/1.09 % clauses 54
% 0.28/1.09 % conjectures 4
% 0.28/1.09 % EPR 28
% 0.28/1.09 % Horn 51
% 0.28/1.09 % unary 32
% 0.28/1.09 % binary 11
% 0.28/1.09 % lits 96
% 0.28/1.09 % lits eq 17
% 0.28/1.09 % fd_pure 0
% 0.28/1.09 % fd_pseudo 0
% 0.28/1.09 % fd_cond 1
% 0.28/1.09 % fd_pseudo_cond 3
% 0.28/1.09 % AC symbols 0
% 0.28/1.09
% 0.28/1.09 % ------ Schedule dynamic 5 is on
% 0.28/1.09
% 0.28/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.28/1.09
% 0.28/1.09
% 0.28/1.09 % ------
% 0.28/1.09 % Current options:
% 0.28/1.09 % ------
% 0.28/1.09
% 0.28/1.09
% 0.28/1.09 %
% 0.28/1.09
% 0.28/1.09 % ------ Proving...
% 0.28/1.09 %
% 0.28/1.09
% 0.28/1.09 % SZS status Theorem for theBenchmark.p
% 0.28/1.09
% 0.28/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.28/1.09
% 0.28/1.09
%------------------------------------------------------------------------------