%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU223+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 2.34s 1.27s
% Output : CNFRefutation 2.34s
% 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(f2,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(f30,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f32,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(f36,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(f37,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)],[f36]) ).
fof(f38,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(f42,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,[],[f2]) ).
fof(f43,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,[],[f42]) ).
fof(f56,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f57,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f58,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ( function(relation_dom_restriction(X0,X1))
& relation(relation_dom_restriction(X0,X1)) ) ),
inference(flattening,[],[f57]) ).
fof(f63,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,[],[f37]) ).
fof(f64,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,[],[f63]) ).
fof(f65,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,[],[f38]) ).
fof(f66,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,[],[f65]) ).
fof(f76,plain,
( function(sK11)
& relation(sK11)
& in(sK10,relation_dom(relation_dom_restriction(sK11,sK9)))
& apply(relation_dom_restriction(sK11,sK9),sK10) != apply(sK11,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f64]) ).
fof(f77,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,[],[f66]) ).
fof(f78,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,[],[f77]) ).
fof(f79,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,[],[f78]) ).
fof(f80,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(sK12(X1,X2),relation_dom(X1))
& apply(X1,sK12(X1,X2)) != apply(X2,sK12(X1,X2)) )
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| X1 = relation_dom_restriction(X2,X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X3,sK12(X1,X2))],[f79]) ).
fof(f84,plain,
! [X0,X1] :
( ~ relation_empty_yielding(X0)
| ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f117,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f120,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f125,plain,
function(sK11),
inference(cnf_transformation,[],[f76]) ).
fof(f126,plain,
relation(sK11),
inference(cnf_transformation,[],[f76]) ).
fof(f127,plain,
in(sK10,relation_dom(relation_dom_restriction(sK11,sK9))),
inference(cnf_transformation,[],[f76]) ).
fof(f128,plain,
apply(relation_dom_restriction(sK11,sK9),sK10) != apply(sK11,sK10),
inference(cnf_transformation,[],[f76]) ).
fof(f129,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,[],[f80]) ).
fof(f134,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,[],[f129]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation_empty_yielding(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_91,negated_conjecture,
apply(relation_dom_restriction(sK11,sK9),sK10) != apply(sK11,sK10),
inference(cnf_transformation,[],[f128]) ).
tcf(c_92,negated_conjecture,
in(sK10,relation_dom(relation_dom_restriction(sK11,sK9))),
inference(cnf_transformation,[],[f127]) ).
tcf(c_93,negated_conjecture,
relation(sK11),
inference(cnf_transformation,[],[f126]) ).
tcf(c_94,negated_conjecture,
function(sK11),
inference(cnf_transformation,[],[f125]) ).
tcf(c_98,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,[],[f134]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_83]) ).
tcf(c_210,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_98,c_121]) ).
tcf(c_246,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_210,c_87]) ).
tcf(c_692,definition,
iPr_def_10 = relation_dom_restriction(sK11,sK9),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_693,definition,
iPr_def_11 = relation_dom(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_694,definition,
iPr_def_12 = apply(iPr_def_10,sK10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_695,definition,
iPr_def_13 = apply(sK11,sK10),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_696,negated_conjecture,
function(sK11),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_697,negated_conjecture,
relation(sK11),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_698,negated_conjecture,
in(sK10,iPr_def_11),
inference(demodulation,[status(thm)],[c_92,c_692,c_693]) ).
tcf(c_699,negated_conjecture,
iPr_def_12 != iPr_def_13,
inference(demodulation,[status(thm)],[c_91,c_695,c_694]) ).
tcf(c_1355,plain,
! [X0: $i] :
( ( apply(relation_dom_restriction(sK11,sK9),X0) = apply(sK11,X0) )
| ~ function(sK11)
| ~ relation(sK11)
| ~ in(X0,relation_dom(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_692,c_246]) ).
tcf(c_1356,plain,
! [X0: $i] :
( ( apply(sK11,X0) = apply(iPr_def_10,X0) )
| ~ function(sK11)
| ~ relation(sK11)
| ~ in(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_1355,c_692,c_693]) ).
tcf(c_1357,plain,
! [X0: $i] :
( ( apply(sK11,X0) = apply(iPr_def_10,X0) )
| ~ in(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1356,c_696,c_697]) ).
tcf(c_1554,plain,
apply(sK11,sK10) = apply(iPr_def_10,sK10),
inference(superposition,[status(thm)],[c_698,c_1357]) ).
tcf(c_1555,plain,
iPr_def_12 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_1554,c_694,c_695]) ).
tcf(c_1556,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1555,c_699]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU223+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 13:16:13 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 2.34/1.27 % SZS status Started for theBenchmark.p
% 2.34/1.27 % SZS status Theorem for theBenchmark.p
% 2.34/1.27
% 2.34/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.34/1.27
% 2.34/1.27 % ------ iProver source info
% 2.34/1.27
% 2.34/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.34/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.34/1.27 % git: non_committed_changes: false
% 2.34/1.27
% 2.34/1.27 % ------ Parsing...
% 2.34/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.34/1.27
% 2.34/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 2.34/1.27
% 2.34/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.34/1.27
% 2.34/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.34/1.27 % ------ Proving...
% 2.34/1.27 % ------ Problem Properties
% 2.34/1.27
% 2.34/1.27 %
% 2.34/1.27 % clauses 44
% 2.34/1.27 % conjectures 4
% 2.34/1.27 % EPR 26
% 2.34/1.27 % Horn 42
% 2.34/1.27 % unary 27
% 2.34/1.27 % binary 9
% 2.34/1.27 % lits 78
% 2.34/1.27 % lits eq 17
% 2.34/1.27 % fd_pure 0
% 2.34/1.27 % fd_pseudo 0
% 2.34/1.27 % fd_cond 1
% 2.34/1.27 % fd_pseudo_cond 3
% 2.34/1.27 % AC symbols 0
% 2.34/1.27
% 2.34/1.27 % ------ Schedule dynamic 5 is on
% 2.34/1.27
% 2.34/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.34/1.27
% 2.34/1.27
% 2.34/1.27 % ------
% 2.34/1.27 % Current options:
% 2.34/1.27 % ------
% 2.34/1.27
% 2.34/1.27
% 2.34/1.27 %
% 2.34/1.27
% 2.34/1.27 % ------ Proving...
% 2.34/1.27 %
% 2.34/1.27
% 2.34/1.27 % SZS status Theorem for theBenchmark.p
% 2.34/1.27
% 2.34/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.34/1.28
% 2.34/1.28
%------------------------------------------------------------------------------