%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU217+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 : n007.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 02:55:57 PM UTC 2026
% Result : Theorem 2.08s 1.30s
% Output : CNFRefutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 17 unt; 2 def)
% Number of atoms : 110 ( 51 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 119 ( 50 ~; 43 |; 19 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 42 !; 5 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f24,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f27,conjecture,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f44,plain,
? [X0,X1] :
( in(X1,X0)
& apply(identity_relation(X0),X1) != X1 ),
inference(ennf_transformation,[],[f28]) ).
fof(f45,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f46,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(flattening,[],[f45]) ).
fof(f54,plain,
( in(sK8,sK7)
& sK8 != apply(identity_relation(sK7),sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f44]) ).
fof(f55,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f56,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK9(X0,X1),X0)
& sK9(X0,X1) != apply(X1,sK9(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X0,X1))],[f57]) ).
fof(f81,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f84,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f88,plain,
in(sK8,sK7),
inference(cnf_transformation,[],[f54]) ).
fof(f89,plain,
sK8 != apply(identity_relation(sK7),sK8),
inference(cnf_transformation,[],[f54]) ).
fof(f90,plain,
! [X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X3,X0)
| apply(X1,X3) = X3 ),
inference(cnf_transformation,[],[f58]) ).
fof(f97,plain,
! [X3,X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(X3,X0)
| apply(identity_relation(X0),X3) = X3 ),
inference(equality_resolution,[],[f90]) ).
tcf(c_71,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f81]) ).
tcf(c_75,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f84]) ).
tcf(c_78,negated_conjecture,
apply(identity_relation(sK7),sK8) != sK8,
inference(cnf_transformation,[],[f89]) ).
tcf(c_79,negated_conjecture,
in(sK8,sK7),
inference(cnf_transformation,[],[f88]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ function(identity_relation(X1))
| ~ relation(identity_relation(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ function(identity_relation(X1))
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_83,c_71]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_124,c_75]) ).
tcf(c_1180,definition,
iPr_def_10 = identity_relation(sK7),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1181,definition,
iPr_def_11 = apply(iPr_def_10,sK8),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1182,negated_conjecture,
in(sK8,sK7),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_1183,negated_conjecture,
iPr_def_11 != sK8,
inference(demodulation,[status(thm)],[c_78,c_1180,c_1181]) ).
tcf(c_1606,plain,
apply(identity_relation(sK7),sK8) = sK8,
inference(superposition,[status(thm)],[c_1182,c_127]) ).
tcf(c_1608,plain,
sK8 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1606,c_1180,c_1181]) ).
tcf(c_1613,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_1183,c_1608]) ).
tcf(c_1615,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1613]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU217+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n007.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 13:11:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 2.08/1.30 % SZS status Started for theBenchmark.p
% 2.08/1.30 % SZS status Theorem for theBenchmark.p
% 2.08/1.30
% 2.08/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.08/1.30
% 2.08/1.30 % ------ iProver source info
% 2.08/1.30
% 2.08/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.08/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.08/1.30 % git: non_committed_changes: false
% 2.08/1.30
% 2.08/1.30 % ------ Parsing...
% 2.08/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.08/1.30
% 2.08/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.08/1.30
% 2.08/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.08/1.30
% 2.08/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.08/1.30 % ------ Proving...
% 2.08/1.30 % ------ Problem Properties
% 2.08/1.30
% 2.08/1.30 %
% 2.08/1.30 % clauses 31
% 2.08/1.30 % conjectures 2
% 2.08/1.30 % EPR 19
% 2.08/1.30 % Horn 29
% 2.08/1.30 % unary 18
% 2.08/1.30 % binary 9
% 2.08/1.30 % lits 50
% 2.08/1.30 % lits eq 10
% 2.08/1.30 % fd_pure 0
% 2.08/1.30 % fd_pseudo 0
% 2.08/1.30 % fd_cond 1
% 2.08/1.30 % fd_pseudo_cond 1
% 2.08/1.30 % AC symbols 0
% 2.08/1.30
% 2.08/1.30 % ------ Schedule dynamic 5 is on
% 2.08/1.30
% 2.08/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.08/1.30
% 2.08/1.30
% 2.08/1.30 % ------
% 2.08/1.30 % Current options:
% 2.08/1.30 % ------
% 2.08/1.30
% 2.08/1.30
% 2.08/1.30 %
% 2.08/1.30
% 2.08/1.30 % ------ Proving...
% 2.08/1.30 %
% 2.08/1.30
% 2.08/1.30 % SZS status Theorem for theBenchmark.p
% 2.08/1.30
% 2.08/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.08/1.30
% 2.08/1.30
%------------------------------------------------------------------------------