%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU217+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 3.69s 1.41s
% Output : CNFRefutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 93 ( 45 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 113 ( 46 ~; 41 |; 19 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 39 !; 5 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f78,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f164,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/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f165,conjecture,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f166,negated_conjecture,
~ ! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f165]) ).
fof(f360,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,[],[f164]) ).
fof(f361,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,[],[f360]) ).
fof(f362,plain,
? [X0,X1] :
( in(X1,X0)
& apply(identity_relation(X0),X1) != X1 ),
inference(ennf_transformation,[],[f166]) ).
fof(f532,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,[],[f361]) ).
fof(f533,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,[],[f532]) ).
fof(f534,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,[],[f533]) ).
fof(f535,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK65(X0,X1),X0)
& sK65(X0,X1) != apply(X1,sK65(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(X2,sK65(X0,X1))],[f534]) ).
fof(f536,plain,
( in(sK67,sK66)
& sK67 != apply(identity_relation(sK66),sK67) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66,sK67]),skolemize(X0,sK66),skolemize(X1,sK67)],[f362]) ).
fof(f727,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f728,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f850,plain,
! [X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X3,X0)
| apply(X1,X3) = X3 ),
inference(cnf_transformation,[],[f535]) ).
fof(f854,plain,
in(sK67,sK66),
inference(cnf_transformation,[],[f536]) ).
fof(f855,plain,
sK67 != apply(identity_relation(sK66),sK67),
inference(cnf_transformation,[],[f536]) ).
fof(f1146,plain,
! [X3,X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(X3,X0)
| apply(identity_relation(X0),X3) = X3 ),
inference(equality_resolution,[],[f850]) ).
tcf(c_217,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f728]) ).
tcf(c_218,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f727]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f1146]) ).
tcf(c_344,negated_conjecture,
apply(identity_relation(sK66),sK67) != sK67,
inference(cnf_transformation,[],[f855]) ).
tcf(c_345,negated_conjecture,
in(sK67,sK66),
inference(cnf_transformation,[],[f854]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_343,c_217,c_218]) ).
tcf(c_535,plain,
apply(identity_relation(sK66),sK67) = sK67,
inference(superposition,[status(thm)],[c_345,c_528]) ).
tcf(c_536,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_344,c_535]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU217+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.42 % Computer : n014.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Thu Sep 24 13:13:32 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.48 Running first-order theorem proving
% 0.17/0.48 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
% 0.26/0.50
% 0.26/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.50
% 0.26/0.50 % Detected problem language: tptp
% 0.26/0.52 % Proving...
% 3.69/1.41 % SZS status Started for theBenchmark.p
% 3.69/1.41 % SZS status Theorem for theBenchmark.p
% 3.69/1.41
% 3.69/1.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.69/1.41
% 3.69/1.41 % ------ iProver source info
% 3.69/1.41
% 3.69/1.41 % git: date: 2026-07-19 20:42:38 +0200
% 3.69/1.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.69/1.41 % git: non_committed_changes: false
% 3.69/1.41
% 3.69/1.41 % ------ Parsing...
% 3.69/1.41 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.69/1.41 % ------ Proving...
% 3.69/1.41 % ------ Problem Properties
% 3.69/1.41
% 3.69/1.41 %
% 3.69/1.41 % clauses 379
% 3.69/1.41 % conjectures 2
% 3.69/1.41 % EPR 43
% 3.69/1.41 % Horn 310
% 3.69/1.41 % unary 66
% 3.69/1.41 % binary 115
% 3.69/1.41 % lits 1029
% 3.69/1.41 % lits eq 187
% 3.69/1.41 % fd_pure 0
% 3.69/1.41 % fd_pseudo 0
% 3.69/1.41 % fd_cond 14
% 3.69/1.41 % fd_pseudo_cond 71
% 3.69/1.41 % AC symbols 0
% 3.69/1.41
% 3.69/1.41 % ------ Input Options Time Limit: Unbounded
% 3.69/1.41
% 3.69/1.41
% 3.69/1.41 % ------
% 3.69/1.41 % Current options:
% 3.69/1.41 % ------
% 3.69/1.41
% 3.69/1.41
% 3.69/1.41 %
% 3.69/1.41
% 3.69/1.41 % ------ Proving...
% 3.69/1.41 %
% 3.69/1.41
% 3.69/1.41 % SZS status Theorem for theBenchmark.p
% 3.69/1.41
% 3.69/1.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.69/1.41
% 3.69/1.41
%------------------------------------------------------------------------------