%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU008+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:55:01 PM UTC 2026
% Result : Theorem 0.50s 1.18s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 16 unt; 0 def)
% Number of atoms : 236 ( 71 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 301 ( 119 ~; 117 |; 51 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 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 : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 111 ( 0 sgn 99 !; 12 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f15,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f31,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f34,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(f35,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(X2,X1) = apply(relation_composition(identity_relation(X0),X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_1) ).
fof(f36,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(X2,X1) = apply(relation_composition(identity_relation(X0),X2),X1) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f66,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f67,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ! [X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ),
inference(flattening,[],[f66]) ).
fof(f70,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,[],[f34]) ).
fof(f71,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,[],[f70]) ).
fof(f72,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,set_intersection2(relation_dom(X2),X0))
& apply(X2,X1) != apply(relation_composition(identity_relation(X0),X2),X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f73,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& in(X1,set_intersection2(relation_dom(X2),X0))
& apply(X2,X1) != apply(relation_composition(identity_relation(X0),X2),X1) ),
inference(flattening,[],[f72]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f82]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f83]) ).
fof(f94,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,[],[f71]) ).
fof(f95,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,[],[f94]) ).
fof(f96,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,[],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK10(X0,X1),X0)
& sK10(X0,X1) != apply(X1,sK10(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f96]) ).
fof(f98,plain,
( function(sK13)
& relation(sK13)
& in(sK12,set_intersection2(relation_dom(sK13),sK11))
& apply(sK13,sK12) != apply(relation_composition(identity_relation(sK11),sK13),sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f73]) ).
fof(f103,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f121,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f122,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f149,plain,
! [X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X3,X0)
| apply(X1,X3) = X3 ),
inference(cnf_transformation,[],[f97]) ).
fof(f150,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| relation_dom(X1) = X0 ),
inference(cnf_transformation,[],[f97]) ).
fof(f153,plain,
function(sK13),
inference(cnf_transformation,[],[f98]) ).
fof(f154,plain,
relation(sK13),
inference(cnf_transformation,[],[f98]) ).
fof(f155,plain,
in(sK12,set_intersection2(relation_dom(sK13),sK11)),
inference(cnf_transformation,[],[f98]) ).
fof(f156,plain,
apply(sK13,sK12) != apply(relation_composition(identity_relation(sK11),sK13),sK12),
inference(cnf_transformation,[],[f98]) ).
fof(f165,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f103]) ).
fof(f168,plain,
! [X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(equality_resolution,[],[f150]) ).
fof(f169,plain,
! [X3,X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(X3,X0)
| apply(identity_relation(X0),X3) = X3 ),
inference(equality_resolution,[],[f149]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_71,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f122]) ).
tcf(c_72,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) )
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_101,plain,
! [X0: $i] :
( ( relation_dom(identity_relation(X0)) = X0 )
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_102,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,[],[f169]) ).
tcf(c_103,negated_conjecture,
apply(relation_composition(identity_relation(sK11),sK13),sK12) != apply(sK13,sK12),
inference(cnf_transformation,[],[f156]) ).
tcf(c_104,negated_conjecture,
in(sK12,set_intersection2(relation_dom(sK13),sK11)),
inference(cnf_transformation,[],[f155]) ).
tcf(c_105,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f154]) ).
tcf(c_106,negated_conjecture,
function(sK13),
inference(cnf_transformation,[],[f153]) ).
tcf(c_204,plain,
in(sK12,sK11),
inference(superposition,[status(thm)],[c_104,c_58]) ).
tcf(c_273,plain,
! [X0: $i] : relation_dom(identity_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_101,c_72,c_71,c_101]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_102,c_71,c_72]) ).
tcf(c_315,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(identity_relation(X1),X2),X0) = apply(X2,apply(identity_relation(X1),X0)) )
| ~ relation(X2)
| ~ function(X2)
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_273,c_96]) ).
tcf(c_329,plain,
apply(identity_relation(sK11),sK12) = sK12,
inference(superposition,[status(thm)],[c_204,c_296]) ).
tcf(c_431,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( apply(relation_composition(identity_relation(X1),X2),X0) = apply(X2,apply(identity_relation(X1),X0)) )
| ~ relation(X2)
| ~ function(X2)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_315,c_71,c_72]) ).
tcf(c_443,plain,
! [X0: $i] :
( ( apply(relation_composition(identity_relation(sK11),X0),sK12) = apply(X0,apply(identity_relation(sK11),sK12)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_204,c_431]) ).
tcf(c_680,plain,
! [X0: $i] :
( ( apply(relation_composition(identity_relation(sK11),X0),sK12) = apply(X0,sK12) )
| ~ relation(X0)
| ~ function(X0) ),
inference(light_normalisation,[status(thm)],[c_443,c_329]) ).
tcf(c_694,plain,
( ( apply(relation_composition(identity_relation(sK11),sK13),sK12) = apply(sK13,sK12) )
| ~ function(sK13) ),
inference(superposition,[status(thm)],[c_105,c_680]) ).
tcf(c_695,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_694,c_103,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU008+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.33 % Computer : n014.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Thu Sep 24 12:33:33 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.33 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 Running first-order theorem proving
% 0.11/0.36 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
% 0.11/0.38
% 0.11/0.38 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.38
% 0.11/0.38 % Detected problem language: tptp
% 0.11/0.39 % Proving...
% 0.50/1.18 % SZS status Started for theBenchmark.p
% 0.50/1.18 % SZS status Theorem for theBenchmark.p
% 0.50/1.18
% 0.50/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.50/1.18
% 0.50/1.18 % ------ iProver source info
% 0.50/1.18
% 0.50/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 0.50/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.50/1.18 % git: non_committed_changes: false
% 0.50/1.18
% 0.50/1.18 % ------ Parsing...
% 0.50/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.50/1.18 % ------ Proving...
% 0.50/1.18 % ------ Problem Properties
% 0.50/1.18
% 0.50/1.18 %
% 0.50/1.18 % clauses 64
% 0.50/1.18 % conjectures 4
% 0.50/1.18 % EPR 25
% 0.50/1.18 % Horn 59
% 0.50/1.18 % unary 29
% 0.50/1.18 % binary 13
% 0.50/1.18 % lits 132
% 0.50/1.18 % lits eq 15
% 0.50/1.18 % fd_pure 0
% 0.50/1.18 % fd_pseudo 0
% 0.50/1.18 % fd_cond 1
% 0.50/1.18 % fd_pseudo_cond 4
% 0.50/1.18 % AC symbols 0
% 0.50/1.18
% 0.50/1.18 % ------ Input Options Time Limit: Unbounded
% 0.50/1.18
% 0.50/1.18
% 0.50/1.18 % ------
% 0.50/1.18 % Current options:
% 0.50/1.18 % ------
% 0.50/1.18
% 0.50/1.18
% 0.50/1.18 %
% 0.50/1.18
% 0.50/1.18 % ------ Proving...
% 0.50/1.18 %
% 0.50/1.18
% 0.50/1.18 % SZS status Theorem for theBenchmark.p
% 0.50/1.18
% 0.50/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.50/1.18
% 0.50/1.18
%------------------------------------------------------------------------------