%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 02:07:40 PM UTC 2026
% Result : Theorem 1.18s 1.27s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 9 unt; 1 def)
% Number of atoms : 422 ( 0 equ)
% Maximal formula atoms : 37 ( 11 avg)
% Number of connectives : 693 ( 309 ~; 247 |; 137 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 110 ( 0 sgn 91 !; 19 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f2,conjecture,
~ ? [X0] :
~ ( ~ ( p100(X0)
& ~ p101(X0)
& ! [X1] :
( ( ( ~ p101(X1)
| p100(X1) )
& ( ~ p102(X1)
| p101(X1) )
& ( ~ p100(X1)
| ( ( ~ p1(X1)
| ! [X0] :
( ~ p100(X0)
| p1(X0)
| ~ r1(X1,X0) ) )
& ( p1(X1)
| ! [X0] :
( ~ p100(X0)
| ~ p1(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p101(X1)
| ( ( ~ p2(X1)
| ! [X0] :
( ~ p101(X0)
| p2(X0)
| ~ r1(X1,X0) ) )
& ( p2(X1)
| ! [X0] :
( ~ p101(X0)
| ~ p2(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ ( p100(X1)
& ~ p101(X1) )
| ( ~ ! [X0] :
( ~ ( p101(X0)
& ~ p102(X0)
& p2(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p101(X0)
& ~ p102(X0)
& ~ p2(X0) )
| ~ r1(X1,X0) ) ) ) )
| ~ r1(X0,X1) ) )
| ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f3,negated_conjecture,
~ ~ ? [X0] :
~ ( ~ ( p100(X0)
& ~ p101(X0)
& ! [X1] :
( ( ( ~ p101(X1)
| p100(X1) )
& ( ~ p102(X1)
| p101(X1) )
& ( ~ p100(X1)
| ( ( ~ p1(X1)
| ! [X0] :
( ~ p100(X0)
| p1(X0)
| ~ r1(X1,X0) ) )
& ( p1(X1)
| ! [X0] :
( ~ p100(X0)
| ~ p1(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ p101(X1)
| ( ( ~ p2(X1)
| ! [X0] :
( ~ p101(X0)
| p2(X0)
| ~ r1(X1,X0) ) )
& ( p2(X1)
| ! [X0] :
( ~ p101(X0)
| ~ p2(X0)
| ~ r1(X1,X0) ) ) ) )
& ( ~ ( p100(X1)
& ~ p101(X1) )
| ( ~ ! [X0] :
( ~ ( p101(X0)
& ~ p102(X0)
& p2(X0) )
| ~ r1(X1,X0) )
& ~ ! [X0] :
( ~ ( p101(X0)
& ~ p102(X0)
& ~ p2(X0) )
| ~ r1(X1,X0) ) ) ) )
| ~ r1(X0,X1) ) )
| ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
~ ~ ? [X0] :
~ ( ~ ( p100(X0)
& ~ p101(X0)
& ! [X2] :
( ( ( ~ p101(X2)
| p100(X2) )
& ( ~ p102(X2)
| p101(X2) )
& ( ~ p100(X2)
| ( ( ~ p1(X2)
| ! [X8] :
( ~ p100(X8)
| p1(X8)
| ~ r1(X2,X8) ) )
& ( p1(X2)
| ! [X7] :
( ~ p100(X7)
| ~ p1(X7)
| ~ r1(X2,X7) ) ) ) )
& ( ~ p101(X2)
| ( ( ~ p2(X2)
| ! [X6] :
( ~ p101(X6)
| p2(X6)
| ~ r1(X2,X6) ) )
& ( p2(X2)
| ! [X5] :
( ~ p101(X5)
| ~ p2(X5)
| ~ r1(X2,X5) ) ) ) )
& ( ~ ( p100(X2)
& ~ p101(X2) )
| ( ~ ! [X4] :
( ~ ( p101(X4)
& ~ p102(X4)
& p2(X4) )
| ~ r1(X2,X4) )
& ~ ! [X3] :
( ~ ( p101(X3)
& ~ p102(X3)
& ~ p2(X3) )
| ~ r1(X2,X3) ) ) ) )
| ~ r1(X0,X2) ) )
| ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f3]) ).
fof(f5,plain,
? [X0] :
~ ( ~ ( p100(X0)
& ~ p101(X0)
& ! [X2] :
( ( ( ~ p101(X2)
| p100(X2) )
& ( ~ p102(X2)
| p101(X2) )
& ( ~ p100(X2)
| ( ( ~ p1(X2)
| ! [X8] :
( ~ p100(X8)
| p1(X8)
| ~ r1(X2,X8) ) )
& ( p1(X2)
| ! [X7] :
( ~ p100(X7)
| ~ p1(X7)
| ~ r1(X2,X7) ) ) ) )
& ( ~ p101(X2)
| ( ( ~ p2(X2)
| ! [X6] :
( ~ p101(X6)
| p2(X6)
| ~ r1(X2,X6) ) )
& ( p2(X2)
| ! [X5] :
( ~ p101(X5)
| ~ p2(X5)
| ~ r1(X2,X5) ) ) ) )
& ( ~ ( p100(X2)
& ~ p101(X2) )
| ( ~ ! [X4] :
( ~ ( p101(X4)
& ~ p102(X4)
& p2(X4) )
| ~ r1(X2,X4) )
& ~ ! [X3] :
( ~ ( p101(X3)
& ~ p102(X3)
& ~ p2(X3) )
| ~ r1(X2,X3) ) ) ) )
| ~ r1(X0,X2) ) )
| ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ~ ( p100(X0)
& ~ p101(X0)
& ! [X2] :
( ( ( ~ p101(X2)
| p100(X2) )
& ( ~ p100(X2)
| ( ( ~ p1(X2)
| ! [X8] :
( ~ p100(X8)
| p1(X8)
| ~ r1(X2,X8) ) )
& ( p1(X2)
| ! [X7] :
( ~ p100(X7)
| ~ p1(X7)
| ~ r1(X2,X7) ) ) ) )
& ( ~ p101(X2)
| ( ( ~ p2(X2)
| ! [X6] :
( ~ p101(X6)
| p2(X6)
| ~ r1(X2,X6) ) )
& ( p2(X2)
| ! [X5] :
( ~ p101(X5)
| ~ p2(X5)
| ~ r1(X2,X5) ) ) ) )
& ( ~ ( p100(X2)
& ~ p101(X2) )
| ( ~ ! [X4] :
( ~ ( p101(X4)
& p2(X4) )
| ~ r1(X2,X4) )
& ~ ! [X3] :
( ~ ( p101(X3)
& ~ p2(X3) )
| ~ r1(X2,X3) ) ) ) )
| ~ r1(X0,X2) ) )
| ~ ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f5]) ).
fof(f7,plain,
? [X0] :
( p100(X0)
& ~ p101(X0)
& ! [X2] :
( ( ( ~ p101(X2)
| p100(X2) )
& ( ~ p100(X2)
| ( ( ~ p1(X2)
| ! [X8] :
( ~ p100(X8)
| p1(X8)
| ~ r1(X2,X8) ) )
& ( p1(X2)
| ! [X7] :
( ~ p100(X7)
| ~ p1(X7)
| ~ r1(X2,X7) ) ) ) )
& ( ~ p101(X2)
| ( ( ~ p2(X2)
| ! [X6] :
( ~ p101(X6)
| p2(X6)
| ~ r1(X2,X6) ) )
& ( p2(X2)
| ! [X5] :
( ~ p101(X5)
| ~ p2(X5)
| ~ r1(X2,X5) ) ) ) )
& ( ~ p100(X2)
| p101(X2)
| ( ? [X4] :
( p101(X4)
& p2(X4)
& r1(X2,X4) )
& ? [X3] :
( p101(X3)
& ~ p2(X3)
& r1(X2,X3) ) ) ) )
| ~ r1(X0,X2) )
& ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
? [X0] :
( p100(X0)
& ~ p101(X0)
& ! [X2] :
( ( ( ~ p101(X2)
| p100(X2) )
& ( ~ p100(X2)
| ( ( ~ p1(X2)
| ! [X8] :
( ~ p100(X8)
| p1(X8)
| ~ r1(X2,X8) ) )
& ( p1(X2)
| ! [X7] :
( ~ p100(X7)
| ~ p1(X7)
| ~ r1(X2,X7) ) ) ) )
& ( ~ p101(X2)
| ( ( ~ p2(X2)
| ! [X6] :
( ~ p101(X6)
| p2(X6)
| ~ r1(X2,X6) ) )
& ( p2(X2)
| ! [X5] :
( ~ p101(X5)
| ~ p2(X5)
| ~ r1(X2,X5) ) ) ) )
& ( ~ p100(X2)
| p101(X2)
| ( ? [X4] :
( p101(X4)
& p2(X4)
& r1(X2,X4) )
& ? [X3] :
( p101(X3)
& ~ p2(X3)
& r1(X2,X3) ) ) ) )
| ~ r1(X0,X2) )
& ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f7]) ).
fof(f14,plain,
? [X0] :
( p100(X0)
& ~ p101(X0)
& ! [X2] :
( ( ( ~ p101(X2)
| p100(X2) )
& ( ~ p100(X2)
| ( ( ~ p1(X2)
| ! [X6] :
( ~ p100(X6)
| p1(X6)
| ~ r1(X2,X6) ) )
& ( p1(X2)
| ! [X5] :
( ~ p100(X5)
| ~ p1(X5)
| ~ r1(X2,X5) ) ) ) )
& ( ~ p101(X2)
| ( ( ~ p2(X2)
| ! [X4] :
( ~ p101(X4)
| p2(X4)
| ~ r1(X2,X4) ) )
& ( p2(X2)
| ! [X3] :
( ~ p101(X3)
| ~ p2(X3)
| ~ r1(X2,X3) ) ) ) )
& sP0(X2) )
| ~ r1(X0,X2) )
& ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f15,plain,
( p100(sK3)
& ~ p101(sK3)
& ! [X2] :
( ( ( ~ p101(X2)
| p100(X2) )
& ( ~ p100(X2)
| ( ( ~ p1(X2)
| ! [X6] :
( ~ p100(X6)
| p1(X6)
| ~ r1(X2,X6) ) )
& ( p1(X2)
| ! [X5] :
( ~ p100(X5)
| ~ p1(X5)
| ~ r1(X2,X5) ) ) ) )
& ( ~ p101(X2)
| ( ( ~ p2(X2)
| ! [X4] :
( ~ p101(X4)
| p2(X4)
| ~ r1(X2,X4) ) )
& ( p2(X2)
| ! [X3] :
( ~ p101(X3)
| ~ p2(X3)
| ~ r1(X2,X3) ) ) ) )
& sP0(X2) )
| ~ r1(sK3,X2) )
& ! [X1] :
( p2(X1)
| ~ r1(sK3,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f14]) ).
fof(f16,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f23,plain,
p100(sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
~ p101(sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X3] :
( ~ p101(X2)
| p2(X2)
| ~ p101(X3)
| ~ p2(X3)
| ~ r1(X2,X3)
| ~ r1(sK3,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X2] :
( sP0(X2)
| ~ r1(sK3,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X1] :
( p2(X1)
| ~ r1(sK3,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_49,plain,
! [X0: $i] : r1(X0,X0),
inference(cnf_transformation,[],[f16]) ).
tcf(c_56,negated_conjecture,
! [X0: $i] :
( p2(X0)
| ~ r1(sK3,X0) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_57,negated_conjecture,
! [X0: $i] :
( sP0(X0)
| ~ r1(sK3,X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,negated_conjecture,
! [X0: $i,X1: $i] :
( p2(X0)
| ~ p2(X1)
| ~ p101(X1)
| ~ p101(X0)
| ~ r1(sK3,X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_63,negated_conjecture,
~ p101(sK3),
inference(cnf_transformation,[],[f24]) ).
tcf(c_64,negated_conjecture,
p100(sK3),
inference(cnf_transformation,[],[f23]) ).
tcf(c_65,plain,
r1(sK3,sK3),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_66,plain,
( sP0(sK3)
| ~ r1(sK3,sK3) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_76,negated_conjecture,
! [X0: $i] :
( p2(X0)
| ~ r1(sK3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_58,c_56]) ).
fof(f9,definition,
! [X2] :
( ~ sP0(X2)
| ~ p100(X2)
| p101(X2)
| ( ? [X4] :
( p101(X4)
& p2(X4)
& r1(X2,X4) )
& ? [X3] :
( p101(X3)
& ~ p2(X3)
& r1(X2,X3) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f10,plain,
? [X0] :
( p100(X0)
& ~ p101(X0)
& ! [X2] :
( ( ( ~ p101(X2)
| p100(X2) )
& ( ~ p100(X2)
| ( ( ~ p1(X2)
| ! [X8] :
( ~ p100(X8)
| p1(X8)
| ~ r1(X2,X8) ) )
& ( p1(X2)
| ! [X7] :
( ~ p100(X7)
| ~ p1(X7)
| ~ r1(X2,X7) ) ) ) )
& ( ~ p101(X2)
| ( ( ~ p2(X2)
| ! [X6] :
( ~ p101(X6)
| p2(X6)
| ~ r1(X2,X6) ) )
& ( p2(X2)
| ! [X5] :
( ~ p101(X5)
| ~ p2(X5)
| ~ r1(X2,X5) ) ) ) )
& sP0(X2) )
| ~ r1(X0,X2) )
& ! [X1] :
( p2(X1)
| ~ r1(X0,X1) ) ),
inference(definition_folding,[],[f8,f9]) ).
fof(f11,plain,
! [X2] :
( ~ sP0(X2)
| ~ p100(X2)
| p101(X2)
| ( ? [X4] :
( p101(X4)
& p2(X4)
& r1(X2,X4) )
& ? [X3] :
( p101(X3)
& ~ p2(X3)
& r1(X2,X3) ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0] :
( ~ sP0(X0)
| ~ p100(X0)
| p101(X0)
| ( ? [X2] :
( p101(X2)
& p2(X2)
& r1(X0,X2) )
& ? [X1] :
( p101(X1)
& ~ p2(X1)
& r1(X0,X1) ) ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ~ sP0(X0)
| ~ p100(X0)
| p101(X0)
| ( p101(sK2(X0))
& p2(sK2(X0))
& r1(X0,sK2(X0))
& p101(sK1(X0))
& ~ p2(sK1(X0))
& r1(X0,sK1(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f12]) ).
fof(f21,plain,
! [X0] :
( ~ sP0(X0)
| ~ p100(X0)
| p101(X0)
| ~ p2(sK1(X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0] :
( ~ sP0(X0)
| ~ p100(X0)
| p101(X0)
| r1(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_50,plain,
! [X0: $i] :
( p101(X0)
| r1(X0,sK1(X0))
| ~ sP0(X0)
| ~ p100(X0) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_51,plain,
! [X0: $i] :
( p101(X0)
| ~ sP0(X0)
| ~ p100(X0)
| ~ p2(sK1(X0)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_73,plain,
( p101(sK3)
| r1(sK3,sK1(sK3))
| ~ sP0(sK3)
| ~ p100(sK3) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_202,plain,
! [X0: $i] :
( p101(X0)
| ~ sP0(X0)
| ~ p100(X0)
| ~ r1(sK3,sK1(X0)) ),
inference(resolution,[status(thm)],[c_51,c_76]) ).
tcf(c_203,plain,
( p101(sK3)
| ~ sP0(sK3)
| ~ p100(sK3)
| ~ r1(sK3,sK1(sK3)) ),
inference(instantiation,[status(thm)],[c_202]) ).
tcf(c_204,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_203,c_73,c_66,c_65,c_63,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n018.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 00:04:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.18/1.27 % SZS status Started for theBenchmark.p
% 1.18/1.27 % SZS status Theorem for theBenchmark.p
% 1.18/1.27
% 1.18/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.18/1.27
% 1.18/1.27 % ------ iProver source info
% 1.18/1.27
% 1.18/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.18/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.18/1.27 % git: non_committed_changes: false
% 1.18/1.27
% 1.18/1.27 % ------ Parsing...
% 1.18/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.18/1.27
% 1.18/1.27 % ------ Preprocessing... sf_s rm: 3 0s sf_e pe_s %
% 1.18/1.27
% 1.18/1.27 % SZS status Theorem for theBenchmark.p
% 1.18/1.27
% 1.18/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.18/1.27
% 1.18/1.27
%------------------------------------------------------------------------------