%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.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 02:08:06 PM UTC 2026
% Result : Theorem 1.66s 1.27s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 8 unt; 0 def)
% Number of atoms : 232 ( 0 equ)
% Maximal formula atoms : 21 ( 9 avg)
% Number of connectives : 408 ( 200 ~; 178 |; 30 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 1 ( 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 : 9 ( 9 usr; 9 con; 0-0 aty)
% Number of variables : 156 ( 0 sgn 129 !; 27 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,conjecture,
~ ? [X0] :
~ ( ! [X1] :
( ! [X0] :
( p11(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p12(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p13(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p15(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( p12(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( p14(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( p12(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( p16(X0)
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(f4,negated_conjecture,
~ ~ ? [X0] :
~ ( ! [X1] :
( ! [X0] :
( p11(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p12(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p13(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( p15(X0)
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ~ ! [X0] :
( p12(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( p14(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( p12(X0)
| ~ r1(X1,X0) )
| ~ ! [X0] :
( p16(X0)
| ~ r1(X1,X0) ) )
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ! [X12] :
( ! [X13] :
( p11(X13)
| ~ r1(X12,X13) )
| ~ r1(X0,X12) )
| ! [X10] :
( ! [X11] :
( p12(X11)
| ~ r1(X10,X11) )
| ~ r1(X0,X10) )
| ! [X8] :
( ! [X9] :
( p13(X9)
| ~ r1(X8,X9) )
| ~ r1(X0,X8) )
| ! [X6] :
( ! [X7] :
( p15(X7)
| ~ r1(X6,X7) )
| ~ r1(X0,X6) )
| ~ ! [X1] :
( ~ ( ~ ! [X5] :
( p12(X5)
| ~ r1(X1,X5) )
| ~ ! [X4] :
( p14(X4)
| ~ r1(X1,X4) )
| ~ ! [X3] :
( p12(X3)
| ~ r1(X1,X3) )
| ~ ! [X2] :
( p16(X2)
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
? [X0] :
~ ( ! [X12] :
( ! [X13] :
( p11(X13)
| ~ r1(X12,X13) )
| ~ r1(X0,X12) )
| ! [X10] :
( ! [X11] :
( p12(X11)
| ~ r1(X10,X11) )
| ~ r1(X0,X10) )
| ! [X8] :
( ! [X9] :
( p13(X9)
| ~ r1(X8,X9) )
| ~ r1(X0,X8) )
| ! [X6] :
( ! [X7] :
( p15(X7)
| ~ r1(X6,X7) )
| ~ r1(X0,X6) )
| ~ ! [X1] :
( ~ ( ~ ! [X5] :
( p12(X5)
| ~ r1(X1,X5) )
| ~ ! [X4] :
( p14(X4)
| ~ r1(X1,X4) )
| ~ ! [X3] :
( p12(X3)
| ~ r1(X1,X3) )
| ~ ! [X2] :
( p16(X2)
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ! [X12] :
( ! [X13] : ~ r1(X12,X13)
| ~ r1(X0,X12) )
| ! [X10] :
( ! [X11] :
( p12(X11)
| ~ r1(X10,X11) )
| ~ r1(X0,X10) )
| ! [X8] :
( ! [X9] :
( p13(X9)
| ~ r1(X8,X9) )
| ~ r1(X0,X8) )
| ! [X6] :
( ! [X7] :
( p15(X7)
| ~ r1(X6,X7) )
| ~ r1(X0,X6) )
| ~ ! [X1] :
( ~ ( ~ ! [X5] :
( p12(X5)
| ~ r1(X1,X5) )
| ~ ! [X4] :
( p14(X4)
| ~ r1(X1,X4) )
| ~ ! [X3] :
( p12(X3)
| ~ r1(X1,X3) )
| ~ ! [X2] :
( p16(X2)
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f6]) ).
fof(f8,plain,
? [X0] :
~ ( ! [X12] :
( ! [X13] : ~ r1(X12,X13)
| ~ r1(X0,X12) )
| ! [X10] :
( ! [X11] :
( p12(X11)
| ~ r1(X10,X11) )
| ~ r1(X0,X10) )
| ! [X8] :
( ! [X9] : ~ r1(X8,X9)
| ~ r1(X0,X8) )
| ! [X6] :
( ! [X7] :
( p15(X7)
| ~ r1(X6,X7) )
| ~ r1(X0,X6) )
| ~ ! [X1] :
( ~ ( ~ ! [X5] :
( p12(X5)
| ~ r1(X1,X5) )
| ~ ! [X4] :
( p14(X4)
| ~ r1(X1,X4) )
| ~ ! [X3] :
( p12(X3)
| ~ r1(X1,X3) )
| ~ ! [X2] :
( p16(X2)
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f7]) ).
fof(f9,plain,
? [X0] :
~ ( ! [X12] :
( ! [X13] : ~ r1(X12,X13)
| ~ r1(X0,X12) )
| ! [X10] :
( ! [X11] :
( p12(X11)
| ~ r1(X10,X11) )
| ~ r1(X0,X10) )
| ! [X8] :
( ! [X9] : ~ r1(X8,X9)
| ~ r1(X0,X8) )
| ! [X6] :
( ! [X7] : ~ r1(X6,X7)
| ~ r1(X0,X6) )
| ~ ! [X1] :
( ~ ( ~ ! [X5] :
( p12(X5)
| ~ r1(X1,X5) )
| ~ ! [X4] :
( p14(X4)
| ~ r1(X1,X4) )
| ~ ! [X3] :
( p12(X3)
| ~ r1(X1,X3) )
| ~ ! [X2] :
( p16(X2)
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f8]) ).
fof(f10,plain,
? [X0] :
~ ( ! [X12] :
( ! [X13] : ~ r1(X12,X13)
| ~ r1(X0,X12) )
| ! [X10] :
( ! [X11] :
( p12(X11)
| ~ r1(X10,X11) )
| ~ r1(X0,X10) )
| ! [X8] :
( ! [X9] : ~ r1(X8,X9)
| ~ r1(X0,X8) )
| ! [X6] :
( ! [X7] : ~ r1(X6,X7)
| ~ r1(X0,X6) )
| ~ ! [X1] :
( ~ ( ~ ! [X5] :
( p12(X5)
| ~ r1(X1,X5) )
| ~ ! [X3] :
( p12(X3)
| ~ r1(X1,X3) )
| ~ ! [X2] :
( p16(X2)
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f9]) ).
fof(f11,plain,
? [X0] :
~ ( ! [X12] :
( ! [X13] : ~ r1(X12,X13)
| ~ r1(X0,X12) )
| ! [X10] :
( ! [X11] :
( p12(X11)
| ~ r1(X10,X11) )
| ~ r1(X0,X10) )
| ! [X8] :
( ! [X9] : ~ r1(X8,X9)
| ~ r1(X0,X8) )
| ! [X6] :
( ! [X7] : ~ r1(X6,X7)
| ~ r1(X0,X6) )
| ~ ! [X1] :
( ~ ( ~ ! [X5] :
( p12(X5)
| ~ r1(X1,X5) )
| ~ ! [X3] :
( p12(X3)
| ~ r1(X1,X3) ) )
| ~ r1(X0,X1) ) ),
inference(pure_predicate_removal,[],[f10]) ).
fof(f14,plain,
? [X0] :
( ? [X12] :
( ? [X13] : r1(X12,X13)
& r1(X0,X12) )
& ? [X10] :
( ? [X11] :
( ~ p12(X11)
& r1(X10,X11) )
& r1(X0,X10) )
& ? [X8] :
( ? [X9] : r1(X8,X9)
& r1(X0,X8) )
& ? [X6] :
( ? [X7] : r1(X6,X7)
& r1(X0,X6) )
& ! [X1] :
( ( ! [X5] :
( p12(X5)
| ~ r1(X1,X5) )
& ! [X3] :
( p12(X3)
| ~ r1(X1,X3) ) )
| ~ r1(X0,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
? [X0] :
( ? [X10] :
( ? [X11] : r1(X10,X11)
& r1(X0,X10) )
& ? [X8] :
( ? [X9] :
( ~ p12(X9)
& r1(X8,X9) )
& r1(X0,X8) )
& ? [X6] :
( ? [X7] : r1(X6,X7)
& r1(X0,X6) )
& ? [X4] :
( ? [X5] : r1(X4,X5)
& r1(X0,X4) )
& ! [X1] :
( ( ! [X3] :
( p12(X3)
| ~ r1(X1,X3) )
& ! [X2] :
( p12(X2)
| ~ r1(X1,X2) ) )
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
( r1(sK7,sK8)
& r1(sK0,sK7)
& ~ p12(sK6)
& r1(sK5,sK6)
& r1(sK0,sK5)
& r1(sK3,sK4)
& r1(sK0,sK3)
& r1(sK1,sK2)
& r1(sK0,sK1)
& ! [X1] :
( ( ! [X3] :
( p12(X3)
| ~ r1(X1,X3) )
& ! [X2] :
( p12(X2)
| ~ r1(X1,X2) ) )
| ~ r1(sK0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X4,sK1),skolemize(X5,sK2),skolemize(X6,sK3),skolemize(X7,sK4),skolemize(X8,sK5),skolemize(X9,sK6),skolemize(X10,sK7),skolemize(X11,sK8)],[f15]) ).
fof(f21,plain,
~ p12(sK6),
inference(cnf_transformation,[],[f16]) ).
fof(f22,plain,
r1(sK5,sK6),
inference(cnf_transformation,[],[f16]) ).
fof(f23,plain,
r1(sK0,sK5),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X3,X1] :
( p12(X3)
| ~ r1(X1,X3)
| ~ r1(sK0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( p12(X1)
| ~ r1(sK0,X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_57,negated_conjecture,
r1(sK0,sK5),
inference(cnf_transformation,[],[f23]) ).
tcf(c_58,negated_conjecture,
r1(sK5,sK6),
inference(cnf_transformation,[],[f22]) ).
tcf(c_59,negated_conjecture,
~ p12(sK6),
inference(cnf_transformation,[],[f21]) ).
tcf(c_67,negated_conjecture,
r1(sK5,sK6),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_73,negated_conjecture,
! [X0: $i,X1: $i] :
( p12(X1)
| ~ r1(sK0,X0)
| ~ r1(X0,X1) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_79,plain,
( p12(sK6)
| ~ r1(sK0,sK5) ),
inference(resolution,[status(thm)],[c_73,c_67]) ).
tcf(c_80,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_79,c_57,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL682+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n020.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
% 0.10/0.37 % DateTime : Thu Sep 24 00:19:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 1.66/1.27 % SZS status Started for theBenchmark.p
% 1.66/1.27 % SZS status Theorem for theBenchmark.p
% 1.66/1.27
% 1.66/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.66/1.27
% 1.66/1.27 % ------ iProver source info
% 1.66/1.27
% 1.66/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.66/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.66/1.27 % git: non_committed_changes: false
% 1.66/1.27
% 1.66/1.27 % ------ Parsing...
% 1.66/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_horn
% 1.66/1.27 %
% 1.66/1.27
% 1.66/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e sf_s rm: 0 0s sf_e %
% 1.66/1.27
% 1.66/1.27 % ------ Preprocessing...% ------ preprocesses with Option_epr_horn
% 1.66/1.27 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.66/1.27 % ------ Proving...
% 1.66/1.27 % ------ Problem Properties
% 1.66/1.27
% 1.66/1.27 %
% 1.66/1.27 % clauses 12
% 1.66/1.27 % conjectures 10
% 1.66/1.27 % EPR 12
% 1.66/1.27 % Horn 12
% 1.66/1.27 % unary 10
% 1.66/1.27 % binary 0
% 1.66/1.27 % lits 16
% 1.66/1.27 % lits eq 0
% 1.66/1.27 % fd_pure 0
% 1.66/1.27 % fd_pseudo 0
% 1.66/1.27 % fd_cond 0
% 1.66/1.27 % fd_pseudo_cond 0
% 1.66/1.27 % AC symbols 0
% 1.66/1.27
% 1.66/1.27 % ------ Schedule EPR Horn non eq is on
% 1.66/1.27
% 1.66/1.27 % ------ no equalities: superposition off
% 1.66/1.27
% 1.66/1.27 % ------ Option_epr_horn Time Limit: Unbounded
% 1.66/1.27
% 1.66/1.27
% 1.66/1.27 % ------
% 1.66/1.27 % Current options:
% 1.66/1.27 % ------
% 1.66/1.27
% 1.66/1.27
% 1.66/1.27 %
% 1.66/1.27
% 1.66/1.27 % ------ Proving...
% 1.66/1.27 %
% 1.66/1.27
% 1.66/1.27 % SZS status Theorem for theBenchmark.p
% 1.66/1.27
% 1.66/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.66/1.27
% 1.66/1.27
%------------------------------------------------------------------------------