%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL686+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 : n013.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 02:08:11 PM UTC 2026
% Result : Theorem 1.17s 1.28s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 189 ( 0 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 313 ( 151 ~; 118 |; 44 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 77 ( 0 sgn 65 !; 12 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : r1(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f3,conjecture,
~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X0] :
( ~ ( ! [X1] :
( ( p1(X1)
& p2(X1) )
| ( ~ p2(X1)
& ~ p1(X1) )
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ( p1(X1)
& ~ p2(X1) )
| ( ~ p1(X1)
& p2(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( $false
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ~ p1(X0)
| ~ r1(X1,X0) )
| ~ p3(X1)
| ~ r1(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(f4,negated_conjecture,
~ ~ ? [X0] :
~ ( ! [X1] :
( ~ ! [X0] :
( ~ ( ! [X1] :
( ( p1(X1)
& p2(X1) )
| ( ~ p2(X1)
& ~ p1(X1) )
| ~ r1(X0,X1) )
| ! [X1] :
( p3(X1)
| ~ r1(X0,X1) )
| ~ ! [X1] :
( ~ ( ( p1(X1)
& ~ p2(X1) )
| ( ~ p1(X1)
& p2(X1) ) )
| ~ r1(X0,X1) )
| ! [X1] :
( $false
| ~ r1(X0,X1) ) )
| ~ r1(X1,X0) )
| ~ r1(X0,X1) )
| ! [X1] :
( ! [X0] :
( ~ p1(X0)
| ~ r1(X1,X0) )
| ~ p3(X1)
| ~ r1(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
~ ~ ? [X0] :
~ ( ! [X3] :
( ~ ! [X4] :
( ~ ( ! [X8] :
( ( p1(X8)
& p2(X8) )
| ( ~ p2(X8)
& ~ p1(X8) )
| ~ r1(X4,X8) )
| ! [X7] :
( p3(X7)
| ~ r1(X4,X7) )
| ~ ! [X6] :
( ~ ( ( p1(X6)
& ~ p2(X6) )
| ( ~ p1(X6)
& p2(X6) ) )
| ~ r1(X4,X6) )
| ! [X5] :
( $false
| ~ r1(X4,X5) ) )
| ~ r1(X3,X4) )
| ~ r1(X0,X3) )
| ! [X1] :
( ! [X2] :
( ~ p1(X2)
| ~ r1(X1,X2) )
| ~ p3(X1)
| ~ r1(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
~ ~ ? [X0] :
~ ( ! [X3] :
( ~ ! [X4] :
( ~ ( ! [X8] :
( ( p1(X8)
& p2(X8) )
| ( ~ p2(X8)
& ~ p1(X8) )
| ~ r1(X4,X8) )
| ! [X7] :
( p3(X7)
| ~ r1(X4,X7) )
| ~ ! [X6] :
( ~ ( ( p1(X6)
& ~ p2(X6) )
| ( ~ p1(X6)
& p2(X6) ) )
| ~ r1(X4,X6) )
| ! [X5] : ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X0,X3) )
| ! [X1] :
( ! [X2] :
( ~ p1(X2)
| ~ r1(X1,X2) )
| ~ p3(X1)
| ~ r1(X0,X1) ) ),
inference(true_and_false_elimination,[],[f5]) ).
fof(f7,plain,
? [X0] :
~ ( ! [X3] :
( ~ ! [X4] :
( ~ ( ! [X8] :
( ( p1(X8)
& p2(X8) )
| ( ~ p2(X8)
& ~ p1(X8) )
| ~ r1(X4,X8) )
| ! [X7] :
( p3(X7)
| ~ r1(X4,X7) )
| ~ ! [X6] :
( ~ ( ( p1(X6)
& ~ p2(X6) )
| ( ~ p1(X6)
& p2(X6) ) )
| ~ r1(X4,X6) )
| ! [X5] : ~ r1(X4,X5) )
| ~ r1(X3,X4) )
| ~ r1(X0,X3) )
| ! [X1] :
( ! [X2] :
( ~ p1(X2)
| ~ r1(X1,X2) )
| ~ p3(X1)
| ~ r1(X0,X1) ) ),
inference(flattening,[],[f6]) ).
fof(f10,plain,
? [X0] :
( ? [X3] :
( ! [X4] :
( ( ? [X8] :
( ( ~ p1(X8)
| ~ p2(X8) )
& ( p2(X8)
| p1(X8) )
& r1(X4,X8) )
& ? [X7] :
( ~ p3(X7)
& r1(X4,X7) )
& ! [X6] :
( ( ( ~ p1(X6)
| p2(X6) )
& ( p1(X6)
| ~ p2(X6) ) )
| ~ r1(X4,X6) )
& ? [X5] : r1(X4,X5) )
| ~ r1(X3,X4) )
& r1(X0,X3) )
& ? [X1] :
( ? [X2] :
( p1(X2)
& r1(X1,X2) )
& p3(X1)
& r1(X0,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f11,plain,
( ! [X4] :
( ( ( ~ p1(sK6(X4))
| ~ p2(sK6(X4)) )
& ( p2(sK6(X4))
| p1(sK6(X4)) )
& r1(X4,sK6(X4))
& ~ p3(sK5(X4))
& r1(X4,sK5(X4))
& ! [X6] :
( ( ( ~ p1(X6)
| p2(X6) )
& ( p1(X6)
| ~ p2(X6) ) )
| ~ r1(X4,X6) )
& r1(X4,sK4(X4)) )
| ~ r1(sK3,X4) )
& r1(sK0,sK3)
& p1(sK2)
& r1(sK1,sK2)
& p3(sK1)
& r1(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4(X4)),skolemize(X7,sK5(X4)),skolemize(X8,sK6(X4))],[f10]) ).
fof(f12,plain,
! [X0] : r1(X0,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X4] :
( ~ p1(sK6(X4))
| ~ p2(sK6(X4))
| ~ r1(sK3,X4) ),
inference(cnf_transformation,[],[f11]) ).
fof(f15,plain,
! [X4] :
( p2(sK6(X4))
| p1(sK6(X4))
| ~ r1(sK3,X4) ),
inference(cnf_transformation,[],[f11]) ).
fof(f16,plain,
! [X4] :
( r1(X4,sK6(X4))
| ~ r1(sK3,X4) ),
inference(cnf_transformation,[],[f11]) ).
fof(f19,plain,
! [X6,X4] :
( ~ p1(X6)
| p2(X6)
| ~ r1(X4,X6)
| ~ r1(sK3,X4) ),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
! [X6,X4] :
( p1(X6)
| ~ p2(X6)
| ~ r1(X4,X6)
| ~ r1(sK3,X4) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_49,plain,
! [X0: $i] : r1(X0,X0),
inference(cnf_transformation,[],[f12]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i] :
( p1(X1)
| ~ p2(X1)
| ~ r1(sK3,X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_58,negated_conjecture,
! [X0: $i,X1: $i] :
( p2(X1)
| ~ p1(X1)
| ~ r1(sK3,X0)
| ~ r1(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_61,negated_conjecture,
! [X0: $i] :
( r1(X0,sK6(X0))
| ~ r1(sK3,X0) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( p2(sK6(X0))
| p1(sK6(X0))
| ~ r1(sK3,X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] :
( ~ p2(sK6(X0))
| ~ p1(sK6(X0))
| ~ r1(sK3,X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_64,plain,
r1(sK3,sK3),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_65,plain,
( r1(sK3,sK6(sK3))
| ~ r1(sK3,sK3) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( ~ p1(sK6(X1))
| ~ r1(sK3,X1)
| ~ r1(sK3,X0)
| ~ r1(X0,sK6(X1)) ),
inference(resolution,[status(thm)],[c_58,c_63]) ).
tcf(c_138,plain,
( ~ p1(sK6(sK3))
| ~ r1(sK3,sK3)
| ~ r1(sK3,sK6(sK3)) ),
inference(instantiation,[status(thm)],[c_137]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] :
( p1(sK6(X1))
| ~ r1(sK3,X1)
| ~ r1(sK3,X0)
| ~ r1(X0,sK6(X1)) ),
inference(resolution,[status(thm)],[c_57,c_62]) ).
tcf(c_152,plain,
( p1(sK6(sK3))
| ~ r1(sK3,sK3)
| ~ r1(sK3,sK6(sK3)) ),
inference(instantiation,[status(thm)],[c_151]) ).
tcf(c_153,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_152,c_138,c_65,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL686+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
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 00:19:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 1.17/1.28 % SZS status Started for theBenchmark.p
% 1.17/1.28 % SZS status Theorem for theBenchmark.p
% 1.17/1.28
% 1.17/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.17/1.28
% 1.17/1.28 % ------ iProver source info
% 1.17/1.28
% 1.17/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.17/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.17/1.28 % git: non_committed_changes: false
% 1.17/1.28
% 1.17/1.28 % ------ Parsing...
% 1.17/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.17/1.28
% 1.17/1.28 % ------ Preprocessing... sf_s rm: 2 0s sf_e pe_s %
% 1.17/1.28
% 1.17/1.28 % SZS status Theorem for theBenchmark.p
% 1.17/1.28
% 1.17/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.17/1.28
% 1.17/1.28
%------------------------------------------------------------------------------