%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 01:54:00 PM UTC 2026
% Result : Unsatisfiable 2.35s 1.50s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 5 unt; 0 def)
% Number of atoms : 215 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 299 ( 146 ~; 153 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f2,negated_conjecture,
~ f(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f3,axiom,
! [X0] :
( ~ a(X0)
| d(X0)
| c(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ c(X1)
| ~ c(X0)
| ~ r(X2,X1)
| ~ r(X2,X0)
| ~ e(X2)
| equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f7,axiom,
! [X0] :
( ~ e(X0)
| r3least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
fof(f8,axiom,
! [X0,X1] :
( ~ r(X1,X0)
| ~ e(X1)
| a(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
fof(f19,axiom,
! [X0] :
( ~ equalish(u2r2(X0),u2r1(X0))
| ~ r3least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
fof(f20,axiom,
! [X0] :
( ~ equalish(u2r3(X0),u2r1(X0))
| ~ r3least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
fof(f21,axiom,
! [X0] :
( ~ equalish(u2r3(X0),u2r2(X0))
| ~ r3least(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21) ).
fof(f22,axiom,
! [X0] :
( ~ r3least(X0)
| r(X0,u2r1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
fof(f23,axiom,
! [X0] :
( ~ r3least(X0)
| r(X0,u2r2(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
fof(f24,axiom,
! [X0] :
( ~ r3least(X0)
| r(X0,u2r3(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
fof(f31,axiom,
! [X2,X0,X1] :
( ~ d(X2)
| ~ d(X1)
| ~ r(X0,X2)
| ~ r(X0,X1)
| equalish(X1,X2)
| f(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
tcf(c_80,negated_conjecture,
e(exist),
inference(cnf_transformation,[],[f1]) ).
tcf(c_81,negated_conjecture,
~ f(exist),
inference(cnf_transformation,[],[f2]) ).
tcf(c_82,plain,
! [X0: $i] :
( d(X0)
| c(X0)
| ~ a(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| ~ c(X2)
| ~ c(X1)
| ~ e(X0)
| ~ r(X0,X2)
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_86,plain,
! [X0: $i] :
( r3least(X0)
| ~ e(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( a(X1)
| ~ e(X0)
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_98,plain,
! [X0: $i] :
( ~ r3least(X0)
| ~ equalish(u2r2(X0),u2r1(X0)) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_99,plain,
! [X0: $i] :
( ~ r3least(X0)
| ~ equalish(u2r3(X0),u2r1(X0)) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_100,plain,
! [X0: $i] :
( ~ r3least(X0)
| ~ equalish(u2r3(X0),u2r2(X0)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_101,plain,
! [X0: $i] :
( r(X0,u2r1(X0))
| ~ r3least(X0) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_102,plain,
! [X0: $i] :
( r(X0,u2r2(X0))
| ~ r3least(X0) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_103,plain,
! [X0: $i] :
( r(X0,u2r3(X0))
| ~ r3least(X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( f(X0)
| equalish(X1,X2)
| ~ d(X2)
| ~ d(X1)
| ~ r(X0,X2)
| ~ r(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_111,plain,
( r3least(exist)
| ~ e(exist) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_114,plain,
( r(exist,u2r3(exist))
| ~ r3least(exist) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_115,plain,
( r(exist,u2r2(exist))
| ~ r3least(exist) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_116,plain,
( r(exist,u2r1(exist))
| ~ r3least(exist) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_118,plain,
( ~ r3least(exist)
| ~ equalish(u2r3(exist),u2r2(exist)) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_119,plain,
( ~ r3least(exist)
| ~ equalish(u2r3(exist),u2r1(exist)) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_120,plain,
( ~ r3least(exist)
| ~ equalish(u2r2(exist),u2r1(exist)) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_1991,plain,
! [X0: $i] :
( a(u2r1(X0))
| ~ e(X0)
| ~ r(X0,u2r1(X0)) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_1992,plain,
( a(u2r1(exist))
| ~ e(exist)
| ~ r(exist,u2r1(exist)) ),
inference(instantiation,[status(thm)],[c_1991]) ).
tcf(c_1993,plain,
! [X0: $i] :
( a(u2r2(X0))
| ~ e(X0)
| ~ r(X0,u2r2(X0)) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_1994,plain,
( a(u2r2(exist))
| ~ e(exist)
| ~ r(exist,u2r2(exist)) ),
inference(instantiation,[status(thm)],[c_1993]) ).
tcf(c_1995,plain,
! [X0: $i] :
( a(u2r3(X0))
| ~ e(X0)
| ~ r(X0,u2r3(X0)) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_1996,plain,
( a(u2r3(exist))
| ~ e(exist)
| ~ r(exist,u2r3(exist)) ),
inference(instantiation,[status(thm)],[c_1995]) ).
tcf(c_1997,plain,
! [X0: $i] :
( d(u2r1(X0))
| c(u2r1(X0))
| ~ a(u2r1(X0)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_1998,plain,
( d(u2r1(exist))
| c(u2r1(exist))
| ~ a(u2r1(exist)) ),
inference(instantiation,[status(thm)],[c_1997]) ).
tcf(c_1999,plain,
! [X0: $i] :
( d(u2r2(X0))
| c(u2r2(X0))
| ~ a(u2r2(X0)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_2000,plain,
( d(u2r2(exist))
| c(u2r2(exist))
| ~ a(u2r2(exist)) ),
inference(instantiation,[status(thm)],[c_1999]) ).
tcf(c_2001,plain,
! [X0: $i] :
( d(u2r3(X0))
| c(u2r3(X0))
| ~ a(u2r3(X0)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_2002,plain,
( d(u2r3(exist))
| c(u2r3(exist))
| ~ a(u2r3(exist)) ),
inference(instantiation,[status(thm)],[c_2001]) ).
tcf(c_2005,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,u2r1(X1))
| ~ c(X2)
| ~ e(X0)
| ~ c(u2r1(X1))
| ~ r(X0,X2)
| ~ r(X0,u2r1(X1)) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_2009,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,u2r2(X1))
| ~ c(X2)
| ~ e(X0)
| ~ c(u2r2(X1))
| ~ r(X0,X2)
| ~ r(X0,u2r2(X1)) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_2015,plain,
! [X0: $i,X1: $i] :
( equalish(u2r2(X1),u2r1(X1))
| ~ e(X0)
| ~ c(u2r1(X1))
| ~ c(u2r2(X1))
| ~ r(X0,u2r1(X1))
| ~ r(X0,u2r2(X1)) ),
inference(instantiation,[status(thm)],[c_2005]) ).
tcf(c_2016,plain,
( equalish(u2r2(exist),u2r1(exist))
| ~ e(exist)
| ~ c(u2r1(exist))
| ~ c(u2r2(exist))
| ~ r(exist,u2r1(exist))
| ~ r(exist,u2r2(exist)) ),
inference(instantiation,[status(thm)],[c_2015]) ).
tcf(c_2017,plain,
! [X0: $i,X1: $i] :
( equalish(u2r3(X1),u2r1(X1))
| ~ e(X0)
| ~ c(u2r3(X1))
| ~ c(u2r1(X1))
| ~ r(X0,u2r3(X1))
| ~ r(X0,u2r1(X1)) ),
inference(instantiation,[status(thm)],[c_2005]) ).
tcf(c_2018,plain,
( equalish(u2r3(exist),u2r1(exist))
| ~ e(exist)
| ~ c(u2r3(exist))
| ~ c(u2r1(exist))
| ~ r(exist,u2r3(exist))
| ~ r(exist,u2r1(exist)) ),
inference(instantiation,[status(thm)],[c_2017]) ).
tcf(c_2019,plain,
! [X0: $i,X1: $i] :
( equalish(u2r3(X1),u2r2(X1))
| ~ e(X0)
| ~ c(u2r3(X1))
| ~ c(u2r2(X1))
| ~ r(X0,u2r3(X1))
| ~ r(X0,u2r2(X1)) ),
inference(instantiation,[status(thm)],[c_2009]) ).
tcf(c_2020,plain,
( equalish(u2r3(exist),u2r2(exist))
| ~ e(exist)
| ~ c(u2r3(exist))
| ~ c(u2r2(exist))
| ~ r(exist,u2r3(exist))
| ~ r(exist,u2r2(exist)) ),
inference(instantiation,[status(thm)],[c_2019]) ).
tcf(c_2030,plain,
! [X0: $i,X1: $i,X2: $i] :
( f(X0)
| equalish(u2r2(X1),X2)
| ~ d(X2)
| ~ d(u2r2(X1))
| ~ r(X0,X2)
| ~ r(X0,u2r2(X1)) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_2032,plain,
! [X0: $i,X1: $i] :
( f(X0)
| equalish(u2r2(X1),u2r1(X1))
| ~ d(u2r1(X1))
| ~ d(u2r2(X1))
| ~ r(X0,u2r1(X1))
| ~ r(X0,u2r2(X1)) ),
inference(instantiation,[status(thm)],[c_2030]) ).
tcf(c_2033,plain,
( f(exist)
| equalish(u2r2(exist),u2r1(exist))
| ~ d(u2r1(exist))
| ~ d(u2r2(exist))
| ~ r(exist,u2r1(exist))
| ~ r(exist,u2r2(exist)) ),
inference(instantiation,[status(thm)],[c_2032]) ).
tcf(c_2040,plain,
! [X0: $i,X1: $i,X2: $i] :
( f(X0)
| equalish(u2r3(X1),X2)
| ~ d(X2)
| ~ d(u2r3(X1))
| ~ r(X0,X2)
| ~ r(X0,u2r3(X1)) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_2042,plain,
! [X0: $i,X1: $i] :
( f(X0)
| equalish(u2r3(X1),u2r1(X1))
| ~ d(u2r3(X1))
| ~ d(u2r1(X1))
| ~ r(X0,u2r3(X1))
| ~ r(X0,u2r1(X1)) ),
inference(instantiation,[status(thm)],[c_2040]) ).
tcf(c_2043,plain,
( f(exist)
| equalish(u2r3(exist),u2r1(exist))
| ~ d(u2r3(exist))
| ~ d(u2r1(exist))
| ~ r(exist,u2r3(exist))
| ~ r(exist,u2r1(exist)) ),
inference(instantiation,[status(thm)],[c_2042]) ).
tcf(c_2044,plain,
! [X0: $i,X1: $i] :
( f(X0)
| equalish(u2r3(X1),u2r2(X1))
| ~ d(u2r3(X1))
| ~ d(u2r2(X1))
| ~ r(X0,u2r3(X1))
| ~ r(X0,u2r2(X1)) ),
inference(instantiation,[status(thm)],[c_2040]) ).
tcf(c_2045,plain,
( f(exist)
| equalish(u2r3(exist),u2r2(exist))
| ~ d(u2r3(exist))
| ~ d(u2r2(exist))
| ~ r(exist,u2r3(exist))
| ~ r(exist,u2r2(exist)) ),
inference(instantiation,[status(thm)],[c_2044]) ).
tcf(c_2046,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2045,c_2043,c_2033,c_2020,c_2018,c_2016,c_2002,c_2000,c_1998,c_1996,c_1994,c_1992,c_120,c_119,c_118,c_116,c_115,c_114,c_111,c_81,c_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.58 % Computer : n001.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Wed Sep 23 19:20:07 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.62 Running first-order theorem proving
% 0.11/0.62 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
% 0.15/0.64
% 0.15/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.64
% 0.15/0.64 % Detected problem language: tptp
% 0.15/0.65 % Proving...
% 2.35/1.50 % SZS status Started for theBenchmark.p
% 2.35/1.50 % SZS status Unsatisfiable for theBenchmark.p
% 2.35/1.50
% 2.35/1.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.35/1.50
% 2.35/1.50 % ------ iProver source info
% 2.35/1.50
% 2.35/1.50 % git: date: 2026-07-19 20:42:38 +0200
% 2.35/1.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.35/1.50 % git: non_committed_changes: false
% 2.35/1.50
% 2.35/1.50 % ------ Parsing...% successful
% 2.35/1.50
% 2.35/1.50
% 2.35/1.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.35/1.50
% 2.35/1.50 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.35/1.50
% 2.35/1.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.35/1.50 % ------ Proving...
% 2.35/1.50 % ------ Problem Properties
% 2.35/1.50
% 2.35/1.50 %
% 2.35/1.50 % clauses 31
% 2.35/1.50 % conjectures 2
% 2.35/1.50 % EPR 10
% 2.35/1.50 % Horn 19
% 2.35/1.50 % unary 2
% 2.35/1.50 % binary 14
% 2.35/1.50 % lits 95
% 2.35/1.50 % lits eq 0
% 2.35/1.50 % fd_pure 0
% 2.35/1.50 % fd_pseudo 0
% 2.35/1.50 % fd_cond 0
% 2.35/1.50 % fd_pseudo_cond 0
% 2.35/1.50 % AC symbols 0
% 2.35/1.50
% 2.35/1.50 % ------ Schedule dynamic 5 is on
% 2.35/1.50
% 2.35/1.50 % ------ no equalities: superposition off
% 2.35/1.50
% 2.35/1.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.35/1.50
% 2.35/1.50
% 2.35/1.50 % ------
% 2.35/1.50 % Current options:
% 2.35/1.50 % ------
% 2.35/1.50
% 2.35/1.50
% 2.35/1.50 %
% 2.35/1.50
% 2.35/1.50 % ------ Proving...
% 2.35/1.50 %
% 2.35/1.50
% 2.35/1.50 % SZS status Unsatisfiable for theBenchmark.p
% 2.35/1.50
% 2.35/1.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.35/1.50
% 2.35/1.50
%------------------------------------------------------------------------------