%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYO630-1 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 03:51:34 PM UTC 2026
% Result : Unsatisfiable 0.28s 6.08s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 63 ( 17 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 171 ( 84 ~; 87 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 73 ( 0 sgn 73 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( 'LE'(f(X0),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8_01) ).
fof(f2,axiom,
! [X0] : iLEQ(X0,g(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_13_02) ).
fof(f4,axiom,
! [X0] : iLEQ(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_18_04) ).
fof(f6,axiom,
! [X0,X1] :
( 'LE'(f(X1),'0')
| 'E'('0',f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1_06) ).
fof(f7,axiom,
! [X0] : ~ 'LE'(f(X0),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6_07) ).
fof(f10,axiom,
! [X0] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s('0'))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s('0'))))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3_10) ).
fof(f11,axiom,
! [X0] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s('0'))),f(g(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_21_11) ).
fof(f12,axiom,
! [X0] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s('0')),f(g(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_27_12) ).
fof(f13,axiom,
! [X0] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s('0'),f(g(X0)))
| ~ 'E'(s('0'),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_30_13) ).
fof(f15,axiom,
! [X0,X1] :
( 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16_15) ).
fof(f16,axiom,
! [X0,X1] :
( 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s('0')))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7_16) ).
fof(f17,axiom,
! [X0,X1] :
( 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_26_17) ).
fof(f24,axiom,
! [X0] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'('0',f(g(X0)))
| ~ 'E'('0',f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_29_24) ).
fof(f30,axiom,
! [X0] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s('0')))),f(g(X0)))
| ~ 'E'(s(s(s(s('0')))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12_30) ).
fof(f31,axiom,
! [X0] : ~ 'E'(f(X0),f(g(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_24_31) ).
fof(f32,axiom,
! [X0,X1] :
( 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_17_32) ).
tcf(c_81,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(X0)) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_82,plain,
! [X0: $i] : iLEQ(X0,g(X0)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_84,plain,
! [X0: $i] : iLEQ(X0,X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( 'LE'(f(X1),'0')
| 'E'('0',f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s('0')) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,plain,
! [X0: $i] : ~ 'LE'(f(X0),'0'),
inference(cnf_transformation,[],[f7]) ).
tcf(c_90,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s('0'))))),f(X0))
| ~ 'E'(s(s(s(s(s('0'))))),f(g(X0))) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_91,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(g(X0))) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_92,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(g(X0))) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_93,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(g(X0))) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s('0')))) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( 'LE'(f(X1),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s('0')))))) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s('0'))))) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_104,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(g(X0))) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_110,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s('0')))),f(X0))
| ~ 'E'(s(s(s(s('0')))),f(g(X0))) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_111,plain,
! [X0: $i] : ~ 'E'(f(X0),f(g(X0))),
inference(cnf_transformation,[],[f31]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s('0'))) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_139,plain,
! [X0: $i] :
( ~ 'E'(s(s(s('0'))),f(g(X0)))
| ~ 'E'(s(s(s('0'))),f(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_91,c_111,c_91]) ).
tcf(c_140,plain,
! [X0: $i] :
( ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(g(X0))) ),
inference(renaming,[status(thm)],[c_139]) ).
tcf(c_142,plain,
! [X0: $i] :
( ~ 'E'(s(s(s(s('0')))),f(g(X0)))
| ~ 'E'(s(s(s(s('0')))),f(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_110,c_111,c_110]) ).
tcf(c_143,plain,
! [X0: $i] :
( ~ 'E'(s(s(s(s('0')))),f(X0))
| ~ 'E'(s(s(s(s('0')))),f(g(X0))) ),
inference(renaming,[status(thm)],[c_142]) ).
tcf(c_145,plain,
! [X0: $i] :
( ~ 'E'(s(s(s(s(s('0'))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s('0'))))),f(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_90,c_111,c_90]) ).
tcf(c_146,plain,
! [X0: $i] :
( ~ 'E'(s(s(s(s(s('0'))))),f(X0))
| ~ 'E'(s(s(s(s(s('0'))))),f(g(X0))) ),
inference(renaming,[status(thm)],[c_145]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] :
( 'E'('0',f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s('0')) ),
inference(backward_subsumption_resolution,[status(thm)],[c_86,c_87]) ).
tcf(c_224,plain,
! [X0: $i] :
( 'E'('0',f(g(X0)))
| ~ 'LE'(f(X0),s('0')) ),
inference(resolution,[status(thm)],[c_82,c_154]) ).
tcf(c_232,plain,
! [X0: $i] :
( 'LE'(f(g(X0)),s('0'))
| 'E'(s('0'),f(g(X0)))
| ~ 'LE'(f(X0),s(s('0'))) ),
inference(resolution,[status(thm)],[c_82,c_112]) ).
tcf(c_243,plain,
! [X0: $i] :
( 'LE'(f(g(X0)),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s('0'))))) ),
inference(resolution,[status(thm)],[c_82,c_97]) ).
tcf(c_254,plain,
! [X0: $i] :
( 'LE'(f(g(X0)),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s('0')))))) ),
inference(resolution,[status(thm)],[c_82,c_96]) ).
tcf(c_265,plain,
! [X0: $i] :
( 'LE'(f(g(X0)),s(s('0')))
| 'E'(s(s('0')),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_82,c_95]) ).
tcf(c_276,plain,
! [X0: $i] :
( 'E'('0',f(X0))
| ~ 'LE'(f(X0),s('0')) ),
inference(resolution,[status(thm)],[c_84,c_154]) ).
tcf(c_278,plain,
! [X0: $i] : ~ 'LE'(f(X0),s('0')),
inference(global_subsumption_just,[status(thm)],[c_276,c_111,c_104,c_224,c_276]) ).
tcf(c_284,plain,
! [X0: $i] :
( 'E'(s('0'),f(g(X0)))
| ~ 'LE'(f(X0),s(s('0'))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_232,c_278]) ).
tcf(c_286,plain,
! [X0: $i] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0))
| ~ 'LE'(f(X0),s(s('0'))) ),
inference(resolution,[status(thm)],[c_84,c_112]) ).
tcf(c_288,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s('0'))),
inference(global_subsumption_just,[status(thm)],[c_286,c_111,c_93,c_278,c_284,c_286]) ).
tcf(c_294,plain,
! [X0: $i] :
( 'E'(s(s('0')),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s('0')))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_265,c_288]) ).
tcf(c_296,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s('0'))))) ),
inference(resolution,[status(thm)],[c_84,c_97]) ).
tcf(c_307,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s('0')))))
| 'E'(s(s(s(s('0')))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s(s('0')))))) ),
inference(resolution,[status(thm)],[c_84,c_96]) ).
tcf(c_318,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s('0')))
| 'E'(s(s('0')),f(X0))
| ~ 'LE'(f(X0),s(s(s('0')))) ),
inference(resolution,[status(thm)],[c_84,c_95]) ).
tcf(c_320,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s('0')))),
inference(global_subsumption_just,[status(thm)],[c_318,c_111,c_92,c_288,c_294,c_318]) ).
tcf(c_326,plain,
! [X0: $i] :
( 'E'(s(s(s('0'))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s('0'))))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_243,c_320]) ).
tcf(c_327,plain,
! [X0: $i] :
( 'E'(s(s(s('0'))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s('0'))))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_296,c_320]) ).
tcf(c_343,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s(s('0'))))),
inference(global_subsumption_just,[status(thm)],[c_327,c_140,c_327,c_326]) ).
tcf(c_346,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s(s('0'))))),
inference(global_subsumption_just,[status(thm)],[c_326,c_140,c_327,c_326]) ).
tcf(c_351,plain,
! [X0: $i] :
( 'LE'(f(g(X0)),s(s(s(s('0')))))
| ~ 'LE'(f(X0),s(s(s(s(s('0')))))) ),
inference(global_subsumption_just,[status(thm)],[c_254,c_143,c_254,c_307,c_343]) ).
tcf(c_362,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s(s(s('0')))))),
inference(backward_subsumption_resolution,[status(thm)],[c_351,c_346]) ).
tcf(c_366,plain,
! [X0: $i] : 'E'(s(s(s(s(s('0'))))),f(X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_81,c_362]) ).
tcf(c_370,plain,
! [X0: $i] : ~ 'E'(s(s(s(s(s('0'))))),f(X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_146,c_366]) ).
tcf(c_371,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_370,c_362,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO630-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n015.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 03:21:18 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.45 % Proving...
% 0.28/6.08 % SZS status Started for theBenchmark.p
% 0.28/6.08 % SZS status Unsatisfiable for theBenchmark.p
% 0.28/6.08
% 0.28/6.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.28/6.08
% 0.28/6.08 % ------ iProver source info
% 0.28/6.08
% 0.28/6.08 % git: date: 2026-07-19 20:42:38 +0200
% 0.28/6.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.28/6.08 % git: non_committed_changes: false
% 0.28/6.08
% 0.28/6.08 % ------ Parsing...% successful
% 0.28/6.08
% 0.28/6.08
% 0.28/6.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.28/6.08
% 0.28/6.08 % ------ Preprocessing... sf_s rm: 2 0s sf_e pe_s pe:1:0s pe_e %
% 0.28/6.08
% 0.28/6.08 % SZS status Unsatisfiable for theBenchmark.p
% 0.28/6.08
% 0.28/6.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.28/6.08
% 0.28/6.08
%------------------------------------------------------------------------------