%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYO631-1 : 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 : n006.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 03:51:35 PM UTC 2026
% Result : Unsatisfiable 0.43s 1.49s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 26
% Syntax : Number of formulae : 106 ( 21 unt; 0 def)
% Number of atoms : 272 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 315 ( 149 ~; 166 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 11 ( 3 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 : 126 ( 0 sgn 126 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_27_01) ).
fof(f2,axiom,
! [X0] : iLEQ(X0,g(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3_02) ).
fof(f3,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_8_03) ).
fof(f4,axiom,
! [X0,X1] :
( 'LE'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_48_04) ).
fof(f6,axiom,
! [X0] : iLEQ(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_18_06) ).
fof(f7,axiom,
! [X0] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_44_07) ).
fof(f11,axiom,
! [X0,X1] :
( 'LE'(f(X1),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s(s('0'))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5_11) ).
fof(f12,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_29_12) ).
fof(f13,axiom,
! [X0,X1] :
( 'LE'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s('0')))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10_13) ).
fof(f16,axiom,
! [X0] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11_16) ).
fof(f19,axiom,
! [X0,X1] :
( 'LE'(f(X1),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s('0'))))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_26_19) ).
fof(f21,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_23_21) ).
fof(f22,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_20_22) ).
fof(f23,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_40_23) ).
fof(f25,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_2_25) ).
fof(f31,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_56_31) ).
fof(f32,axiom,
! [X0] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_42_32) ).
fof(f35,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_35) ).
fof(f36,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_0_36) ).
fof(f39,axiom,
! [X0] :
( 'LE'(f(X0),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_49_39) ).
fof(f45,axiom,
! [X0,X1] :
( 'LE'(f(X1),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s(s(s('0')))))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_54_45) ).
fof(f48,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_55_48) ).
fof(f50,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_51_50) ).
fof(f52,axiom,
! [X0] : ~ 'LE'(f(X0),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_38_52) ).
fof(f54,axiom,
! [X0] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_31_54) ).
fof(f55,axiom,
! [X0] : ~ 'E'(f(X0),f(g(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_34_55) ).
tcf(c_106,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X0))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0))) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_107,plain,
! [X0: $i] : iLEQ(X0,g(X0)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_108,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,[],[f3]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( 'LE'(f(X1),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_111,plain,
! [X0: $i] : iLEQ(X0,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_112,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(X0))
| ~ 'E'(s(s(s(s(s(s(s('0'))))))),f(g(X0))) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( 'LE'(f(X1),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s(s('0'))))))) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_117,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,[],[f12]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( 'LE'(f(X1),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s('0')))))))))) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_121,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(X0))
| ~ 'E'(s(s(s(s(s(s('0')))))),f(g(X0))) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i] :
( 'LE'(f(X1),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s('0'))))))))) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_126,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,[],[f21]) ).
tcf(c_127,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,[],[f22]) ).
tcf(c_128,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,[],[f23]) ).
tcf(c_130,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(g(X0))) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] :
( 'LE'(f(X1),'0')
| 'E'('0',f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s('0')) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_137,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(g(X0))) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_140,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(g(X0))) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_141,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,[],[f36]) ).
tcf(c_144,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s(s(s(s(s(s(s('0')))))))))))
| 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( 'LE'(f(X1),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s(s(s(s(s(s(s('0')))))))) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_153,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,[],[f48]) ).
tcf(c_155,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,[],[f50]) ).
tcf(c_157,plain,
! [X0: $i] : ~ 'LE'(f(X0),'0'),
inference(cnf_transformation,[],[f52]) ).
tcf(c_159,plain,
! [X0: $i] :
( 'E'(f(X0),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(X0))
| ~ 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(X0))) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_160,plain,
! [X0: $i] : ~ 'E'(f(X0),f(g(X0))),
inference(cnf_transformation,[],[f55]) ).
tcf(c_196,plain,
! [X0: $i] :
( ~ 'E'(s(s('0')),f(g(X0)))
| ~ 'E'(s(s('0')),f(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_127,c_160,c_127]) ).
tcf(c_197,plain,
! [X0: $i] :
( ~ 'E'(s(s('0')),f(X0))
| ~ 'E'(s(s('0')),f(g(X0))) ),
inference(renaming,[status(thm)],[c_196]) ).
tcf(c_199,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_117,c_160,c_117]) ).
tcf(c_200,plain,
! [X0: $i] :
( ~ 'E'(s(s(s('0'))),f(X0))
| ~ 'E'(s(s(s('0'))),f(g(X0))) ),
inference(renaming,[status(thm)],[c_199]) ).
tcf(c_217,plain,
! [X0: $i] :
( ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_106,c_160,c_106]) ).
tcf(c_218,plain,
! [X0: $i] :
( ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X0))
| ~ 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0))) ),
inference(renaming,[status(thm)],[c_217]) ).
tcf(c_220,plain,
! [X0: $i] :
( ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(g(X0)))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_137,c_160,c_137]) ).
tcf(c_221,plain,
! [X0: $i] :
( ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0))
| ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(g(X0))) ),
inference(renaming,[status(thm)],[c_220]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] :
( 'E'('0',f(X1))
| ~ iLEQ(X0,X1)
| ~ 'LE'(f(X0),s('0')) ),
inference(backward_subsumption_resolution,[status(thm)],[c_136,c_157]) ).
tcf(c_359,plain,
! [X0: $i] :
( 'E'('0',f(g(X0)))
| ~ 'LE'(f(X0),s('0')) ),
inference(resolution,[status(thm)],[c_107,c_229]) ).
tcf(c_367,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_107,c_155]) ).
tcf(c_378,plain,
! [X0: $i] :
( 'LE'(f(g(X0)),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s('0')))))))) ),
inference(resolution,[status(thm)],[c_107,c_150]) ).
tcf(c_389,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_107,c_141]) ).
tcf(c_400,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_107,c_126]) ).
tcf(c_411,plain,
! [X0: $i] :
( 'LE'(f(g(X0)),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s('0'))))))))) ),
inference(resolution,[status(thm)],[c_107,c_124]) ).
tcf(c_422,plain,
! [X0: $i] :
( 'LE'(f(g(X0)),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s('0')))))))))) ),
inference(resolution,[status(thm)],[c_107,c_118]) ).
tcf(c_433,plain,
! [X0: $i] :
( 'LE'(f(g(X0)),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s(s('0'))))))) ),
inference(resolution,[status(thm)],[c_107,c_116]) ).
tcf(c_444,plain,
! [X0: $i] :
( 'LE'(f(g(X0)),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
inference(resolution,[status(thm)],[c_107,c_109]) ).
tcf(c_455,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_107,c_108]) ).
tcf(c_466,plain,
! [X0: $i] :
( 'E'('0',f(X0))
| ~ 'LE'(f(X0),s('0')) ),
inference(resolution,[status(thm)],[c_229,c_111]) ).
tcf(c_468,plain,
! [X0: $i] : ~ 'LE'(f(X0),s('0')),
inference(global_subsumption_just,[status(thm)],[c_466,c_160,c_130,c_359,c_466]) ).
tcf(c_474,plain,
! [X0: $i] :
( 'E'(s('0'),f(g(X0)))
| ~ 'LE'(f(X0),s(s('0'))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_400,c_468]) ).
tcf(c_476,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_155,c_111]) ).
tcf(c_487,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s(s(s('0')))))))
| 'E'(s(s(s(s(s(s('0')))))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s('0')))))))) ),
inference(resolution,[status(thm)],[c_150,c_111]) ).
tcf(c_498,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_141,c_111]) ).
tcf(c_509,plain,
! [X0: $i] :
( 'LE'(f(X0),s('0'))
| 'E'(s('0'),f(X0))
| ~ 'LE'(f(X0),s(s('0'))) ),
inference(resolution,[status(thm)],[c_126,c_111]) ).
tcf(c_511,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s('0'))),
inference(global_subsumption_just,[status(thm)],[c_509,c_160,c_140,c_468,c_474,c_509]) ).
tcf(c_517,plain,
! [X0: $i] :
( 'E'(s(s('0')),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s('0')))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_367,c_511]) ).
tcf(c_518,plain,
! [X0: $i] :
( 'E'(s(s('0')),f(X0))
| ~ 'LE'(f(X0),s(s(s('0')))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_476,c_511]) ).
tcf(c_521,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s(s(s(s('0'))))))))
| 'E'(s(s(s(s(s(s(s('0'))))))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s('0'))))))))) ),
inference(resolution,[status(thm)],[c_124,c_111]) ).
tcf(c_532,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s(s(s(s(s('0')))))))))
| 'E'(s(s(s(s(s(s(s(s('0')))))))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s('0')))))))))) ),
inference(resolution,[status(thm)],[c_118,c_111]) ).
tcf(c_543,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s(s('0'))))))
| 'E'(s(s(s(s(s('0'))))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s(s(s('0'))))))) ),
inference(resolution,[status(thm)],[c_116,c_111]) ).
tcf(c_554,plain,
! [X0: $i] :
( 'LE'(f(X0),s(s(s(s(s(s(s(s(s('0'))))))))))
| 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
inference(resolution,[status(thm)],[c_109,c_111]) ).
tcf(c_565,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_108,c_111]) ).
tcf(c_567,plain,
! [X0: $i] :
( ~ 'LE'(f(X0),s(s(s(s('0')))))
| 'E'(s(s(s('0'))),f(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_565,c_197,c_518,c_517,c_565]) ).
tcf(c_568,plain,
! [X0: $i] :
( 'E'(s(s(s('0'))),f(X0))
| ~ 'LE'(f(X0),s(s(s(s('0'))))) ),
inference(renaming,[status(thm)],[c_567]) ).
tcf(c_626,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s('0')))),
inference(global_subsumption_just,[status(thm)],[c_517,c_197,c_518,c_517]) ).
tcf(c_628,plain,
! [X0: $i] :
( 'LE'(f(g(X0)),s(s(s('0'))))
| ~ 'LE'(f(X0),s(s(s(s('0'))))) ),
inference(global_subsumption_just,[status(thm)],[c_455,c_200,c_455,c_568]) ).
tcf(c_637,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s(s('0'))))),
inference(backward_subsumption_resolution,[status(thm)],[c_628,c_626]) ).
tcf(c_642,plain,
! [X0: $i] :
( 'E'(s(s(s(s('0')))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s('0')))))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_389,c_637]) ).
tcf(c_644,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s(s(s('0')))))),
inference(global_subsumption_just,[status(thm)],[c_642,c_160,c_153,c_498,c_637,c_642]) ).
tcf(c_650,plain,
! [X0: $i] :
( 'E'(s(s(s(s(s('0'))))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s(s('0'))))))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_433,c_644]) ).
tcf(c_652,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s(s(s(s('0'))))))),
inference(global_subsumption_just,[status(thm)],[c_650,c_160,c_128,c_543,c_644,c_650]) ).
tcf(c_658,plain,
! [X0: $i] :
( 'E'(s(s(s(s(s(s('0')))))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s('0')))))))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_378,c_652]) ).
tcf(c_660,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s(s(s(s(s('0')))))))),
inference(global_subsumption_just,[status(thm)],[c_658,c_160,c_121,c_487,c_652,c_658]) ).
tcf(c_666,plain,
! [X0: $i] :
( 'E'(s(s(s(s(s(s(s('0'))))))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s('0'))))))))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_411,c_660]) ).
tcf(c_668,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s(s(s(s(s(s('0'))))))))),
inference(global_subsumption_just,[status(thm)],[c_666,c_160,c_112,c_521,c_660,c_666]) ).
tcf(c_674,plain,
! [X0: $i] :
( 'E'(s(s(s(s(s(s(s(s('0')))))))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s('0')))))))))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_422,c_668]) ).
tcf(c_676,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s('0')))))))))),
inference(global_subsumption_just,[status(thm)],[c_674,c_160,c_159,c_532,c_668,c_674]) ).
tcf(c_682,plain,
! [X0: $i] :
( 'E'(s(s(s(s(s(s(s(s(s('0'))))))))),f(g(X0)))
| ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s(s('0'))))))))))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_444,c_676]) ).
tcf(c_684,plain,
! [X0: $i] : ~ 'LE'(f(X0),s(s(s(s(s(s(s(s(s(s('0'))))))))))),
inference(global_subsumption_just,[status(thm)],[c_682,c_218,c_554,c_676,c_682]) ).
tcf(c_689,plain,
! [X0: $i] : 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_144,c_684]) ).
tcf(c_693,plain,
! [X0: $i] : ~ 'E'(s(s(s(s(s(s(s(s(s(s('0')))))))))),f(X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_221,c_689]) ).
tcf(c_694,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_693,c_684,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO631-1 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.58 % Computer : n006.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 : Fri Sep 25 03:17:42 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.62 Running first-order theorem proving
% 0.11/0.62 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
% 0.16/0.64
% 0.16/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.64
% 0.16/0.64 % Detected problem language: tptp
% 0.16/0.65 % Proving...
% 0.43/1.49 % SZS status Started for theBenchmark.p
% 0.43/1.49 % SZS status Unsatisfiable for theBenchmark.p
% 0.43/1.49
% 0.43/1.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.43/1.49
% 0.43/1.49 % ------ iProver source info
% 0.43/1.49
% 0.43/1.49 % git: date: 2026-07-19 20:42:38 +0200
% 0.43/1.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.43/1.49 % git: non_committed_changes: false
% 0.43/1.49
% 0.43/1.49 % ------ Parsing...% successful
% 0.43/1.49
% 0.43/1.49
% 0.43/1.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.43/1.49
% 0.43/1.49 % ------ Preprocessing... sf_s rm: 2 0s sf_e pe_s pe:1:0s pe_e %
% 0.43/1.49
% 0.43/1.49 % SZS status Unsatisfiable for theBenchmark.p
% 0.43/1.49
% 0.43/1.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.43/1.50
% 0.43/1.50
%------------------------------------------------------------------------------