%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL901+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 02:08:39 PM UTC 2026
% Result : Theorem 0.67s 1.14s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 17
% Syntax : Number of formulae : 136 ( 93 unt; 3 def)
% Number of atoms : 297 ( 71 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 119 ( 60 ~; 52 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 155 ( 0 sgn 154 !; 1 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
fof(f2,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(f3,axiom,
! [X0] : '+'(X0,'0') = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
fof(f4,axiom,
! [X0] : '>='(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( '>='(X1,X2)
& '>='(X0,X1) )
=> '>='(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
fof(f6,axiom,
! [X0,X1] :
( ( '>='(X1,X0)
& '>='(X0,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
fof(f7,axiom,
! [X0,X1,X2] :
( '>='('+'(X0,X1),X2)
<=> '>='(X1,'==>'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(f8,axiom,
! [X0] : '>='(X0,'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(f9,axiom,
! [X0,X1,X2] :
( '>='(X0,X1)
=> '>='('+'(X0,X2),'+'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
fof(f12,axiom,
! [X0] : '+'(X0,'1') = '1',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
fof(f13,axiom,
! [X0,X1] : '==>'('==>'(X0,X1),X1) = '==>'('==>'(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
fof(f14,axiom,
! [X0] : '+'(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_14) ).
fof(f15,conjecture,
! [X0] : '==>'('==>'('==>'(X0,'1'),X0),X0) = '0',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
fof(f16,negated_conjecture,
~ ! [X0] : '==>'('==>'('==>'(X0,'1'),X0),X0) = '0',
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ '>='(X1,X2)
| ~ '>='(X0,X1)
| '>='(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ '>='(X1,X2)
| ~ '>='(X0,X1)
| '>='(X0,X2) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ~ '>='(X1,X0)
| ~ '>='(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1] :
( ~ '>='(X1,X0)
| ~ '>='(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ '>='(X0,X1)
| '>='('+'(X0,X2),'+'(X1,X2)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f24,plain,
? [X0] : '0' != '==>'('==>'('==>'(X0,'1'),X0),X0),
inference(ennf_transformation,[],[f16]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ~ '>='('+'(X0,X1),X2)
| '>='(X1,'==>'(X0,X2)) )
& ( ~ '>='(X1,'==>'(X0,X2))
| '>='('+'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f26,plain,
'0' != '==>'('==>'('==>'(sK0,'1'),sK0),sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f24]) ).
fof(f27,plain,
! [X2,X0,X1] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f29,plain,
! [X0] : '+'(X0,'0') = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f30,plain,
! [X0] : '>='(X0,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ '>='(X1,X2)
| ~ '>='(X0,X1)
| '>='(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X0,X1] :
( ~ '>='(X1,X0)
| ~ '>='(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ '>='('+'(X0,X1),X2)
| '>='(X1,'==>'(X0,X2)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ '>='(X1,'==>'(X0,X2))
| '>='('+'(X0,X1),X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f35,plain,
! [X0] : '>='(X0,'0'),
inference(cnf_transformation,[],[f8]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ '>='(X0,X1)
| '>='('+'(X0,X2),'+'(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X0] : '1' = '+'(X0,'1'),
inference(cnf_transformation,[],[f12]) ).
fof(f40,plain,
! [X0,X1] : '==>'('==>'(X0,X1),X1) = '==>'('==>'(X1,X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f41,plain,
! [X0] : '+'(X0,X0) = X0,
inference(cnf_transformation,[],[f14]) ).
fof(f42,plain,
'0' != '==>'('==>'('==>'(sK0,'1'),sK0),sK0),
inference(cnf_transformation,[],[f26]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[],[f28]) ).
tcf(c_51,plain,
! [X0: $i] : '+'(X0,'0') = X0,
inference(cnf_transformation,[],[f29]) ).
tcf(c_52,plain,
! [X0: $i] : '>='(X0,X0),
inference(cnf_transformation,[],[f30]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( '>='(X0,X2)
| ~ '>='(X1,X2)
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ '>='(X1,X0)
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( '>='('+'(X1,X0),X2)
| ~ '>='(X0,'==>'(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( '>='(X1,'==>'(X0,X2))
| ~ '>='('+'(X0,X1),X2) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_57,plain,
! [X0: $i] : '>='(X0,'0'),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( '>='('+'(X0,X2),'+'(X1,X2))
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i] : '+'(X0,'1') = '1',
inference(cnf_transformation,[],[f39]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : '==>'('==>'(X0,X1),X1) = '==>'('==>'(X1,X0),X0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_63,plain,
! [X0: $i] : '+'(X0,X0) = X0,
inference(cnf_transformation,[],[f41]) ).
tcf(c_64,negated_conjecture,
'==>'('==>'('==>'(sK0,'1'),sK0),sK0) != '0',
inference(cnf_transformation,[],[f42]) ).
tcf(c_162,definition,
iPr_def_10 = '==>'(sK0,'1'),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_163,definition,
iPr_def_11 = '==>'(iPr_def_10,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_164,definition,
iPr_def_12 = '==>'(iPr_def_11,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_165,negated_conjecture,
iPr_def_12 != '0',
inference(demodulation,[status(thm)],[c_64,c_162,c_163,c_164]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_345,plain,
! [X0: $i,X1: $i,X2: $i] : '+'(X0,'+'(X1,X2)) = '+'(X1,'+'(X0,X2)),
inference(superposition,[status(thm)],[c_49,c_50]) ).
tcf(c_354,plain,
! [X0: $i] : '+'('0',X0) = X0,
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_355,plain,
! [X0: $i] : '+'('1',X0) = '1',
inference(superposition,[status(thm)],[c_50,c_61]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i] :
( '>='(X1,X0)
| ~ '>='('0',X0) ),
inference(superposition,[status(thm)],[c_57,c_53]) ).
tcf(c_368,plain,
! [X0: $i,X1: $i] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(superposition,[status(thm)],[c_52,c_55]) ).
tcf(c_371,plain,
! [X0: $i] :
( '>='('+'(iPr_def_11,X0),sK0)
| ~ '>='(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_164,c_55]) ).
tcf(c_379,plain,
( '>='('+'(iPr_def_11,'0'),sK0)
| ~ '>='('0',iPr_def_12) ),
inference(instantiation,[status(thm)],[c_371]) ).
tcf(c_386,plain,
! [X0: $i,X1: $i] : '>='(X0,'==>'(X1,'+'(X1,X0))),
inference(superposition,[status(thm)],[c_52,c_56]) ).
tcf(c_432,plain,
! [X0: $i] : '>='('==>'('0',X0),X0),
inference(superposition,[status(thm)],[c_354,c_368]) ).
tcf(c_433,plain,
! [X0: $i] : '>='('1',X0),
inference(superposition,[status(thm)],[c_355,c_368]) ).
tcf(c_434,plain,
'>='('+'(sK0,iPr_def_10),'1'),
inference(superposition,[status(thm)],[c_162,c_368]) ).
tcf(c_436,plain,
'>='('+'(iPr_def_11,iPr_def_12),sK0),
inference(superposition,[status(thm)],[c_164,c_368]) ).
tcf(c_440,plain,
'>='('+'(iPr_def_10,sK0),'1'),
inference(theory_normalisation,[status(thm)],[c_434,c_49,c_50]) ).
tcf(c_447,plain,
! [X0: $i] :
( ( iPr_def_12 = '0' )
| ( iPr_def_12 != X0 )
| ( '0' != X0 ) ),
inference(instantiation,[status(thm)],[c_168]) ).
tcf(c_474,plain,
( ( iPr_def_12 = '0' )
| ( iPr_def_12 != '==>'(iPr_def_11,sK0) )
| ( '0' != '==>'(iPr_def_11,sK0) ) ),
inference(instantiation,[status(thm)],[c_447]) ).
tcf(c_475,plain,
! [X0: $i] :
( '>='('+'(iPr_def_10,sK0),X0)
| ~ '>='('1',X0) ),
inference(superposition,[status(thm)],[c_440,c_53]) ).
tcf(c_477,plain,
! [X0: $i] : '>='('+'(iPr_def_10,sK0),X0),
inference(forward_subsumption_resolution,[status(thm)],[c_475,c_433]) ).
tcf(c_480,plain,
! [X0: $i] : '>='(sK0,'==>'(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_477,c_56]) ).
tcf(c_484,plain,
'>='(sK0,iPr_def_11),
inference(superposition,[status(thm)],[c_163,c_480]) ).
tcf(c_529,plain,
( ( '0' = '==>'(iPr_def_11,sK0) )
| ~ '>='('0','==>'(iPr_def_11,sK0))
| ~ '>='('==>'(iPr_def_11,sK0),'0') ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i] :
( '>='('+'(X0,X1),X1)
| ~ '>='(X0,'0') ),
inference(superposition,[status(thm)],[c_354,c_58]) ).
tcf(c_558,plain,
! [X0: $i,X1: $i] : '>='('+'(X0,X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[c_551,c_57]) ).
tcf(c_648,plain,
'>='('==>'(iPr_def_11,sK0),'0'),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_735,plain,
! [X0: $i] :
( '>='(X0,'==>'(iPr_def_11,sK0))
| ~ '>='('+'(iPr_def_11,X0),sK0) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_736,plain,
( '>='('0','==>'(iPr_def_11,sK0))
| ~ '>='('+'(iPr_def_11,'0'),sK0) ),
inference(instantiation,[status(thm)],[c_735]) ).
tcf(c_756,plain,
! [X0: $i] :
( '>='(sK0,X0)
| ~ '>='(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_484,c_53]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i] : '>='('+'(X0,X1),X0),
inference(superposition,[status(thm)],[c_50,c_558]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i] : '>='(X0,'==>'(X1,X0)),
inference(superposition,[status(thm)],[c_558,c_56]) ).
tcf(c_810,plain,
! [X0: $i,X1: $i] : '>='(X0,'==>'(X1,X1)),
inference(superposition,[status(thm)],[c_763,c_56]) ).
tcf(c_835,plain,
'>='(sK0,iPr_def_12),
inference(superposition,[status(thm)],[c_164,c_771]) ).
tcf(c_843,plain,
! [X0: $i] :
( '>='(sK0,X0)
| ~ '>='(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_835,c_53]) ).
tcf(c_928,plain,
! [X0: $i] : '>='(sK0,'==>'(X0,'+'(X0,iPr_def_11))),
inference(superposition,[status(thm)],[c_386,c_756]) ).
tcf(c_949,plain,
! [X0: $i] :
( ( X0 = '0' )
| ~ '>='('0',X0) ),
inference(superposition,[status(thm)],[c_57,c_54]) ).
tcf(c_956,plain,
! [X0: $i] :
( ( X0 = '1' )
| ~ '>='(X0,'1') ),
inference(superposition,[status(thm)],[c_433,c_54]) ).
tcf(c_958,plain,
! [X0: $i] :
( ( '==>'('0',X0) = X0 )
| ~ '>='(X0,'==>'('0',X0)) ),
inference(superposition,[status(thm)],[c_432,c_54]) ).
tcf(c_964,plain,
( ( sK0 = iPr_def_11 )
| ~ '>='(iPr_def_11,sK0) ),
inference(superposition,[status(thm)],[c_484,c_54]) ).
tcf(c_1000,plain,
! [X0: $i] : '==>'('0',X0) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_958,c_771]) ).
tcf(c_1127,plain,
! [X0: $i,X1: $i] : '>='(X0,'==>'('==>'(X0,X1),X1)),
inference(superposition,[status(thm)],[c_62,c_771]) ).
tcf(c_1349,plain,
! [X0: $i] : '>='(sK0,'==>'(X0,'+'(X0,iPr_def_12))),
inference(superposition,[status(thm)],[c_386,c_843]) ).
tcf(c_1607,plain,
'>='(iPr_def_10,'==>'(iPr_def_11,sK0)),
inference(superposition,[status(thm)],[c_163,c_1127]) ).
tcf(c_1617,plain,
'>='(iPr_def_10,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_1607,c_164]) ).
tcf(c_1627,plain,
! [X0: $i] :
( '>='(iPr_def_10,X0)
| ~ '>='(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_1617,c_53]) ).
tcf(c_1703,plain,
! [X0: $i] : '>='('+'(X0,sK0),'+'(X0,iPr_def_11)),
inference(superposition,[status(thm)],[c_928,c_55]) ).
tcf(c_1947,plain,
! [X0: $i] : '>='('+'(X0,sK0),'+'(X0,iPr_def_12)),
inference(superposition,[status(thm)],[c_1349,c_55]) ).
tcf(c_2254,plain,
! [X0: $i] : '>='(iPr_def_10,'==>'(X0,'+'(X0,iPr_def_12))),
inference(superposition,[status(thm)],[c_386,c_1627]) ).
tcf(c_2401,plain,
'>='(sK0,'+'(sK0,iPr_def_11)),
inference(superposition,[status(thm)],[c_63,c_1703]) ).
tcf(c_2415,plain,
'>='(sK0,'+'(iPr_def_11,sK0)),
inference(theory_normalisation,[status(thm)],[c_2401,c_49,c_50]) ).
tcf(c_2426,plain,
( ( '+'(iPr_def_11,sK0) = sK0 )
| ~ '>='('+'(iPr_def_11,sK0),sK0) ),
inference(superposition,[status(thm)],[c_2415,c_54]) ).
tcf(c_2430,plain,
'+'(iPr_def_11,sK0) = sK0,
inference(forward_subsumption_resolution,[status(thm)],[c_2426,c_558]) ).
tcf(c_2665,plain,
'>='(sK0,'+'(iPr_def_11,iPr_def_12)),
inference(superposition,[status(thm)],[c_2430,c_1947]) ).
tcf(c_2688,plain,
( ( '+'(iPr_def_11,iPr_def_12) = sK0 )
| ~ '>='('+'(iPr_def_11,iPr_def_12),sK0) ),
inference(superposition,[status(thm)],[c_2665,c_54]) ).
tcf(c_2692,plain,
'+'(iPr_def_11,iPr_def_12) = sK0,
inference(forward_subsumption_resolution,[status(thm)],[c_2688,c_436]) ).
tcf(c_2718,plain,
! [X0: $i] : '+'(iPr_def_11,'+'(X0,iPr_def_12)) = '+'(X0,sK0),
inference(superposition,[status(thm)],[c_2692,c_345]) ).
tcf(c_2974,plain,
! [X0: $i] : '>='('+'(X0,iPr_def_10),'+'(X0,iPr_def_12)),
inference(superposition,[status(thm)],[c_2254,c_55]) ).
tcf(c_3573,plain,
'>='(iPr_def_10,'+'(iPr_def_10,iPr_def_12)),
inference(superposition,[status(thm)],[c_63,c_2974]) ).
tcf(c_3619,plain,
( ( '+'(iPr_def_10,iPr_def_12) = iPr_def_10 )
| ~ '>='('+'(iPr_def_10,iPr_def_12),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3573,c_54]) ).
tcf(c_3623,plain,
'+'(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_3619,c_763]) ).
tcf(c_4386,plain,
! [X0: $i] : '==>'(X0,X0) = '0',
inference(superposition,[status(thm)],[c_810,c_949]) ).
tcf(c_4466,plain,
! [X0: $i] : '+'(X0,'==>'(X0,'1')) = '1',
inference(superposition,[status(thm)],[c_368,c_956]) ).
tcf(c_4468,plain,
'+'(iPr_def_10,sK0) = '1',
inference(superposition,[status(thm)],[c_477,c_956]) ).
tcf(c_5100,plain,
( '>='(iPr_def_11,sK0)
| ~ '>='('0',iPr_def_12) ),
inference(superposition,[status(thm)],[c_51,c_371]) ).
tcf(c_5133,plain,
~ '>='('0',iPr_def_12),
inference(global_subsumption_just,[status(thm)],[c_5100,c_164,c_165,c_379,c_474,c_529,c_648,c_736]) ).
tcf(c_5230,plain,
! [X0: $i,X1: $i] :
( '>='('==>'(X1,'1'),'==>'(X1,X0))
| ~ '>='('1',X0) ),
inference(superposition,[status(thm)],[c_4466,c_56]) ).
tcf(c_5295,plain,
! [X0: $i,X1: $i] : '>='('==>'(X0,'1'),'==>'(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_5230,c_433]) ).
tcf(c_5340,plain,
! [X0: $i] : '>='('0','==>'('1',X0)),
inference(superposition,[status(thm)],[c_4386,c_5295]) ).
tcf(c_5519,plain,
! [X0: $i,X1: $i] : '>='(X0,'==>'('1',X1)),
inference(superposition,[status(thm)],[c_5340,c_361]) ).
tcf(c_5536,plain,
! [X0: $i] : '==>'('1',X0) = '0',
inference(superposition,[status(thm)],[c_5519,c_949]) ).
tcf(c_5563,plain,
! [X0: $i] : '==>'('==>'(X0,'1'),'1') = '==>'('0',X0),
inference(superposition,[status(thm)],[c_5536,c_62]) ).
tcf(c_5603,plain,
! [X0: $i] : '==>'('==>'(X0,'1'),'1') = X0,
inference(light_normalisation,[status(thm)],[c_5563,c_1000]) ).
tcf(c_5893,plain,
'==>'(iPr_def_10,'1') = sK0,
inference(superposition,[status(thm)],[c_162,c_5603]) ).
tcf(c_6361,plain,
'+'(iPr_def_10,sK0) = '+'(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_3623,c_2718]) ).
tcf(c_6394,plain,
'+'(iPr_def_10,sK0) = '+'(iPr_def_10,iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_6361,c_49,c_50]) ).
tcf(c_6395,plain,
'+'(iPr_def_10,iPr_def_11) = '1',
inference(light_normalisation,[status(thm)],[c_6394,c_4468]) ).
tcf(c_6474,plain,
'>='(iPr_def_11,'==>'(iPr_def_10,'1')),
inference(superposition,[status(thm)],[c_6395,c_386]) ).
tcf(c_6492,plain,
'>='(iPr_def_11,sK0),
inference(light_normalisation,[status(thm)],[c_6474,c_5893]) ).
tcf(c_6501,plain,
sK0 = iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_964,c_6492]) ).
tcf(c_6582,plain,
'==>'(iPr_def_11,iPr_def_11) = iPr_def_12,
inference(demodulation,[status(thm)],[c_164,c_6501]) ).
tcf(c_6909,plain,
'0' = iPr_def_12,
inference(demodulation,[status(thm)],[c_6582,c_4386]) ).
tcf(c_6913,plain,
~ '>='(iPr_def_12,iPr_def_12),
inference(demodulation,[status(thm)],[c_5133,c_6909]) ).
tcf(c_6923,plain,
! [X0: $i] : '>='(X0,iPr_def_12),
inference(demodulation,[status(thm)],[c_57,c_6909]) ).
tcf(c_6925,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6913,c_6923]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL901+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.34 % Computer : n012.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Thu Sep 24 00:39:36 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 Running first-order theorem proving
% 0.12/0.37 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
% 0.12/0.38
% 0.12/0.38 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.38
% 0.12/0.38 % Detected problem language: tptp
% 0.12/0.39 % Proving...
% 0.67/1.14 % SZS status Started for theBenchmark.p
% 0.67/1.14 % SZS status Theorem for theBenchmark.p
% 0.67/1.14
% 0.67/1.14 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.67/1.14
% 0.67/1.14 % ------ iProver source info
% 0.67/1.14
% 0.67/1.14 % git: date: 2026-07-19 20:42:38 +0200
% 0.67/1.14 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.67/1.14 % git: non_committed_changes: false
% 0.67/1.14
% 0.67/1.14 % ------ Parsing...
% 0.67/1.14 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.67/1.14
% 0.67/1.14 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.67/1.14
% 0.67/1.14 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.67/1.14
% 0.67/1.14 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.67/1.14 % ------ Proving...
% 0.67/1.14 % ------ Problem Properties
% 0.67/1.14
% 0.67/1.14 %
% 0.67/1.14 % clauses 19
% 0.67/1.14 % conjectures 1
% 0.67/1.14 % EPR 5
% 0.67/1.14 % Horn 19
% 0.67/1.14 % unary 12
% 0.67/1.14 % binary 5
% 0.67/1.14 % lits 28
% 0.67/1.14 % lits eq 11
% 0.67/1.14 % fd_pure 0
% 0.67/1.14 % fd_pseudo 0
% 0.67/1.14 % fd_cond 0
% 0.67/1.14 % fd_pseudo_cond 1
% 0.67/1.14 % AC symbols 1
% 0.67/1.14
% 0.67/1.14 % ------ Schedule dynamic 5 is on
% 0.67/1.14
% 0.67/1.14 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.67/1.14
% 0.67/1.14
% 0.67/1.14 % ------
% 0.67/1.14 % Current options:
% 0.67/1.14 % ------
% 0.67/1.14
% 0.67/1.14
% 0.67/1.14 %
% 0.67/1.14
% 0.67/1.14 % ------ Proving...
% 0.67/1.14 %
% 0.67/1.14
% 0.67/1.14 % SZS status Theorem for theBenchmark.p
% 0.67/1.14
% 0.67/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.67/1.14
% 0.67/1.14
%------------------------------------------------------------------------------