%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG055+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 12:53:18 PM UTC 2026
% Result : Theorem 1.73s 1.09s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f150ERROR: Could not build tree for root c_17531ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ( op(e4,e4) = e4
| op(e4,e4) = e3
| op(e4,e4) = e2
| op(e4,e4) = e1
| op(e4,e4) = e0 )
& ( op(e4,e3) = e4
| op(e4,e3) = e3
| op(e4,e3) = e2
| op(e4,e3) = e1
| op(e4,e3) = e0 )
& ( op(e4,e2) = e4
| op(e4,e2) = e3
| op(e4,e2) = e2
| op(e4,e2) = e1
| op(e4,e2) = e0 )
& ( op(e4,e1) = e4
| op(e4,e1) = e3
| op(e4,e1) = e2
| op(e4,e1) = e1
| op(e4,e1) = e0 )
& ( op(e4,e0) = e4
| op(e4,e0) = e3
| op(e4,e0) = e2
| op(e4,e0) = e1
| op(e4,e0) = e0 )
& ( op(e3,e4) = e4
| op(e3,e4) = e3
| op(e3,e4) = e2
| op(e3,e4) = e1
| op(e3,e4) = e0 )
& ( op(e3,e3) = e4
| op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0 )
& ( op(e3,e2) = e4
| op(e3,e2) = e3
| op(e3,e2) = e2
| op(e3,e2) = e1
| op(e3,e2) = e0 )
& ( op(e3,e1) = e4
| op(e3,e1) = e3
| op(e3,e1) = e2
| op(e3,e1) = e1
| op(e3,e1) = e0 )
& ( op(e3,e0) = e4
| op(e3,e0) = e3
| op(e3,e0) = e2
| op(e3,e0) = e1
| op(e3,e0) = e0 )
& ( op(e2,e4) = e4
| op(e2,e4) = e3
| op(e2,e4) = e2
| op(e2,e4) = e1
| op(e2,e4) = e0 )
& ( op(e2,e3) = e4
| op(e2,e3) = e3
| op(e2,e3) = e2
| op(e2,e3) = e1
| op(e2,e3) = e0 )
& ( op(e2,e2) = e4
| op(e2,e2) = e3
| op(e2,e2) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0 )
& ( op(e2,e1) = e4
| op(e2,e1) = e3
| op(e2,e1) = e2
| op(e2,e1) = e1
| op(e2,e1) = e0 )
& ( op(e2,e0) = e4
| op(e2,e0) = e3
| op(e2,e0) = e2
| op(e2,e0) = e1
| op(e2,e0) = e0 )
& ( op(e1,e4) = e4
| op(e1,e4) = e3
| op(e1,e4) = e2
| op(e1,e4) = e1
| op(e1,e4) = e0 )
& ( op(e1,e3) = e4
| op(e1,e3) = e3
| op(e1,e3) = e2
| op(e1,e3) = e1
| op(e1,e3) = e0 )
& ( op(e1,e2) = e4
| op(e1,e2) = e3
| op(e1,e2) = e2
| op(e1,e2) = e1
| op(e1,e2) = e0 )
& ( op(e1,e1) = e4
| op(e1,e1) = e3
| op(e1,e1) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0 )
& ( op(e1,e0) = e4
| op(e1,e0) = e3
| op(e1,e0) = e2
| op(e1,e0) = e1
| op(e1,e0) = e0 )
& ( op(e0,e4) = e4
| op(e0,e4) = e3
| op(e0,e4) = e2
| op(e0,e4) = e1
| op(e0,e4) = e0 )
& ( op(e0,e3) = e4
| op(e0,e3) = e3
| op(e0,e3) = e2
| op(e0,e3) = e1
| op(e0,e3) = e0 )
& ( op(e0,e2) = e4
| op(e0,e2) = e3
| op(e0,e2) = e2
| op(e0,e2) = e1
| op(e0,e2) = e0 )
& ( op(e0,e1) = e4
| op(e0,e1) = e3
| op(e0,e1) = e2
| op(e0,e1) = e1
| op(e0,e1) = e0 )
& ( op(e0,e0) = e4
| op(e0,e0) = e3
| op(e0,e0) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f2,axiom,
( ( unit = e4
| unit = e3
| unit = e2
| unit = e1
| unit = e0 )
& op(e4,unit) = e4
& op(unit,e4) = e4
& op(e3,unit) = e3
& op(unit,e3) = e3
& op(e2,unit) = e2
& op(unit,e2) = e2
& op(e1,unit) = e1
& op(unit,e1) = e1
& op(e0,unit) = e0
& op(unit,e0) = e0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f3,axiom,
( ( op(e4,e4) = e4
| op(e3,e4) = e4
| op(e2,e4) = e4
| op(e1,e4) = e4
| op(e0,e4) = e4 )
& ( op(e4,e4) = e4
| op(e4,e3) = e4
| op(e4,e2) = e4
| op(e4,e1) = e4
| op(e4,e0) = e4 )
& ( op(e4,e4) = e3
| op(e3,e4) = e3
| op(e2,e4) = e3
| op(e1,e4) = e3
| op(e0,e4) = e3 )
& ( op(e4,e4) = e3
| op(e4,e3) = e3
| op(e4,e2) = e3
| op(e4,e1) = e3
| op(e4,e0) = e3 )
& ( op(e4,e4) = e2
| op(e3,e4) = e2
| op(e2,e4) = e2
| op(e1,e4) = e2
| op(e0,e4) = e2 )
& ( op(e4,e4) = e2
| op(e4,e3) = e2
| op(e4,e2) = e2
| op(e4,e1) = e2
| op(e4,e0) = e2 )
& ( op(e4,e4) = e1
| op(e3,e4) = e1
| op(e2,e4) = e1
| op(e1,e4) = e1
| op(e0,e4) = e1 )
& ( op(e4,e4) = e1
| op(e4,e3) = e1
| op(e4,e2) = e1
| op(e4,e1) = e1
| op(e4,e0) = e1 )
& ( op(e4,e4) = e0
| op(e3,e4) = e0
| op(e2,e4) = e0
| op(e1,e4) = e0
| op(e0,e4) = e0 )
& ( op(e4,e4) = e0
| op(e4,e3) = e0
| op(e4,e2) = e0
| op(e4,e1) = e0
| op(e4,e0) = e0 )
& ( op(e4,e3) = e4
| op(e3,e3) = e4
| op(e2,e3) = e4
| op(e1,e3) = e4
| op(e0,e3) = e4 )
& ( op(e3,e4) = e4
| op(e3,e3) = e4
| op(e3,e2) = e4
| op(e3,e1) = e4
| op(e3,e0) = e4 )
& ( op(e4,e3) = e3
| op(e3,e3) = e3
| op(e2,e3) = e3
| op(e1,e3) = e3
| op(e0,e3) = e3 )
& ( op(e3,e4) = e3
| op(e3,e3) = e3
| op(e3,e2) = e3
| op(e3,e1) = e3
| op(e3,e0) = e3 )
& ( op(e4,e3) = e2
| op(e3,e3) = e2
| op(e2,e3) = e2
| op(e1,e3) = e2
| op(e0,e3) = e2 )
& ( op(e3,e4) = e2
| op(e3,e3) = e2
| op(e3,e2) = e2
| op(e3,e1) = e2
| op(e3,e0) = e2 )
& ( op(e4,e3) = e1
| op(e3,e3) = e1
| op(e2,e3) = e1
| op(e1,e3) = e1
| op(e0,e3) = e1 )
& ( op(e3,e4) = e1
| op(e3,e3) = e1
| op(e3,e2) = e1
| op(e3,e1) = e1
| op(e3,e0) = e1 )
& ( op(e4,e3) = e0
| op(e3,e3) = e0
| op(e2,e3) = e0
| op(e1,e3) = e0
| op(e0,e3) = e0 )
& ( op(e3,e4) = e0
| op(e3,e3) = e0
| op(e3,e2) = e0
| op(e3,e1) = e0
| op(e3,e0) = e0 )
& ( op(e4,e2) = e4
| op(e3,e2) = e4
| op(e2,e2) = e4
| op(e1,e2) = e4
| op(e0,e2) = e4 )
& ( op(e2,e4) = e4
| op(e2,e3) = e4
| op(e2,e2) = e4
| op(e2,e1) = e4
| op(e2,e0) = e4 )
& ( op(e4,e2) = e3
| op(e3,e2) = e3
| op(e2,e2) = e3
| op(e1,e2) = e3
| op(e0,e2) = e3 )
& ( op(e2,e4) = e3
| op(e2,e3) = e3
| op(e2,e2) = e3
| op(e2,e1) = e3
| op(e2,e0) = e3 )
& ( op(e4,e2) = e2
| op(e3,e2) = e2
| op(e2,e2) = e2
| op(e1,e2) = e2
| op(e0,e2) = e2 )
& ( op(e2,e4) = e2
| op(e2,e3) = e2
| op(e2,e2) = e2
| op(e2,e1) = e2
| op(e2,e0) = e2 )
& ( op(e4,e2) = e1
| op(e3,e2) = e1
| op(e2,e2) = e1
| op(e1,e2) = e1
| op(e0,e2) = e1 )
& ( op(e2,e4) = e1
| op(e2,e3) = e1
| op(e2,e2) = e1
| op(e2,e1) = e1
| op(e2,e0) = e1 )
& ( op(e4,e2) = e0
| op(e3,e2) = e0
| op(e2,e2) = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 )
& ( op(e2,e4) = e0
| op(e2,e3) = e0
| op(e2,e2) = e0
| op(e2,e1) = e0
| op(e2,e0) = e0 )
& ( op(e4,e1) = e4
| op(e3,e1) = e4
| op(e2,e1) = e4
| op(e1,e1) = e4
| op(e0,e1) = e4 )
& ( op(e1,e4) = e4
| op(e1,e3) = e4
| op(e1,e2) = e4
| op(e1,e1) = e4
| op(e1,e0) = e4 )
& ( op(e4,e1) = e3
| op(e3,e1) = e3
| op(e2,e1) = e3
| op(e1,e1) = e3
| op(e0,e1) = e3 )
& ( op(e1,e4) = e3
| op(e1,e3) = e3
| op(e1,e2) = e3
| op(e1,e1) = e3
| op(e1,e0) = e3 )
& ( op(e4,e1) = e2
| op(e3,e1) = e2
| op(e2,e1) = e2
| op(e1,e1) = e2
| op(e0,e1) = e2 )
& ( op(e1,e4) = e2
| op(e1,e3) = e2
| op(e1,e2) = e2
| op(e1,e1) = e2
| op(e1,e0) = e2 )
& ( op(e4,e1) = e1
| op(e3,e1) = e1
| op(e2,e1) = e1
| op(e1,e1) = e1
| op(e0,e1) = e1 )
& ( op(e1,e4) = e1
| op(e1,e3) = e1
| op(e1,e2) = e1
| op(e1,e1) = e1
| op(e1,e0) = e1 )
& ( op(e4,e1) = e0
| op(e3,e1) = e0
| op(e2,e1) = e0
| op(e1,e1) = e0
| op(e0,e1) = e0 )
& ( op(e1,e4) = e0
| op(e1,e3) = e0
| op(e1,e2) = e0
| op(e1,e1) = e0
| op(e1,e0) = e0 )
& ( op(e4,e0) = e4
| op(e3,e0) = e4
| op(e2,e0) = e4
| op(e1,e0) = e4
| op(e0,e0) = e4 )
& ( op(e0,e4) = e4
| op(e0,e3) = e4
| op(e0,e2) = e4
| op(e0,e1) = e4
| op(e0,e0) = e4 )
& ( op(e4,e0) = e3
| op(e3,e0) = e3
| op(e2,e0) = e3
| op(e1,e0) = e3
| op(e0,e0) = e3 )
& ( op(e0,e4) = e3
| op(e0,e3) = e3
| op(e0,e2) = e3
| op(e0,e1) = e3
| op(e0,e0) = e3 )
& ( op(e4,e0) = e2
| op(e3,e0) = e2
| op(e2,e0) = e2
| op(e1,e0) = e2
| op(e0,e0) = e2 )
& ( op(e0,e4) = e2
| op(e0,e3) = e2
| op(e0,e2) = e2
| op(e0,e1) = e2
| op(e0,e0) = e2 )
& ( op(e4,e0) = e1
| op(e3,e0) = e1
| op(e2,e0) = e1
| op(e1,e0) = e1
| op(e0,e0) = e1 )
& ( op(e0,e4) = e1
| op(e0,e3) = e1
| op(e0,e2) = e1
| op(e0,e1) = e1
| op(e0,e0) = e1 )
& ( op(e4,e0) = e0
| op(e3,e0) = e0
| op(e2,e0) = e0
| op(e1,e0) = e0
| op(e0,e0) = e0 )
& ( op(e0,e4) = e0
| op(e0,e3) = e0
| op(e0,e2) = e0
| op(e0,e1) = e0
| op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f4,axiom,
( op(e4,e3) != op(e4,e4)
& op(e4,e2) != op(e4,e4)
& op(e4,e2) != op(e4,e3)
& op(e4,e1) != op(e4,e4)
& op(e4,e1) != op(e4,e3)
& op(e4,e1) != op(e4,e2)
& op(e4,e0) != op(e4,e4)
& op(e4,e0) != op(e4,e3)
& op(e4,e0) != op(e4,e2)
& op(e4,e0) != op(e4,e1)
& op(e3,e3) != op(e3,e4)
& op(e3,e2) != op(e3,e4)
& op(e3,e2) != op(e3,e3)
& op(e3,e1) != op(e3,e4)
& op(e3,e1) != op(e3,e3)
& op(e3,e1) != op(e3,e2)
& op(e3,e0) != op(e3,e4)
& op(e3,e0) != op(e3,e3)
& op(e3,e0) != op(e3,e2)
& op(e3,e0) != op(e3,e1)
& op(e2,e3) != op(e2,e4)
& op(e2,e2) != op(e2,e4)
& op(e2,e2) != op(e2,e3)
& op(e2,e1) != op(e2,e4)
& op(e2,e1) != op(e2,e3)
& op(e2,e1) != op(e2,e2)
& op(e2,e0) != op(e2,e4)
& op(e2,e0) != op(e2,e3)
& op(e2,e0) != op(e2,e2)
& op(e2,e0) != op(e2,e1)
& op(e1,e3) != op(e1,e4)
& op(e1,e2) != op(e1,e4)
& op(e1,e2) != op(e1,e3)
& op(e1,e1) != op(e1,e4)
& op(e1,e1) != op(e1,e3)
& op(e1,e1) != op(e1,e2)
& op(e1,e0) != op(e1,e4)
& op(e1,e0) != op(e1,e3)
& op(e1,e0) != op(e1,e2)
& op(e1,e0) != op(e1,e1)
& op(e0,e3) != op(e0,e4)
& op(e0,e2) != op(e0,e4)
& op(e0,e2) != op(e0,e3)
& op(e0,e1) != op(e0,e4)
& op(e0,e1) != op(e0,e3)
& op(e0,e1) != op(e0,e2)
& op(e0,e0) != op(e0,e4)
& op(e0,e0) != op(e0,e3)
& op(e0,e0) != op(e0,e2)
& op(e0,e0) != op(e0,e1)
& op(e3,e4) != op(e4,e4)
& op(e2,e4) != op(e4,e4)
& op(e2,e4) != op(e3,e4)
& op(e1,e4) != op(e4,e4)
& op(e1,e4) != op(e3,e4)
& op(e1,e4) != op(e2,e4)
& op(e0,e4) != op(e4,e4)
& op(e0,e4) != op(e3,e4)
& op(e0,e4) != op(e2,e4)
& op(e0,e4) != op(e1,e4)
& op(e3,e3) != op(e4,e3)
& op(e2,e3) != op(e4,e3)
& op(e2,e3) != op(e3,e3)
& op(e1,e3) != op(e4,e3)
& op(e1,e3) != op(e3,e3)
& op(e1,e3) != op(e2,e3)
& op(e0,e3) != op(e4,e3)
& op(e0,e3) != op(e3,e3)
& op(e0,e3) != op(e2,e3)
& op(e0,e3) != op(e1,e3)
& op(e3,e2) != op(e4,e2)
& op(e2,e2) != op(e4,e2)
& op(e2,e2) != op(e3,e2)
& op(e1,e2) != op(e4,e2)
& op(e1,e2) != op(e3,e2)
& op(e1,e2) != op(e2,e2)
& op(e0,e2) != op(e4,e2)
& op(e0,e2) != op(e3,e2)
& op(e0,e2) != op(e2,e2)
& op(e0,e2) != op(e1,e2)
& op(e3,e1) != op(e4,e1)
& op(e2,e1) != op(e4,e1)
& op(e2,e1) != op(e3,e1)
& op(e1,e1) != op(e4,e1)
& op(e1,e1) != op(e3,e1)
& op(e1,e1) != op(e2,e1)
& op(e0,e1) != op(e4,e1)
& op(e0,e1) != op(e3,e1)
& op(e0,e1) != op(e2,e1)
& op(e0,e1) != op(e1,e1)
& op(e3,e0) != op(e4,e0)
& op(e2,e0) != op(e4,e0)
& op(e2,e0) != op(e3,e0)
& op(e1,e0) != op(e4,e0)
& op(e1,e0) != op(e3,e0)
& op(e1,e0) != op(e2,e0)
& op(e0,e0) != op(e4,e0)
& op(e0,e0) != op(e3,e0)
& op(e0,e0) != op(e2,e0)
& op(e0,e0) != op(e1,e0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f5,axiom,
( e3 != e4
& e2 != e4
& e2 != e3
& e1 != e4
& e1 != e3
& e1 != e2
& e0 != e4
& e0 != e3
& e0 != e2
& e0 != e1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f6,axiom,
( e4 = op(e2,e2)
& e3 = op(e2,op(e2,e2))
& e1 = op(op(e2,op(e2,e2)),op(e2,e2))
& e0 = op(op(e2,e2),op(e2,e2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(f161,plain,
( ~ sP129
| ( sP100
& sP101
& sP102
& sP103
& sP104
& sP105
& sP106
& sP107
& sP108
& sP109
& sP110
& sP111
& sP112
& sP113
& sP114
& sP115
& sP116
& sP117
& sP118
& sP119
& sP120
& sP121
& sP122
& sP123
& sP124 ) ),
inference(nnf_transformation,[],[f139]) ).
fof(f162,plain,
( ~ sP128
| ( sP75
& sP76
& sP77
& sP78
& sP79
& sP80
& sP81
& sP82
& sP83
& sP84
& sP85
& sP86
& sP87
& sP88
& sP89
& sP90
& sP91
& sP92
& sP93
& sP94
& sP95
& sP96
& sP97
& sP98
& sP99 ) ),
inference(nnf_transformation,[],[f138]) ).
fof(f163,plain,
( ~ sP127
| ( sP50
& sP51
& sP52
& sP53
& sP54
& sP55
& sP56
& sP57
& sP58
& sP59
& sP60
& sP61
& sP62
& sP63
& sP64
& sP65
& sP66
& sP67
& sP68
& sP69
& sP70
& sP71
& sP72
& sP73
& sP74 ) ),
inference(nnf_transformation,[],[f137]) ).
fof(f164,plain,
( ~ sP126
| ( sP25
& sP26
& sP27
& sP28
& sP29
& sP30
& sP31
& sP32
& sP33
& sP34
& sP35
& sP36
& sP37
& sP38
& sP39
& sP40
& sP41
& sP42
& sP43
& sP44
& sP45
& sP46
& sP47
& sP48
& sP49 ) ),
inference(nnf_transformation,[],[f136]) ).
fof(f165,plain,
( ~ sP125
| ( sP0
& sP1
& sP2
& sP3
& sP4
& sP5
& sP6
& sP7
& sP8
& sP9
& sP10
& sP11
& sP12
& sP13
& sP14
& sP15
& sP16
& sP17
& sP18
& sP19
& sP20
& sP21
& sP22
& sP23
& sP24 ) ),
inference(nnf_transformation,[],[f135]) ).
fof(f166,plain,
( ~ sP124
| ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ),
inference(nnf_transformation,[],[f134]) ).
fof(f190,plain,
( ~ sP100
| ( e0 != unit
& op(e4,e0) = e4 )
| op(e4,e4) != e0 ),
inference(nnf_transformation,[],[f110]) ).
fof(f192,plain,
( ~ sP98
| ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 ),
inference(nnf_transformation,[],[f108]) ).
fof(f204,plain,
( ~ sP86
| ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 ),
inference(nnf_transformation,[],[f96]) ).
fof(f210,plain,
( ~ sP80
| ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 ),
inference(nnf_transformation,[],[f90]) ).
fof(f220,plain,
( ~ sP70
| ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 ),
inference(nnf_transformation,[],[f80]) ).
fof(f225,plain,
( ~ sP65
| ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 ),
inference(nnf_transformation,[],[f75]) ).
fof(f255,plain,
( ~ sP35
| ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 ),
inference(nnf_transformation,[],[f45]) ).
fof(f278,plain,
( ~ sP12
| ( e4 != unit
& op(e2,e4) = e2 )
| op(e2,e2) != e4 ),
inference(nnf_transformation,[],[f22]) ).
fof(f303,plain,
( e4 = op(e2,e2)
| e3 = op(e2,e2)
| e2 = op(e2,e2)
| e1 = op(e2,e2)
| e0 = op(e2,e2) ),
inference(cnf_transformation,[],[f1]) ).
fof(f316,plain,
( e4 = unit
| e3 = unit
| e2 = unit
| e1 = unit
| e0 = unit ),
inference(cnf_transformation,[],[f2]) ).
fof(f317,plain,
e4 = op(e4,unit),
inference(cnf_transformation,[],[f2]) ).
fof(f318,plain,
e4 = op(unit,e4),
inference(cnf_transformation,[],[f2]) ).
fof(f321,plain,
e2 = op(e2,unit),
inference(cnf_transformation,[],[f2]) ).
fof(f324,plain,
e1 = op(unit,e1),
inference(cnf_transformation,[],[f2]) ).
fof(f331,plain,
( e2 = op(e4,e4)
| e2 = op(e3,e4)
| e2 = op(e2,e4)
| e2 = op(e1,e4)
| e2 = op(e0,e4) ),
inference(cnf_transformation,[],[f3]) ).
fof(f354,plain,
( e1 = op(e2,e4)
| e1 = op(e2,e3)
| e1 = op(e2,e2)
| e1 = op(e2,e1)
| e1 = op(e2,e0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f384,plain,
op(e4,e0) != op(e4,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f386,plain,
op(e4,e0) != op(e4,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f399,plain,
op(e2,e2) != op(e2,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f400,plain,
op(e2,e1) != op(e2,e4),
inference(cnf_transformation,[],[f4]) ).
fof(f448,plain,
op(e2,e2) != op(e4,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f452,plain,
op(e1,e2) != op(e2,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f455,plain,
op(e0,e2) != op(e2,e2),
inference(cnf_transformation,[],[f4]) ).
fof(f465,plain,
op(e0,e1) != op(e2,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f479,plain,
e2 != e3,
inference(cnf_transformation,[],[f5]) ).
fof(f480,plain,
e1 != e4,
inference(cnf_transformation,[],[f5]) ).
fof(f481,plain,
e1 != e3,
inference(cnf_transformation,[],[f5]) ).
fof(f482,plain,
e1 != e2,
inference(cnf_transformation,[],[f5]) ).
fof(f483,plain,
e0 != e4,
inference(cnf_transformation,[],[f5]) ).
fof(f485,plain,
e0 != e2,
inference(cnf_transformation,[],[f5]) ).
fof(f487,plain,
e4 = op(e2,e2),
inference(cnf_transformation,[],[f6]) ).
fof(f488,plain,
e3 = op(e2,op(e2,e2)),
inference(cnf_transformation,[],[f6]) ).
fof(f489,plain,
e1 = op(op(e2,op(e2,e2)),op(e2,e2)),
inference(cnf_transformation,[],[f6]) ).
fof(f490,plain,
e0 = op(op(e2,e2),op(e2,e2)),
inference(cnf_transformation,[],[f6]) ).
fof(f511,plain,
( ~ sP129
| sP100 ),
inference(cnf_transformation,[],[f161]) ).
fof(f535,plain,
( ~ sP129
| sP124 ),
inference(cnf_transformation,[],[f161]) ).
fof(f541,plain,
( ~ sP128
| sP80 ),
inference(cnf_transformation,[],[f162]) ).
fof(f547,plain,
( ~ sP128
| sP86 ),
inference(cnf_transformation,[],[f162]) ).
fof(f559,plain,
( ~ sP128
| sP98 ),
inference(cnf_transformation,[],[f162]) ).
fof(f576,plain,
( ~ sP127
| sP65 ),
inference(cnf_transformation,[],[f163]) ).
fof(f581,plain,
( ~ sP127
| sP70 ),
inference(cnf_transformation,[],[f163]) ).
fof(f596,plain,
( ~ sP126
| sP35 ),
inference(cnf_transformation,[],[f164]) ).
fof(f623,plain,
( ~ sP125
| sP12 ),
inference(cnf_transformation,[],[f165]) ).
fof(f636,plain,
( ~ sP124
| e0 != unit
| e0 != op(e0,e0) ),
inference(cnf_transformation,[],[f166]) ).
fof(f684,plain,
( ~ sP100
| e0 != unit
| e0 != op(e4,e4) ),
inference(cnf_transformation,[],[f190]) ).
fof(f685,plain,
( ~ sP100
| e4 = op(e4,e0)
| e0 != op(e4,e4) ),
inference(cnf_transformation,[],[f190]) ).
fof(f688,plain,
( ~ sP98
| e1 != unit
| e1 != op(e0,e1) ),
inference(cnf_transformation,[],[f192]) ).
fof(f713,plain,
( ~ sP86
| e3 = op(e2,e1)
| e1 != op(e2,e3) ),
inference(cnf_transformation,[],[f204]) ).
fof(f724,plain,
( ~ sP80
| e1 != unit
| e1 != op(e3,e4) ),
inference(cnf_transformation,[],[f210]) ).
fof(f745,plain,
( ~ sP70
| e4 = op(e0,e2)
| e2 != op(e0,e4) ),
inference(cnf_transformation,[],[f220]) ).
fof(f755,plain,
( ~ sP65
| e4 = op(e1,e2)
| e2 != op(e1,e4) ),
inference(cnf_transformation,[],[f225]) ).
fof(f815,plain,
( ~ sP35
| e4 = op(e2,e3)
| e3 != op(e2,e4) ),
inference(cnf_transformation,[],[f255]) ).
fof(f861,plain,
( ~ sP12
| e2 = op(e2,e4)
| e4 != op(e2,e2) ),
inference(cnf_transformation,[],[f278]) ).
fof(f886,plain,
( sP125
| sP126
| sP127
| sP128
| sP129 ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_61,plain,
( ( op(e2,e2) = e4 )
| ( op(e2,e2) = e3 )
| ( op(e2,e2) = e2 )
| ( op(e2,e2) = e1 )
| ( op(e2,e2) = e0 ) ),
inference(cnf_transformation,[],[f303]) ).
tcf(c_76,plain,
op(unit,e1) = e1,
inference(cnf_transformation,[],[f324]) ).
tcf(c_79,plain,
op(e2,unit) = e2,
inference(cnf_transformation,[],[f321]) ).
tcf(c_82,plain,
op(unit,e4) = e4,
inference(cnf_transformation,[],[f318]) ).
tcf(c_83,plain,
op(e4,unit) = e4,
inference(cnf_transformation,[],[f317]) ).
tcf(c_84,plain,
( ( e4 = unit )
| ( e3 = unit )
| ( e2 = unit )
| ( e1 = unit )
| ( e0 = unit ) ),
inference(cnf_transformation,[],[f316]) ).
tcf(c_107,plain,
( ( op(e2,e4) = e1 )
| ( op(e2,e3) = e1 )
| ( op(e2,e2) = e1 )
| ( op(e2,e1) = e1 )
| ( op(e2,e0) = e1 ) ),
inference(cnf_transformation,[],[f354]) ).
tcf(c_130,plain,
( ( op(e4,e4) = e2 )
| ( op(e3,e4) = e2 )
| ( op(e2,e4) = e2 )
| ( op(e1,e4) = e2 )
| ( op(e0,e4) = e2 ) ),
inference(cnf_transformation,[],[f331]) ).
tcf(c_146,plain,
op(e0,e1) != op(e2,e1),
inference(cnf_transformation,[],[f465]) ).
tcf(c_156,plain,
op(e0,e2) != op(e2,e2),
inference(cnf_transformation,[],[f455]) ).
tcf(c_159,plain,
op(e1,e2) != op(e2,e2),
inference(cnf_transformation,[],[f452]) ).
tcf(c_163,plain,
op(e2,e2) != op(e4,e2),
inference(cnf_transformation,[],[f448]) ).
tcf(c_211,plain,
op(e2,e1) != op(e2,e4),
inference(cnf_transformation,[],[f400]) ).
tcf(c_212,plain,
op(e2,e2) != op(e2,e3),
inference(cnf_transformation,[],[f399]) ).
tcf(c_225,plain,
op(e4,e0) != op(e4,e1),
inference(cnf_transformation,[],[f386]) ).
tcf(c_227,plain,
op(e4,e0) != op(e4,e3),
inference(cnf_transformation,[],[f384]) ).
tcf(c_236,plain,
e0 != e2,
inference(cnf_transformation,[],[f485]) ).
tcf(c_238,plain,
e0 != e4,
inference(cnf_transformation,[],[f483]) ).
tcf(c_239,plain,
e1 != e2,
inference(cnf_transformation,[],[f482]) ).
tcf(c_240,plain,
e1 != e3,
inference(cnf_transformation,[],[f481]) ).
tcf(c_241,plain,
e1 != e4,
inference(cnf_transformation,[],[f480]) ).
tcf(c_242,plain,
e2 != e3,
inference(cnf_transformation,[],[f479]) ).
tcf(c_245,plain,
op(op(e2,e2),op(e2,e2)) = e0,
inference(cnf_transformation,[],[f490]) ).
tcf(c_246,plain,
op(op(e2,op(e2,e2)),op(e2,e2)) = e1,
inference(cnf_transformation,[],[f489]) ).
tcf(c_247,plain,
op(e2,op(e2,e2)) = e3,
inference(cnf_transformation,[],[f488]) ).
tcf(c_248,plain,
op(e2,e2) = e4,
inference(cnf_transformation,[],[f487]) ).
tcf(c_269,plain,
( sP124
| ~ sP129 ),
inference(cnf_transformation,[],[f535]) ).
tcf(c_293,plain,
( sP100
| ~ sP129 ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_295,plain,
( sP98
| ~ sP128 ),
inference(cnf_transformation,[],[f559]) ).
tcf(c_307,plain,
( sP86
| ~ sP128 ),
inference(cnf_transformation,[],[f547]) ).
tcf(c_313,plain,
( sP80
| ~ sP128 ),
inference(cnf_transformation,[],[f541]) ).
tcf(c_323,plain,
( sP70
| ~ sP127 ),
inference(cnf_transformation,[],[f581]) ).
tcf(c_328,plain,
( sP65
| ~ sP127 ),
inference(cnf_transformation,[],[f576]) ).
tcf(c_358,plain,
( sP35
| ~ sP126 ),
inference(cnf_transformation,[],[f596]) ).
tcf(c_381,plain,
( sP12
| ~ sP125 ),
inference(cnf_transformation,[],[f623]) ).
tcf(c_394,plain,
( ~ sP124
| ( e0 != unit )
| ( op(e0,e0) != e0 ) ),
inference(cnf_transformation,[],[f636]) ).
tcf(c_437,plain,
( ( op(e4,e0) = e4 )
| ~ sP100
| ( op(e4,e4) != e0 ) ),
inference(cnf_transformation,[],[f685]) ).
tcf(c_438,plain,
( ~ sP100
| ( e0 != unit )
| ( op(e4,e4) != e0 ) ),
inference(cnf_transformation,[],[f684]) ).
tcf(c_441,plain,
( ~ sP98
| ( e1 != unit )
| ( op(e0,e1) != e1 ) ),
inference(cnf_transformation,[],[f688]) ).
tcf(c_462,plain,
( ( op(e2,e1) = e3 )
| ~ sP86
| ( op(e2,e3) != e1 ) ),
inference(cnf_transformation,[],[f713]) ).
tcf(c_474,plain,
( ~ sP80
| ( e1 != unit )
| ( op(e3,e4) != e1 ) ),
inference(cnf_transformation,[],[f724]) ).
tcf(c_491,plain,
( ( op(e0,e2) = e4 )
| ~ sP70
| ( op(e0,e4) != e2 ) ),
inference(cnf_transformation,[],[f745]) ).
tcf(c_500,plain,
( ( op(e1,e2) = e4 )
| ~ sP65
| ( op(e1,e4) != e2 ) ),
inference(cnf_transformation,[],[f755]) ).
tcf(c_554,plain,
( ( op(e2,e3) = e4 )
| ~ sP35
| ( op(e2,e4) != e3 ) ),
inference(cnf_transformation,[],[f815]) ).
tcf(c_596,plain,
( ( op(e2,e4) = e2 )
| ~ sP12
| ( op(e2,e2) != e4 ) ),
inference(cnf_transformation,[],[f861]) ).
tcf(c_659,negated_conjecture,
( sP125
| sP126
| sP127
| sP128
| sP129 ),
inference(cnf_transformation,[],[f886]) ).
tcf(c_670,plain,
( ( op(e2,e4) = e2 )
| ~ sP12 ),
inference(global_subsumption_just,[status(thm)],[c_596,c_248,c_596]) ).
tcf(c_758,plain,
op(e2,e2) = e4,
inference(global_subsumption_just,[status(thm)],[c_61,c_248]) ).
tcf(c_4396,plain,
op(e2,e4) = e3,
inference(light_normalisation,[status(thm)],[c_247,c_758]) ).
tcf(c_4397,plain,
( ( e2 = e3 )
| ~ sP12 ),
inference(demodulation,[status(thm)],[c_670,c_4396]) ).
tcf(c_4398,plain,
~ sP12,
inference(forward_subsumption_resolution,[status(thm)],[c_4397,c_242]) ).
tcf(c_4399,plain,
~ sP125,
inference(backward_subsumption_resolution,[status(thm)],[c_381,c_4398]) ).
tcf(c_4400,plain,
( sP126
| sP127
| sP128
| sP129 ),
inference(backward_subsumption_resolution,[status(thm)],[c_659,c_4399]) ).
tcf(c_4411,plain,
op(e2,e3) != e4,
inference(light_normalisation,[status(thm)],[c_212,c_758]) ).
tcf(c_4412,plain,
op(e2,e1) != e3,
inference(light_normalisation,[status(thm)],[c_211,c_4396]) ).
tcf(c_4420,plain,
op(e4,e2) != e4,
inference(light_normalisation,[status(thm)],[c_163,c_758]) ).
tcf(c_4422,plain,
op(e1,e2) != e4,
inference(light_normalisation,[status(thm)],[c_159,c_758]) ).
tcf(c_4423,plain,
op(e0,e2) != e4,
inference(light_normalisation,[status(thm)],[c_156,c_758]) ).
tcf(c_4456,plain,
op(e4,e4) = e0,
inference(light_normalisation,[status(thm)],[c_245,c_758]) ).
tcf(c_4497,plain,
op(e3,e4) = e1,
inference(light_normalisation,[status(thm)],[c_246,c_758,c_4396]) ).
tcf(c_4941,plain,
( ~ sP100
| ( e0 != unit )
| ( e0 != e0 ) ),
inference(demodulation,[status(thm)],[c_438,c_4456]) ).
tcf(c_4942,plain,
( ~ sP100
| ( e0 != unit ) ),
inference(equality_resolution_simp,[status(thm)],[c_4941]) ).
tcf(c_5156,plain,
( ( op(e2,e3) = e4 )
| ~ sP35
| ( e3 != e3 ) ),
inference(demodulation,[status(thm)],[c_554,c_4396]) ).
tcf(c_5157,plain,
( ( op(e2,e3) = e4 )
| ~ sP35 ),
inference(equality_resolution_simp,[status(thm)],[c_5156]) ).
tcf(c_5158,plain,
~ sP35,
inference(forward_subsumption_resolution,[status(thm)],[c_5157,c_4411]) ).
tcf(c_5159,plain,
~ sP126,
inference(backward_subsumption_resolution,[status(thm)],[c_358,c_5158]) ).
tcf(c_5160,plain,
( sP127
| sP128
| sP129 ),
inference(backward_subsumption_resolution,[status(thm)],[c_4400,c_5159]) ).
tcf(c_5293,plain,
( ~ sP70
| ( op(e0,e4) != e2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_491,c_4423]) ).
tcf(c_5347,plain,
( ~ sP86
| ( op(e2,e3) != e1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_462,c_4412]) ).
tcf(c_5397,plain,
( ( op(e4,e0) = e4 )
| ~ sP100
| ( e0 != e0 ) ),
inference(demodulation,[status(thm)],[c_437,c_4456]) ).
tcf(c_5398,plain,
( ( op(e4,e0) = e4 )
| ~ sP100 ),
inference(equality_resolution_simp,[status(thm)],[c_5397]) ).
tcf(c_5735,plain,
( ( e2 = e3 )
| ( e1 = e2 )
| ( e0 = e2 )
| ( op(e1,e4) = e2 )
| ( op(e0,e4) = e2 ) ),
inference(light_normalisation,[status(thm)],[c_130,c_4396,c_4456,c_4497]) ).
tcf(c_5736,plain,
( ( op(e1,e4) = e2 )
| ( op(e0,e4) = e2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5735,c_242,c_239,c_236]) ).
tcf(c_5936,plain,
( ( e1 = e4 )
| ( e1 = e3 )
| ( op(e2,e3) = e1 )
| ( op(e2,e1) = e1 )
| ( op(e2,e0) = e1 ) ),
inference(light_normalisation,[status(thm)],[c_107,c_758,c_4396]) ).
tcf(c_5937,plain,
( ( op(e2,e3) = e1 )
| ( op(e2,e1) = e1 )
| ( op(e2,e0) = e1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5936,c_241,c_240]) ).
tcf(c_6466,plain,
( ~ sP128
| ( op(e2,e3) != e1 ) ),
inference(resolution,[status(thm)],[c_307,c_5347]) ).
tcf(c_6484,plain,
( ~ sP127
| ( op(e0,e4) != e2 ) ),
inference(resolution,[status(thm)],[c_323,c_5293]) ).
tcf(c_6485,plain,
~ sP127,
inference(global_subsumption_just,[status(thm)],[c_6484,c_328,c_500,c_4422,c_5736,c_6484]) ).
tcf(c_6491,plain,
( sP128
| sP129 ),
inference(backward_subsumption_resolution,[status(thm)],[c_5160,c_6485]) ).
tcf(c_6492,plain,
( ~ sP129
| ( e0 != unit )
| ( op(e0,e0) != e0 ) ),
inference(resolution,[status(thm)],[c_269,c_394]) ).
tcf(c_6493,plain,
( ~ sP129
| ( e0 != unit ) ),
inference(global_subsumption_just,[status(thm)],[c_6492,c_293,c_4942]) ).
tcf(c_6506,plain,
( ~ sP128
| ( e1 != unit )
| ( op(e0,e1) != e1 ) ),
inference(resolution,[status(thm)],[c_295,c_441]) ).
tcf(c_6507,plain,
( ~ sP128
| ( e1 != unit ) ),
inference(global_subsumption_just,[status(thm)],[c_6506,c_313,c_474,c_4497]) ).
tcf(c_6520,plain,
( ( op(e4,e0) = e4 )
| ~ sP129 ),
inference(resolution,[status(thm)],[c_293,c_5398]) ).
tcf(c_7834,plain,
( sP128
| ( op(e4,e0) = e4 ) ),
inference(resolution,[status(thm)],[c_6491,c_6520]) ).
tcf(c_7841,plain,
( sP128
| ( e0 != unit ) ),
inference(resolution,[status(thm)],[c_6491,c_6493]) ).
tcf(c_16226,definition,
iPr_def_10 = op(e4,e0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_16271,plain,
( sP128
| ( e0 != unit ) ),
inference(demodulation,[status(thm)],[c_7841]) ).
tcf(c_16272,plain,
( sP128
| ( iPr_def_10 = e4 ) ),
inference(demodulation,[status(thm)],[c_7834]) ).
tcf(c_17531,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_16272,c_16226,c_16271,c_6507,c_6466,c_5937,c_4497,c_4456,c_4420,c_241,c_239,c_238,c_227,c_225,c_146,c_84,c_83,c_82,c_79,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG055+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 04:39:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.73/1.09 % SZS status Started for theBenchmark.p
% 1.73/1.09 % SZS status Theorem for theBenchmark.p
% 1.73/1.09
% 1.73/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.73/1.09
% 1.73/1.09 % ------ iProver source info
% 1.73/1.09
% 1.73/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 1.73/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.73/1.09 % git: non_committed_changes: false
% 1.73/1.09
% 1.73/1.09 % ------ Parsing...
% 1.73/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.73/1.09
% 1.73/1.09 % ------ Preprocessing... sup_sim: 242 sf_s rm: 68 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.73/1.09
% 1.73/1.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.73/1.09
% 1.73/1.09 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.73/1.09 % ------ Proving...
% 1.73/1.09 % ------ Problem Properties
% 1.73/1.09
% 1.73/1.09 %
% 1.73/1.09 % clauses 291
% 1.73/1.09 % conjectures 20
% 1.73/1.09 % EPR 51
% 1.73/1.09 % Horn 194
% 1.73/1.09 % unary 161
% 1.73/1.09 % binary 28
% 1.73/1.09 % lits 603
% 1.73/1.09 % lits eq 525
% 1.73/1.09 % fd_pure 0
% 1.73/1.09 % fd_pseudo 0
% 1.73/1.09 % fd_cond 0
% 1.73/1.09 % fd_pseudo_cond 0
% 1.73/1.09 % AC symbols 0
% 1.73/1.09
% 1.73/1.09 % ------ Schedule dynamic 5 is on
% 1.73/1.09
% 1.73/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.73/1.09
% 1.73/1.09
% 1.73/1.09 % ------
% 1.73/1.09 % Current options:
% 1.73/1.09 % ------
% 1.73/1.09
% 1.73/1.09
% 1.73/1.09 %
% 1.73/1.09
% 1.73/1.09 % ------ Proving...
% 1.73/1.09 %
% 1.73/1.09
% 1.73/1.09 % SZS status Theorem for theBenchmark.p
% 1.73/1.09
% 1.73/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.73/1.09
% 1.73/1.09
%------------------------------------------------------------------------------