%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG036+1 : TPTP v9.2.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:04:16 PM UTC 2026
% Result : Theorem 0.31s 1.61s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_7)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(ax1,axiom,
( ( op(e0,e0) = e0
| op(e0,e0) = e1
| op(e0,e0) = e2
| op(e0,e0) = e3 )
& ( op(e0,e1) = e0
| op(e0,e1) = e1
| op(e0,e1) = e2
| op(e0,e1) = e3 )
& ( op(e0,e2) = e0
| op(e0,e2) = e1
| op(e0,e2) = e2
| op(e0,e2) = e3 )
& ( op(e0,e3) = e0
| op(e0,e3) = e1
| op(e0,e3) = e2
| op(e0,e3) = e3 )
& ( op(e1,e0) = e0
| op(e1,e0) = e1
| op(e1,e0) = e2
| op(e1,e0) = e3 )
& ( op(e1,e1) = e0
| op(e1,e1) = e1
| op(e1,e1) = e2
| op(e1,e1) = e3 )
& ( op(e1,e2) = e0
| op(e1,e2) = e1
| op(e1,e2) = e2
| op(e1,e2) = e3 )
& ( op(e1,e3) = e0
| op(e1,e3) = e1
| op(e1,e3) = e2
| op(e1,e3) = e3 )
& ( op(e2,e0) = e0
| op(e2,e0) = e1
| op(e2,e0) = e2
| op(e2,e0) = e3 )
& ( op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2
| op(e2,e1) = e3 )
& ( op(e2,e2) = e0
| op(e2,e2) = e1
| op(e2,e2) = e2
| op(e2,e2) = e3 )
& ( op(e2,e3) = e0
| op(e2,e3) = e1
| op(e2,e3) = e2
| op(e2,e3) = e3 )
& ( op(e3,e0) = e0
| op(e3,e0) = e1
| op(e3,e0) = e2
| op(e3,e0) = e3 )
& ( op(e3,e1) = e0
| op(e3,e1) = e1
| op(e3,e1) = e2
| op(e3,e1) = e3 )
& ( op(e3,e2) = e0
| op(e3,e2) = e1
| op(e3,e2) = e2
| op(e3,e2) = e3 )
& ( op(e3,e3) = e0
| op(e3,e3) = e1
| op(e3,e3) = e2
| op(e3,e3) = e3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(ax3,axiom,
( ( op(e0,e0) = e0
| op(e0,e1) = e0
| op(e0,e2) = e0
| op(e0,e3) = e0 )
& ( op(e0,e0) = e0
| op(e1,e0) = e0
| op(e2,e0) = e0
| op(e3,e0) = e0 )
& ( op(e0,e0) = e1
| op(e0,e1) = e1
| op(e0,e2) = e1
| op(e0,e3) = e1 )
& ( op(e0,e0) = e1
| op(e1,e0) = e1
| op(e2,e0) = e1
| op(e3,e0) = e1 )
& ( op(e0,e0) = e2
| op(e0,e1) = e2
| op(e0,e2) = e2
| op(e0,e3) = e2 )
& ( op(e0,e0) = e2
| op(e1,e0) = e2
| op(e2,e0) = e2
| op(e3,e0) = e2 )
& ( op(e0,e0) = e3
| op(e0,e1) = e3
| op(e0,e2) = e3
| op(e0,e3) = e3 )
& ( op(e0,e0) = e3
| op(e1,e0) = e3
| op(e2,e0) = e3
| op(e3,e0) = e3 )
& ( op(e1,e0) = e0
| op(e1,e1) = e0
| op(e1,e2) = e0
| op(e1,e3) = e0 )
& ( op(e0,e1) = e0
| op(e1,e1) = e0
| op(e2,e1) = e0
| op(e3,e1) = e0 )
& ( op(e1,e0) = e1
| op(e1,e1) = e1
| op(e1,e2) = e1
| op(e1,e3) = e1 )
& ( op(e0,e1) = e1
| op(e1,e1) = e1
| op(e2,e1) = e1
| op(e3,e1) = e1 )
& ( op(e1,e0) = e2
| op(e1,e1) = e2
| op(e1,e2) = e2
| op(e1,e3) = e2 )
& ( op(e0,e1) = e2
| op(e1,e1) = e2
| op(e2,e1) = e2
| op(e3,e1) = e2 )
& ( op(e1,e0) = e3
| op(e1,e1) = e3
| op(e1,e2) = e3
| op(e1,e3) = e3 )
& ( op(e0,e1) = e3
| op(e1,e1) = e3
| op(e2,e1) = e3
| op(e3,e1) = e3 )
& ( op(e2,e0) = e0
| op(e2,e1) = e0
| op(e2,e2) = e0
| op(e2,e3) = e0 )
& ( op(e0,e2) = e0
| op(e1,e2) = e0
| op(e2,e2) = e0
| op(e3,e2) = e0 )
& ( op(e2,e0) = e1
| op(e2,e1) = e1
| op(e2,e2) = e1
| op(e2,e3) = e1 )
& ( op(e0,e2) = e1
| op(e1,e2) = e1
| op(e2,e2) = e1
| op(e3,e2) = e1 )
& ( op(e2,e0) = e2
| op(e2,e1) = e2
| op(e2,e2) = e2
| op(e2,e3) = e2 )
& ( op(e0,e2) = e2
| op(e1,e2) = e2
| op(e2,e2) = e2
| op(e3,e2) = e2 )
& ( op(e2,e0) = e3
| op(e2,e1) = e3
| op(e2,e2) = e3
| op(e2,e3) = e3 )
& ( op(e0,e2) = e3
| op(e1,e2) = e3
| op(e2,e2) = e3
| op(e3,e2) = e3 )
& ( op(e3,e0) = e0
| op(e3,e1) = e0
| op(e3,e2) = e0
| op(e3,e3) = e0 )
& ( op(e0,e3) = e0
| op(e1,e3) = e0
| op(e2,e3) = e0
| op(e3,e3) = e0 )
& ( op(e3,e0) = e1
| op(e3,e1) = e1
| op(e3,e2) = e1
| op(e3,e3) = e1 )
& ( op(e0,e3) = e1
| op(e1,e3) = e1
| op(e2,e3) = e1
| op(e3,e3) = e1 )
& ( op(e3,e0) = e2
| op(e3,e1) = e2
| op(e3,e2) = e2
| op(e3,e3) = e2 )
& ( op(e0,e3) = e2
| op(e1,e3) = e2
| op(e2,e3) = e2
| op(e3,e3) = e2 )
& ( op(e3,e0) = e3
| op(e3,e1) = e3
| op(e3,e2) = e3
| op(e3,e3) = e3 )
& ( op(e0,e3) = e3
| op(e1,e3) = e3
| op(e2,e3) = e3
| op(e3,e3) = e3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(ax5,axiom,
( op(e0,e0) != op(e1,e0)
& op(e0,e0) != op(e2,e0)
& op(e0,e0) != op(e3,e0)
& op(e1,e0) != op(e2,e0)
& op(e1,e0) != op(e3,e0)
& op(e2,e0) != op(e3,e0)
& op(e0,e1) != op(e1,e1)
& op(e0,e1) != op(e2,e1)
& op(e0,e1) != op(e3,e1)
& op(e1,e1) != op(e2,e1)
& op(e1,e1) != op(e3,e1)
& op(e2,e1) != op(e3,e1)
& op(e0,e2) != op(e1,e2)
& op(e0,e2) != op(e2,e2)
& op(e0,e2) != op(e3,e2)
& op(e1,e2) != op(e2,e2)
& op(e1,e2) != op(e3,e2)
& op(e2,e2) != op(e3,e2)
& op(e0,e3) != op(e1,e3)
& op(e0,e3) != op(e2,e3)
& op(e0,e3) != op(e3,e3)
& op(e1,e3) != op(e2,e3)
& op(e1,e3) != op(e3,e3)
& op(e2,e3) != op(e3,e3)
& op(e0,e0) != op(e0,e1)
& op(e0,e0) != op(e0,e2)
& op(e0,e0) != op(e0,e3)
& op(e0,e1) != op(e0,e2)
& op(e0,e1) != op(e0,e3)
& op(e0,e2) != op(e0,e3)
& op(e1,e0) != op(e1,e1)
& op(e1,e0) != op(e1,e2)
& op(e1,e0) != op(e1,e3)
& op(e1,e1) != op(e1,e2)
& op(e1,e1) != op(e1,e3)
& op(e1,e2) != op(e1,e3)
& op(e2,e0) != op(e2,e1)
& op(e2,e0) != op(e2,e2)
& op(e2,e0) != op(e2,e3)
& op(e2,e1) != op(e2,e2)
& op(e2,e1) != op(e2,e3)
& op(e2,e2) != op(e2,e3)
& op(e3,e0) != op(e3,e1)
& op(e3,e0) != op(e3,e2)
& op(e3,e0) != op(e3,e3)
& op(e3,e1) != op(e3,e2)
& op(e3,e1) != op(e3,e3)
& op(e3,e2) != op(e3,e3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(ax2,axiom,
( op(unit,e0) = e0
& op(e0,unit) = e0
& op(unit,e1) = e1
& op(e1,unit) = e1
& op(unit,e2) = e2
& op(e2,unit) = e2
& op(unit,e3) = e3
& op(e3,unit) = e3
& ( unit = e0
| unit = e1
| unit = e2
| unit = e3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(ax6,axiom,
( e0 != e1
& e0 != e2
& e0 != e3
& e1 != e2
& e1 != e3
& e2 != e3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(ax4,axiom,
unit = e0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(i_0_7,plain,
( epred1_0
<=> ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 ) ) ),
introduced(definition) ).
fof(i_0_8,negated_conjecture,
~ ( epred1_0
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ ( epred1_0
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[co1]),c_0_7]),c_0_7]) ).
fof(i_0_9,plain,
( ( op(e0,e0) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e2,e2) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e2,e2) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e2,e2) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e2,e2) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e3,e3) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e3,e3) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e3,e3) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e3,e3) = e1
| op(e0,e0) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e0,e0) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e0,e0) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e0,e0) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e0,e0) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e2,e2) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e2,e2) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e2,e2) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e2,e2) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e3,e3) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e3,e3) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e3,e3) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e3,e3) = e1
| op(e1,e1) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e0,e0) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e0,e0) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e0,e0) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e0,e0) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e1,e1) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e1,e1) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e1,e1) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e1,e1) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e3,e3) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e3,e3) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e3,e3) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e3,e3) = e1
| op(e2,e2) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e0,e0) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e0,e0) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e0,e0) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e0,e0) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e2,e2) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e2,e2) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e2,e2) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e2,e2) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e0,e0) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e1,e1) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e2,e2) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0
| ~ epred1_0 )
& ( op(e0,e0) != e0
| op(e1,e1) != e0
| op(e2,e2) != e0
| op(e3,e3) != e0
| epred1_0 )
& ( op(e0,e0) != e1
| op(e1,e1) != e1
| op(e2,e2) != e1
| op(e3,e3) != e1
| epred1_0 )
& ( op(e0,e0) != e2
| op(e1,e1) != e2
| op(e2,e2) != e2
| op(e3,e3) != e2
| epred1_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_7])]) ).
fof(i_0_10,negated_conjecture,
( ~ epred1_0
& ( op(e0,e0) != e3
| op(e1,e1) != e3
| op(e2,e2) != e3
| op(e3,e3) != e3 )
& ( op(e0,e0) = e3
| epred1_0 )
& ( op(e1,e1) = e3
| epred1_0 )
& ( op(e2,e2) = e3
| epred1_0 )
& ( op(e3,e3) = e3
| epred1_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_8])]) ).
cnf(i_0_11,plain,
( epred1_0
| op(e0,e0) != e2
| op(e1,e1) != e2
| op(e2,e2) != e2
| op(e3,e3) != e2 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_12,plain,
( epred1_0
| op(e0,e0) != e1
| op(e1,e1) != e1
| op(e2,e2) != e1
| op(e3,e3) != e1 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_13,plain,
( epred1_0
| op(e0,e0) != e0
| op(e1,e1) != e0
| op(e2,e2) != e0
| op(e3,e3) != e0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_14,negated_conjecture,
( op(e0,e0) != e3
| op(e1,e1) != e3
| op(e2,e2) != e3
| op(e3,e3) != e3 ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_15,plain,
( op(e3,e3) = e0
| op(e3,e3) = e1
| op(e3,e3) = e2
| op(e3,e3) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_16,plain,
( op(e3,e2) = e0
| op(e3,e2) = e1
| op(e3,e2) = e2
| op(e3,e2) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_17,plain,
( op(e3,e1) = e0
| op(e3,e1) = e1
| op(e3,e1) = e2
| op(e3,e1) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_18,plain,
( op(e3,e0) = e3
| op(e3,e1) = e3
| op(e3,e2) = e3
| op(e3,e3) = e3 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_19,plain,
( op(e3,e0) = e2
| op(e3,e1) = e2
| op(e3,e2) = e2
| op(e3,e3) = e2 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_20,plain,
( op(e3,e0) = e1
| op(e3,e1) = e1
| op(e3,e2) = e1
| op(e3,e3) = e1 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_21,plain,
( op(e3,e0) = e0
| op(e3,e1) = e0
| op(e3,e2) = e0
| op(e3,e3) = e0 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_22,plain,
( op(e3,e0) = e0
| op(e3,e0) = e1
| op(e3,e0) = e2
| op(e3,e0) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_23,plain,
( op(e2,e3) = e0
| op(e2,e3) = e1
| op(e2,e3) = e2
| op(e2,e3) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_24,plain,
( op(e2,e2) = e0
| op(e2,e2) = e1
| op(e2,e2) = e2
| op(e2,e2) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_25,plain,
( op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2
| op(e2,e1) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_26,plain,
( op(e2,e0) = e3
| op(e2,e1) = e3
| op(e2,e2) = e3
| op(e2,e3) = e3 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_27,plain,
( op(e2,e0) = e2
| op(e2,e1) = e2
| op(e2,e2) = e2
| op(e2,e3) = e2 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_28,plain,
( op(e2,e0) = e1
| op(e2,e1) = e1
| op(e2,e2) = e1
| op(e2,e3) = e1 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_29,plain,
( op(e2,e0) = e0
| op(e2,e1) = e0
| op(e2,e2) = e0
| op(e2,e3) = e0 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_30,plain,
( op(e2,e0) = e0
| op(e2,e0) = e1
| op(e2,e0) = e2
| op(e2,e0) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_31,plain,
( op(e1,e3) = e0
| op(e1,e3) = e1
| op(e1,e3) = e2
| op(e1,e3) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_32,plain,
( op(e1,e2) = e0
| op(e1,e2) = e1
| op(e1,e2) = e2
| op(e1,e2) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_33,plain,
( op(e1,e1) = e0
| op(e1,e1) = e1
| op(e1,e1) = e2
| op(e1,e1) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_34,plain,
( op(e1,e0) = e3
| op(e1,e1) = e3
| op(e1,e2) = e3
| op(e1,e3) = e3 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_35,plain,
( op(e1,e0) = e2
| op(e1,e1) = e2
| op(e1,e2) = e2
| op(e1,e3) = e2 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_36,plain,
( op(e1,e0) = e1
| op(e1,e1) = e1
| op(e1,e2) = e1
| op(e1,e3) = e1 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_37,plain,
( op(e1,e0) = e0
| op(e1,e1) = e0
| op(e1,e2) = e0
| op(e1,e3) = e0 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_38,plain,
( op(e1,e0) = e0
| op(e1,e0) = e1
| op(e1,e0) = e2
| op(e1,e0) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_39,plain,
( op(e0,e3) = e3
| op(e1,e3) = e3
| op(e2,e3) = e3
| op(e3,e3) = e3 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_40,plain,
( op(e0,e3) = e2
| op(e1,e3) = e2
| op(e2,e3) = e2
| op(e3,e3) = e2 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_41,plain,
( op(e0,e3) = e1
| op(e1,e3) = e1
| op(e2,e3) = e1
| op(e3,e3) = e1 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_42,plain,
( op(e0,e3) = e0
| op(e1,e3) = e0
| op(e2,e3) = e0
| op(e3,e3) = e0 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_43,plain,
( op(e0,e3) = e0
| op(e0,e3) = e1
| op(e0,e3) = e2
| op(e0,e3) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_44,plain,
( op(e0,e2) = e3
| op(e1,e2) = e3
| op(e2,e2) = e3
| op(e3,e2) = e3 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_45,plain,
( op(e0,e2) = e2
| op(e1,e2) = e2
| op(e2,e2) = e2
| op(e3,e2) = e2 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_46,plain,
( op(e0,e2) = e1
| op(e1,e2) = e1
| op(e2,e2) = e1
| op(e3,e2) = e1 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_47,plain,
( op(e0,e2) = e0
| op(e1,e2) = e0
| op(e2,e2) = e0
| op(e3,e2) = e0 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_48,plain,
( op(e0,e2) = e0
| op(e0,e2) = e1
| op(e0,e2) = e2
| op(e0,e2) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_49,plain,
( op(e0,e1) = e3
| op(e1,e1) = e3
| op(e2,e1) = e3
| op(e3,e1) = e3 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_50,plain,
( op(e0,e1) = e2
| op(e1,e1) = e2
| op(e2,e1) = e2
| op(e3,e1) = e2 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_51,plain,
( op(e0,e1) = e1
| op(e1,e1) = e1
| op(e2,e1) = e1
| op(e3,e1) = e1 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_52,plain,
( op(e0,e1) = e0
| op(e1,e1) = e0
| op(e2,e1) = e0
| op(e3,e1) = e0 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_53,plain,
( op(e0,e1) = e0
| op(e0,e1) = e1
| op(e0,e1) = e2
| op(e0,e1) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_54,plain,
( op(e0,e0) = e3
| op(e1,e0) = e3
| op(e2,e0) = e3
| op(e3,e0) = e3 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_55,plain,
( op(e0,e0) = e3
| op(e0,e1) = e3
| op(e0,e2) = e3
| op(e0,e3) = e3 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_56,plain,
( op(e0,e0) = e2
| op(e1,e0) = e2
| op(e2,e0) = e2
| op(e3,e0) = e2 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_57,plain,
( op(e0,e0) = e2
| op(e0,e1) = e2
| op(e0,e2) = e2
| op(e0,e3) = e2 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_58,plain,
( op(e0,e0) = e1
| op(e1,e0) = e1
| op(e2,e0) = e1
| op(e3,e0) = e1 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_59,plain,
( op(e0,e0) = e1
| op(e0,e1) = e1
| op(e0,e2) = e1
| op(e0,e3) = e1 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_60,plain,
( op(e0,e0) = e0
| op(e1,e0) = e0
| op(e2,e0) = e0
| op(e3,e0) = e0 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_61,plain,
( op(e0,e0) = e0
| op(e0,e1) = e0
| op(e0,e2) = e0
| op(e0,e3) = e0 ),
inference(split_conjunct,[status(thm)],[ax3]),
[final] ).
cnf(i_0_62,plain,
( op(e0,e0) = e0
| op(e0,e0) = e1
| op(e0,e0) = e2
| op(e0,e0) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]),
[final] ).
cnf(i_0_63,plain,
( op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_64,plain,
( op(e2,e2) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_65,plain,
( op(e3,e3) = e2
| op(e2,e2) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_66,plain,
( op(e2,e2) = e2
| op(e2,e2) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_67,plain,
( op(e3,e3) = e2
| op(e3,e3) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_68,plain,
( op(e2,e2) = e2
| op(e3,e3) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_69,plain,
( op(e3,e3) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_70,plain,
( op(e2,e2) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_71,plain,
( op(e1,e1) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_72,plain,
( op(e1,e1) = e2
| op(e2,e2) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_73,plain,
( op(e1,e1) = e2
| op(e3,e3) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_74,plain,
( op(e1,e1) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_75,plain,
( op(e3,e3) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_76,plain,
( op(e2,e2) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_77,plain,
( op(e3,e3) = e2
| op(e1,e1) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_78,plain,
( op(e2,e2) = e2
| op(e1,e1) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_79,plain,
( op(e1,e1) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_80,plain,
( op(e1,e1) = e2
| op(e1,e1) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_81,plain,
( op(e3,e3) = e2
| op(e3,e3) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_82,plain,
( op(e2,e2) = e2
| op(e3,e3) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_83,plain,
( op(e3,e3) = e2
| op(e2,e2) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_84,plain,
( op(e2,e2) = e2
| op(e2,e2) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_85,plain,
( op(e1,e1) = e2
| op(e3,e3) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_86,plain,
( op(e1,e1) = e2
| op(e2,e2) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_87,plain,
( op(e3,e3) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_88,plain,
( op(e2,e2) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_89,plain,
( op(e1,e1) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_90,plain,
( op(e0,e0) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_91,plain,
( op(e0,e0) = e2
| op(e2,e2) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_92,plain,
( op(e0,e0) = e2
| op(e3,e3) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_93,plain,
( op(e0,e0) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_94,plain,
( op(e0,e0) = e2
| op(e1,e1) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_95,plain,
( op(e0,e0) = e2
| op(e1,e1) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_96,plain,
( op(e0,e0) = e2
| op(e3,e3) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_97,plain,
( op(e0,e0) = e2
| op(e2,e2) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_98,plain,
( op(e0,e0) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_99,plain,
( op(e3,e3) = e2
| op(e0,e0) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_100,plain,
( op(e2,e2) = e2
| op(e0,e0) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_101,plain,
( op(e3,e3) = e2
| op(e0,e0) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_102,plain,
( op(e2,e2) = e2
| op(e0,e0) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_103,plain,
( op(e1,e1) = e2
| op(e0,e0) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_104,plain,
( op(e1,e1) = e2
| op(e0,e0) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_105,plain,
( op(e3,e3) = e2
| op(e0,e0) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_106,plain,
( op(e2,e2) = e2
| op(e0,e0) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_107,plain,
( op(e1,e1) = e2
| op(e0,e0) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_108,plain,
( op(e0,e0) = e2
| op(e0,e0) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_109,plain,
( op(e0,e0) = e2
| op(e0,e0) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_110,plain,
( op(e0,e0) = e2
| op(e0,e0) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_111,plain,
( op(e3,e3) = e2
| op(e3,e3) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_112,plain,
( op(e2,e2) = e2
| op(e3,e3) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_113,plain,
( op(e3,e3) = e2
| op(e2,e2) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_114,plain,
( op(e2,e2) = e2
| op(e2,e2) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_115,plain,
( op(e1,e1) = e2
| op(e3,e3) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_116,plain,
( op(e1,e1) = e2
| op(e2,e2) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_117,plain,
( op(e3,e3) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_118,plain,
( op(e2,e2) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_119,plain,
( op(e1,e1) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_120,plain,
( op(e0,e0) = e2
| op(e3,e3) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_121,plain,
( op(e0,e0) = e2
| op(e2,e2) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_122,plain,
( op(e0,e0) = e2
| op(e1,e1) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_123,plain,
( op(e3,e3) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_124,plain,
( op(e2,e2) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_125,plain,
( op(e1,e1) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_126,plain,
( op(e0,e0) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_127,plain,
op(e3,e2) != op(e3,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_128,plain,
op(e3,e1) != op(e3,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_129,plain,
op(e3,e0) != op(e3,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_130,plain,
op(e2,e3) != op(e3,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_131,plain,
op(e1,e3) != op(e3,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_132,plain,
op(e0,e3) != op(e3,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_133,plain,
op(e3,e1) != op(e3,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_134,plain,
op(e3,e0) != op(e3,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_135,plain,
op(e2,e2) != op(e3,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_136,plain,
op(e1,e2) != op(e3,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_137,plain,
op(e0,e2) != op(e3,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_138,plain,
op(e3,e0) != op(e3,e1),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_139,plain,
op(e2,e1) != op(e3,e1),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_140,plain,
op(e1,e1) != op(e3,e1),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_141,plain,
op(e0,e1) != op(e3,e1),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_142,plain,
op(e2,e0) != op(e3,e0),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_143,plain,
op(e1,e0) != op(e3,e0),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_144,plain,
op(e0,e0) != op(e3,e0),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_145,plain,
op(e2,e2) != op(e2,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_146,plain,
op(e2,e1) != op(e2,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_147,plain,
op(e2,e0) != op(e2,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_148,plain,
op(e1,e3) != op(e2,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_149,plain,
op(e0,e3) != op(e2,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_150,plain,
op(e2,e1) != op(e2,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_151,plain,
op(e2,e0) != op(e2,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_152,plain,
op(e1,e2) != op(e2,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_153,plain,
op(e0,e2) != op(e2,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_154,plain,
op(e2,e0) != op(e2,e1),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_155,plain,
op(e1,e1) != op(e2,e1),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_156,plain,
op(e0,e1) != op(e2,e1),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_157,plain,
op(e1,e0) != op(e2,e0),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_158,plain,
op(e0,e0) != op(e2,e0),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_159,plain,
op(e1,e2) != op(e1,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_160,plain,
op(e1,e1) != op(e1,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_161,plain,
op(e1,e0) != op(e1,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_162,plain,
op(e0,e3) != op(e1,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_163,plain,
op(e1,e1) != op(e1,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_164,plain,
op(e1,e0) != op(e1,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_165,plain,
op(e0,e2) != op(e1,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_166,plain,
op(e1,e0) != op(e1,e1),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_167,plain,
op(e0,e1) != op(e1,e1),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_168,plain,
op(e0,e0) != op(e1,e0),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_169,plain,
op(e0,e2) != op(e0,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_170,plain,
op(e0,e1) != op(e0,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_171,plain,
op(e0,e0) != op(e0,e3),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_172,plain,
op(e0,e1) != op(e0,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_173,plain,
op(e0,e0) != op(e0,e2),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_174,plain,
op(e0,e0) != op(e0,e1),
inference(split_conjunct,[status(thm)],[ax5]),
[final] ).
cnf(i_0_175,negated_conjecture,
( op(e3,e3) = e3
| epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_176,negated_conjecture,
( op(e2,e2) = e3
| epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_177,negated_conjecture,
( op(e1,e1) = e3
| epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_178,negated_conjecture,
( op(e0,e0) = e3
| epred1_0 ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_179,plain,
op(unit,e3) = e3,
inference(split_conjunct,[status(thm)],[ax2]),
[final] ).
cnf(i_0_180,plain,
op(unit,e2) = e2,
inference(split_conjunct,[status(thm)],[ax2]),
[final] ).
cnf(i_0_181,plain,
op(unit,e1) = e1,
inference(split_conjunct,[status(thm)],[ax2]),
[final] ).
cnf(i_0_182,plain,
op(unit,e0) = e0,
inference(split_conjunct,[status(thm)],[ax2]),
[final] ).
cnf(i_0_183,plain,
op(e3,unit) = e3,
inference(split_conjunct,[status(thm)],[ax2]),
[final] ).
cnf(i_0_184,plain,
op(e2,unit) = e2,
inference(split_conjunct,[status(thm)],[ax2]),
[final] ).
cnf(i_0_185,plain,
op(e1,unit) = e1,
inference(split_conjunct,[status(thm)],[ax2]),
[final] ).
cnf(i_0_186,plain,
op(e0,unit) = e0,
inference(split_conjunct,[status(thm)],[ax2]),
[final] ).
cnf(i_0_187,plain,
( unit = e0
| unit = e1
| unit = e2
| unit = e3 ),
inference(split_conjunct,[status(thm)],[ax2]),
[final] ).
cnf(i_0_188,negated_conjecture,
~ epred1_0,
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_189,plain,
e2 != e3,
inference(split_conjunct,[status(thm)],[ax6]),
[final] ).
cnf(i_0_190,plain,
e1 != e3,
inference(split_conjunct,[status(thm)],[ax6]),
[final] ).
cnf(i_0_191,plain,
e0 != e3,
inference(split_conjunct,[status(thm)],[ax6]),
[final] ).
cnf(i_0_192,plain,
e1 != e2,
inference(split_conjunct,[status(thm)],[ax6]),
[final] ).
cnf(i_0_193,plain,
e0 != e2,
inference(split_conjunct,[status(thm)],[ax6]),
[final] ).
cnf(i_0_194,plain,
e0 != e1,
inference(split_conjunct,[status(thm)],[ax6]),
[final] ).
cnf(i_0_195,plain,
unit = e0,
inference(split_conjunct,[status(thm)],[ax4]),
[final] ).
cnf(i_0_196,axiom,
X1 = X1 ).
cnf(i_0_197,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_198,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_199,axiom,
( X1 != X2
| op(X1,X3) = op(X2,X3) ) ).
cnf(i_0_200,axiom,
( X1 != X2
| op(X3,X1) = op(X3,X2) ) ).
cnf(i_0_196_001,axiom,
X1 = X1 ).
cnf(i_0_197_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_198_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_199_004,axiom,
( X1 != X2
| op(X1,X3) = op(X2,X3) ) ).
cnf(i_0_200_005,axiom,
( X1 != X2
| op(X3,X1) = op(X3,X2) ) ).
cnf(i_0_201,plain,
( op(e0,e0) != e2
| op(e1,e1) != e2
| op(e2,e2) != e2
| op(e3,e3) != e2 ),
inference(scs_inference,[],[i_0_188,i_0_11]) ).
cnf(i_0_202,plain,
( op(e0,e0) != e1
| op(e1,e1) != e1
| op(e2,e2) != e1
| op(e3,e3) != e1 ),
inference(scs_inference,[],[i_0_188,i_0_12]) ).
cnf(i_0_203,plain,
( op(e0,e0) != e0
| op(e1,e1) != e0
| op(e2,e2) != e0
| op(e3,e3) != e0 ),
inference(scs_inference,[],[i_0_188,i_0_13]) ).
cnf(i_0_204,plain,
op(e3,e3) = e3,
inference(scs_inference,[],[i_0_188,i_0_175]) ).
cnf(i_0_205,plain,
op(e2,e2) = e3,
inference(scs_inference,[],[i_0_188,i_0_176]) ).
cnf(i_0_206,plain,
op(e1,e1) = e3,
inference(scs_inference,[],[i_0_188,i_0_177]) ).
cnf(i_0_207,plain,
op(e0,e0) = e3,
inference(scs_inference,[],[i_0_188,i_0_178]) ).
cnf(i_0_208,plain,
e0 = unit,
inference(scs_inference,[],[i_0_195,i_0_197]) ).
cnf(i_0_209,plain,
e2 != op(unit,e3),
inference(scs_inference,[],[i_0_195,i_0_189,i_0_179,i_0_197,i_0_198]) ).
cnf(i_0_210,plain,
e3 = op(e3,e3),
inference(scs_inference,[],[i_0_204,i_0_197]) ).
cnf(i_0_211,plain,
e1 != op(e3,e3),
inference(scs_inference,[],[i_0_204,i_0_190,i_0_197,i_0_198]) ).
cnf(i_0_212,plain,
$false,
inference(scs_inference,[],[i_0_204,i_0_205,i_0_206,i_0_207,i_0_190,i_0_197,i_0_198,i_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG036+1 : TPTP v9.2.1. Released v2.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 10:20:18 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.31/1.61 % Version : CSE_E---1.7
% 0.31/1.61 % Problem : theBenchmark.p
% 0.31/1.61 % SZS status Theorem for theBenchmark.p
% 0.31/1.61 % SZS output start CNFRefutation
% See solution above
% 0.31/1.65 % Total time : 1.273s
%------------------------------------------------------------------------------