%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG045+1 : TPTP v9.2.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 04:04:18 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.67s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 105 ( 31 unt; 0 def)
% Number of atoms : 784 ( 694 equ)
% Maximal formula atoms : 256 ( 7 avg)
% Number of connectives : 848 ( 169 ~; 468 |; 209 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 68 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax6,axiom,
( ( 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/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(ax28,axiom,
~ ( e3 = op(e1,e1)
& e2 = op(e0,e1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
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/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(ax4,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/sandbox2/benchmark/theBenchmark.p',ax4) ).
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/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(ax5,axiom,
( e0 != e1
& e0 != e2
& e0 != e3
& e1 != e2
& e1 != e3
& e2 != e3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(ax21,axiom,
~ ( e2 = op(e1,e1)
& e0 = op(e3,e1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
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/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(ax13,axiom,
~ ( e1 = op(e0,e0)
& e2 = op(e3,e0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
fof(ax12,axiom,
~ ( e0 = op(e3,e3)
& e2 = op(e1,e3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).
fof(c_0_10,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(c_0_11,axiom,
( epred1_0
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ),
inference(apply_def,[status(thm)],[ax6,c_0_10]) ).
fof(c_0_12,plain,
( ( 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)],[c_0_11]) ).
fof(c_0_13,plain,
( e3 != op(e1,e1)
| e2 != op(e0,e1) ),
inference(fof_nnf,[status(thm)],[ax28]) ).
cnf(c_0_14,plain,
op(unit,e1) = e1,
inference(split_conjunct,[status(thm)],[ax2]) ).
cnf(c_0_15,plain,
( unit = e0
| unit = e1
| unit = e2
| unit = e3 ),
inference(split_conjunct,[status(thm)],[ax2]) ).
cnf(c_0_16,plain,
op(e0,e1) != op(e1,e1),
inference(split_conjunct,[status(thm)],[ax4]) ).
cnf(c_0_17,plain,
( op(e1,e1) = e3
| epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( e3 != op(e1,e1)
| e2 != op(e0,e1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
op(e0,unit) = e0,
inference(split_conjunct,[status(thm)],[ax2]) ).
cnf(c_0_20,plain,
op(e0,e1) != op(e3,e1),
inference(split_conjunct,[status(thm)],[ax4]) ).
cnf(c_0_21,plain,
( op(e3,e1) = e1
| unit = e2
| unit = e1
| unit = e0 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( epred1_0
| op(e0,e1) != e3 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( op(e0,e1) = e0
| op(e0,e1) = e1
| op(e0,e1) = e2
| op(e0,e1) = e3 ),
inference(split_conjunct,[status(thm)],[ax1]) ).
cnf(c_0_24,plain,
( epred1_0
| op(e0,e1) != e2 ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_25,plain,
op(e0,e1) != op(e0,e3),
inference(split_conjunct,[status(thm)],[ax4]) ).
cnf(c_0_26,plain,
( op(e0,e3) = e0
| unit = e2
| unit = e1
| unit = e0 ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_27,plain,
( unit = e0
| unit = e1
| unit = e2
| op(e0,e1) != e1 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( op(e0,e1) = e1
| op(e0,e1) = e0
| epred1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_29,plain,
( unit = e0
| unit = e1
| unit = e2
| op(e0,e1) != e0 ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
op(e2,unit) = e2,
inference(split_conjunct,[status(thm)],[ax2]) ).
cnf(c_0_31,plain,
( unit = e2
| unit = e1
| unit = e0
| epred1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,plain,
( op(e2,e2) = e3
| epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_33,plain,
( op(e2,e2) = e2
| unit = e0
| unit = e1
| epred1_0 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
e2 != e3,
inference(split_conjunct,[status(thm)],[ax5]) ).
cnf(c_0_35,plain,
op(e1,unit) = e1,
inference(split_conjunct,[status(thm)],[ax2]) ).
cnf(c_0_36,plain,
( unit = e1
| unit = e0
| epred1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_37,plain,
( op(e1,e1) = e1
| unit = e0
| epred1_0 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
e1 != e3,
inference(split_conjunct,[status(thm)],[ax5]) ).
fof(c_0_39,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 ) ) ),
inference(split_equiv,[status(thm)],[c_0_10]) ).
cnf(c_0_40,plain,
( unit = e0
| epred1_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_37]),c_0_38]) ).
fof(c_0_41,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 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])]) ).
cnf(c_0_42,plain,
( op(e0,e0) = e3
| epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_43,plain,
( op(e0,e0) = e0
| epred1_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_40]) ).
cnf(c_0_44,plain,
e0 != e3,
inference(split_conjunct,[status(thm)],[ax5]) ).
cnf(c_0_45,plain,
op(e3,unit) = e3,
inference(split_conjunct,[status(thm)],[ax2]) ).
cnf(c_0_46,plain,
( op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
epred1_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_48,plain,
( op(e3,e3) = e3
| unit = e2
| unit = e1
| unit = e0 ),
inference(spm,[status(thm)],[c_0_45,c_0_15]) ).
cnf(c_0_49,plain,
( op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_50,plain,
( op(e3,e3) = e0
| op(e3,e3) = e1
| unit = e0
| unit = e1
| unit = e2 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_34]) ).
cnf(c_0_51,plain,
( op(e3,e3) = e0
| unit = e0
| unit = e1
| unit = e2 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_50]),c_0_38]) ).
fof(c_0_52,plain,
( e2 != op(e1,e1)
| e0 != op(e3,e1) ),
inference(fof_nnf,[status(thm)],[ax21]) ).
cnf(c_0_53,plain,
( op(e1,e1) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
( unit = e0
| unit = e1
| unit = e2 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_51]),c_0_44]) ).
cnf(c_0_55,plain,
( e2 != op(e1,e1)
| e0 != op(e3,e1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_56,plain,
( op(e0,e1) = e0
| op(e1,e1) = e0
| op(e2,e1) = e0
| op(e3,e1) = e0 ),
inference(split_conjunct,[status(thm)],[ax3]) ).
cnf(c_0_57,plain,
( op(e2,e2) = e1
| op(e2,e2) = e0
| op(e1,e1) = e2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_47])]) ).
cnf(c_0_58,plain,
( op(e2,e2) = e2
| unit = e1
| unit = e0 ),
inference(spm,[status(thm)],[c_0_30,c_0_54]) ).
cnf(c_0_59,plain,
e1 != e2,
inference(split_conjunct,[status(thm)],[ax5]) ).
cnf(c_0_60,plain,
e0 != e2,
inference(split_conjunct,[status(thm)],[ax5]) ).
cnf(c_0_61,plain,
op(e0,e1) != op(e0,e2),
inference(split_conjunct,[status(thm)],[ax4]) ).
cnf(c_0_62,plain,
( op(e0,e2) = e0
| unit = e1
| unit = e0 ),
inference(spm,[status(thm)],[c_0_19,c_0_54]) ).
cnf(c_0_63,plain,
( op(e2,e1) = e0
| op(e1,e1) = e0
| op(e0,e1) = e0
| op(e1,e1) != e2 ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_64,plain,
( op(e1,e1) = e2
| unit = e0
| unit = e1 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60]) ).
cnf(c_0_65,plain,
( unit = e0
| unit = e1
| op(e0,e1) != e0 ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,plain,
( op(e2,e1) = e1
| unit = e1
| unit = e0 ),
inference(spm,[status(thm)],[c_0_14,c_0_54]) ).
cnf(c_0_67,plain,
( op(e2,e1) = e0
| unit = e1
| unit = e0 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_60]),c_0_65]) ).
cnf(c_0_68,plain,
e0 != e1,
inference(split_conjunct,[status(thm)],[ax5]) ).
fof(c_0_69,plain,
( e1 != op(e0,e0)
| e2 != op(e3,e0) ),
inference(fof_nnf,[status(thm)],[ax13]) ).
cnf(c_0_70,plain,
( op(e1,e1) = e2
| op(e0,e0) = e1
| op(e1,e1) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_71,plain,
( unit = e0
| unit = e1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_72,plain,
op(unit,e2) = e2,
inference(split_conjunct,[status(thm)],[ax2]) ).
cnf(c_0_73,plain,
( e1 != op(e0,e0)
| e2 != op(e3,e0) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_74,plain,
( op(e0,e0) = e2
| op(e1,e0) = e2
| op(e2,e0) = e2
| op(e3,e0) = e2 ),
inference(split_conjunct,[status(thm)],[ax3]) ).
cnf(c_0_75,plain,
( op(e1,e1) = e2
| op(e1,e1) = e0
| op(e0,e0) = e1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_47])]) ).
cnf(c_0_76,plain,
( op(e1,e1) = e1
| unit = e0 ),
inference(spm,[status(thm)],[c_0_35,c_0_71]) ).
cnf(c_0_77,plain,
op(e1,e0) != op(e1,e2),
inference(split_conjunct,[status(thm)],[ax4]) ).
cnf(c_0_78,plain,
( op(e1,e2) = e2
| unit = e0 ),
inference(spm,[status(thm)],[c_0_72,c_0_71]) ).
cnf(c_0_79,plain,
op(e2,e0) != op(e2,e1),
inference(split_conjunct,[status(thm)],[ax4]) ).
cnf(c_0_80,plain,
( op(e2,e1) = e2
| unit = e0 ),
inference(spm,[status(thm)],[c_0_30,c_0_71]) ).
cnf(c_0_81,plain,
( op(e2,e0) = e2
| op(e1,e0) = e2
| op(e0,e0) = e2
| op(e0,e0) != e1 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,plain,
( op(e0,e0) = e1
| unit = e0 ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_59]),c_0_68]) ).
cnf(c_0_83,plain,
( unit = e0
| op(e1,e0) != e2 ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_84,plain,
( unit = e0
| op(e2,e0) != e2 ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
( op(e3,e3) = e2
| op(e0,e0) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_86,plain,
( e0 != op(e3,e3)
| e2 != op(e1,e3) ),
inference(fof_nnf,[status(thm)],[ax12]) ).
cnf(c_0_87,plain,
( op(e0,e0) = e2
| op(e0,e0) = e1
| op(e3,e3) = e0
| ~ epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_88,plain,
op(unit,e0) = e0,
inference(split_conjunct,[status(thm)],[ax2]) ).
cnf(c_0_89,plain,
unit = e0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_59]),c_0_83]),c_0_84]) ).
cnf(c_0_90,plain,
op(e1,e3) != op(e3,e3),
inference(split_conjunct,[status(thm)],[ax4]) ).
cnf(c_0_91,plain,
( op(e3,e3) = e2
| op(e3,e3) = e0
| op(e0,e0) = e1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_47])]) ).
cnf(c_0_92,plain,
( e0 != op(e3,e3)
| e2 != op(e1,e3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_93,plain,
op(unit,e3) = e3,
inference(split_conjunct,[status(thm)],[ax2]) ).
cnf(c_0_94,plain,
( op(e3,e3) = e0
| op(e0,e0) = e2
| op(e0,e0) = e1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_47])]) ).
cnf(c_0_95,plain,
op(e0,e0) = e0,
inference(rw,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,plain,
( op(e0,e0) = e1
| op(e1,e3) != e2 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]) ).
cnf(c_0_97,plain,
op(e2,e0) != op(e2,e3),
inference(split_conjunct,[status(thm)],[ax4]) ).
cnf(c_0_98,plain,
op(e2,e0) = e2,
inference(rw,[status(thm)],[c_0_30,c_0_89]) ).
cnf(c_0_99,plain,
( op(e0,e3) = e2
| op(e1,e3) = e2
| op(e2,e3) = e2
| op(e3,e3) = e2 ),
inference(split_conjunct,[status(thm)],[ax3]) ).
cnf(c_0_100,plain,
op(e0,e3) = e3,
inference(rw,[status(thm)],[c_0_93,c_0_89]) ).
cnf(c_0_101,plain,
op(e3,e3) = e0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_95]),c_0_60]),c_0_68]) ).
cnf(c_0_102,plain,
op(e1,e3) != e2,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_95]),c_0_68]) ).
cnf(c_0_103,plain,
op(e2,e3) != e2,
inference(rw,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_104,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100]),c_0_34]),c_0_101]),c_0_102]),c_0_103]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : ALG045+1 : TPTP v9.2.1. Released v2.7.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 10:17:31 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.26/1.67 % Version : CSE_E---1.7
% 1.26/1.67 % Problem : theBenchmark.p
% 1.26/1.67 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.67 % SZS output start CNFRefutation
% See solution above
% 1.26/1.67 % Total time : 1.363s
%------------------------------------------------------------------------------