%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL895+1 : TPTP v9.2.1. Released v5.5.0.
% 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 : n018.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 04:45:19 PM UTC 2026
% Result : Theorem 236.45s 205.16s
% Output : CNFRefutation 237.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 50 unt; 0 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 29 ( 10 ~; 13 |; 4 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 99 ( 10 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_01,axiom,
! [X1,X2,X3] : '+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
fof(sos_08,axiom,
! [X1,X2] : '+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(sos_07,axiom,
! [X1,X2,X3] : '==>'('+'(X1,X2),X3) = '==>'(X1,'==>'(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
fof(sos_04,axiom,
! [X1] : '==>'(X1,X1) = '0',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
fof(goals_09,conjecture,
( ( '==>'(c,a) = '0'
& '==>'(c,b) = '0' )
<=> '==>'(c,'+'(a,'==>'(a,b))) = '0' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_09) ).
fof(sos_05,axiom,
! [X1] : '==>'(X1,'0') = '0',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
fof(sos_06,axiom,
! [X1] : '==>'('0',X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
fof(c_0_9,plain,
! [X18,X19,X20] : '+'('+'(X18,X19),X20) = '+'(X18,'+'(X19,X20)),
inference(variable_rename,[status(thm)],[sos_01]) ).
fof(c_0_10,plain,
! [X30,X31] : '+'(X30,'==>'(X30,X31)) = '+'(X31,'==>'(X31,X30)),
inference(variable_rename,[status(thm)],[sos_08]) ).
fof(c_0_11,plain,
! [X27,X28,X29] : '==>'('+'(X27,X28),X29) = '==>'(X27,'==>'(X28,X29)),
inference(variable_rename,[status(thm)],[sos_07]) ).
fof(c_0_12,plain,
! [X21,X22] : '+'(X21,X22) = '+'(X22,X21),
inference(variable_rename,[status(thm)],[sos_02]) ).
cnf(c_0_13,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
'==>'('+'(X1,X2),X3) = '==>'(X1,'==>'(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X24] : '==>'(X24,X24) = '0',
inference(variable_rename,[status(thm)],[sos_04]) ).
fof(c_0_17,plain,
! [X23] : '+'(X23,'0') = X23,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_18,negated_conjecture,
~ ( ( '==>'(c,a) = '0'
& '==>'(c,b) = '0' )
<=> '==>'(c,'+'(a,'==>'(a,b))) = '0' ),
inference(assume_negation,[status(cth)],[goals_09]) ).
cnf(c_0_19,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X25] : '==>'(X25,'0') = '0',
inference(variable_rename,[status(thm)],[sos_05]) ).
cnf(c_0_21,plain,
'+'(X1,'==>'(X1,'+'(X2,X3))) = '+'(X2,'+'(X3,'==>'(X2,'==>'(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_22,plain,
'==>'(X1,X1) = '0',
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,negated_conjecture,
( ( '==>'(c,a) != '0'
| '==>'(c,b) != '0'
| '==>'(c,'+'(a,'==>'(a,b))) != '0' )
& ( '==>'(c,a) = '0'
| '==>'(c,'+'(a,'==>'(a,b))) = '0' )
& ( '==>'(c,b) = '0'
| '==>'(c,'+'(a,'==>'(a,b))) = '0' ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
cnf(c_0_25,plain,
'==>'(X1,'==>'(X2,X3)) = '==>'(X2,'==>'(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_19]),c_0_15]) ).
cnf(c_0_26,plain,
'==>'(X1,'0') = '0',
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
'+'(X1,'==>'(X1,'+'(X2,'==>'(X2,X1)))) = '+'(X2,'==>'(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_19]),c_0_19]) ).
cnf(c_0_28,negated_conjecture,
( '==>'(c,b) = '0'
| '==>'(c,'+'(a,'==>'(a,b))) = '0' ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
'==>'(X1,'==>'(X2,X1)) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( '==>'(c,a) = '0'
| '==>'(c,'+'(a,'==>'(a,b))) = '0' ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( '+'(c,'==>'(c,'+'(a,'==>'(a,b)))) = c
| '==>'(c,b) = '0' ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23]),c_0_15]),c_0_13]),c_0_23]),c_0_21]) ).
cnf(c_0_32,plain,
'==>'(X1,'==>'('==>'(X1,X2),'==>'(X3,X2))) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_25]) ).
cnf(c_0_33,plain,
'==>'(X1,'==>'('==>'(X1,'+'(X2,X3)),X4)) = '==>'(X2,'==>'(X3,'==>'('==>'(X2,'==>'(X3,X1)),X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_21]),c_0_15]),c_0_15]) ).
cnf(c_0_34,negated_conjecture,
( '+'(c,'==>'(c,'+'(a,'==>'(a,b)))) = c
| '==>'(c,a) = '0' ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_23]),c_0_15]),c_0_13]),c_0_23]),c_0_21]) ).
cnf(c_0_35,plain,
'==>'(X1,'==>'(X2,'==>'(X3,X1))) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_29]),c_0_26]) ).
cnf(c_0_36,plain,
'==>'(X1,'==>'('==>'(X1,X2),X2)) = '0',
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_37,negated_conjecture,
( '==>'(c,'==>'('==>'(c,'+'(a,'==>'(a,b))),X1)) = '==>'(c,X1)
| '==>'(c,b) = '0' ),
inference(spm,[status(thm)],[c_0_15,c_0_31]) ).
cnf(c_0_38,plain,
'==>'(X1,'==>'('==>'(X1,'+'(X2,'==>'(X2,X3))),X3)) = '0',
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( '==>'(c,'==>'('==>'(c,'+'(a,'==>'(a,b))),X1)) = '==>'(c,X1)
| '==>'(c,a) = '0' ),
inference(spm,[status(thm)],[c_0_15,c_0_34]) ).
cnf(c_0_40,plain,
'==>'(X1,'==>'('==>'(X1,'+'(X2,X3)),X2)) = '0',
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
fof(c_0_41,plain,
! [X26] : '==>'('0',X26) = X26,
inference(variable_rename,[status(thm)],[sos_06]) ).
cnf(c_0_42,plain,
'==>'(X1,'==>'('==>'(X1,X2),X3)) = '==>'(X2,'==>'('==>'(X2,X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_14]),c_0_15]) ).
cnf(c_0_43,plain,
'==>'(X1,'==>'(X2,'==>'('==>'(X1,X3),X3))) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_36]),c_0_26]) ).
cnf(c_0_44,negated_conjecture,
'==>'(c,b) = '0',
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
'==>'(X1,'==>'(X2,'==>'(X3,'+'(X1,X2)))) = '0',
inference(spm,[status(thm)],[c_0_15,c_0_29]) ).
cnf(c_0_46,negated_conjecture,
'==>'(c,a) = '0',
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
'==>'('0',X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
'==>'(X1,'==>'('==>'(X1,X2),'==>'('==>'(X2,X3),X3))) = '0',
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
'==>'(c,'==>'(X1,b)) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_44]),c_0_26]) ).
cnf(c_0_50,plain,
'==>'(X1,'==>'(X2,'==>'('==>'(X2,X3),'+'(X1,X3)))) = '0',
inference(spm,[status(thm)],[c_0_45,c_0_42]) ).
cnf(c_0_51,negated_conjecture,
'==>'(a,'==>'('==>'(a,c),X1)) = '==>'(c,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_46]),c_0_47]) ).
cnf(c_0_52,plain,
'==>'(X1,'==>'(X2,'==>'('==>'(X2,X3),X4))) = '==>'(X3,'==>'(X1,'==>'('==>'(X3,X2),X4))),
inference(spm,[status(thm)],[c_0_25,c_0_42]) ).
cnf(c_0_53,negated_conjecture,
'==>'(X1,'==>'('==>'(X1,c),'==>'(X2,b))) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( '==>'(c,a) != '0'
| '==>'(c,b) != '0'
| '==>'(c,'+'(a,'==>'(a,b))) != '0' ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_55,negated_conjecture,
'==>'(c,'==>'('==>'('==>'(a,c),X1),'+'(a,X1))) = '0',
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
'==>'('==>'(X1,c),'==>'(X2,'==>'('==>'(X2,X1),b))) = '0',
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
( '==>'(c,'+'(a,'==>'(a,b))) != '0'
| '==>'(c,b) != '0' ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_46])]) ).
cnf(c_0_58,negated_conjecture,
'==>'(c,'+'(a,'==>'(X1,'==>'('==>'(X1,a),b)))) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_47]) ).
cnf(c_0_59,negated_conjecture,
'==>'(c,'+'(a,'==>'(a,b))) != '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_44])]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_47]),c_0_47]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL895+1 : TPTP v9.2.1. Released v5.5.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 23:15:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 236.45/205.16 % Version : CSE_E---1.7
% 236.45/205.16 % Problem : theBenchmark.p
% 236.45/205.16 % SZS status Theorem for theBenchmark.p
% 236.45/205.16 % SZS output start CNFRefutation
% See solution above
% 237.72/206.47 % Total time : 151.213s
%------------------------------------------------------------------------------