%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL900+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 : Sun Sep 27 08:00:00 AM UTC 2026
% Result : Theorem 81.38s 10.68s
% Output : CNFRefutation 81.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 13
% Syntax : Number of formulae : 139 ( 113 unt; 0 def)
% Number of atoms : 169 ( 95 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 27 ~; 23 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 281 ( 28 sgn 29 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_01,axiom,
! [A,B,C] : '+'('+'(A,B),C) = '+'(A,'+'(B,C)),
file('theBenchmark.p',sos_01) ).
fof(sos_02,axiom,
! [A,B] : '+'(A,B) = '+'(B,A),
file('theBenchmark.p',sos_02) ).
fof(sos_03,axiom,
! [A] : '+'(A,'0') = A,
file('theBenchmark.p',sos_03) ).
fof(sos_04,axiom,
! [A] : '>='(A,A),
file('theBenchmark.p',sos_04) ).
fof(sos_05,axiom,
! [X0,X1,X2] :
( ( '>='(X1,X2)
& '>='(X0,X1) )
=> '>='(X0,X2) ),
file('theBenchmark.p',sos_05) ).
fof(sos_06,axiom,
! [X3,X4] :
( ( '>='(X4,X3)
& '>='(X3,X4) )
=> X3 = X4 ),
file('theBenchmark.p',sos_06) ).
fof(sos_07,axiom,
! [X5,X6,X7] :
( '>='('+'(X5,X6),X7)
<=> '>='(X6,'==>'(X5,X7)) ),
file('theBenchmark.p',sos_07) ).
fof(sos_08,axiom,
! [A] : '>='(A,'0'),
file('theBenchmark.p',sos_08) ).
fof(sos_09,axiom,
! [X8,X9,X10] :
( '>='(X8,X9)
=> '>='('+'(X8,X10),'+'(X9,X10)) ),
file('theBenchmark.p',sos_09) ).
fof(sos_11,axiom,
! [X14,X15,X16] :
( '>='(X14,X15)
=> '>='('==>'(X16,X14),'==>'(X16,X15)) ),
file('theBenchmark.p',sos_11) ).
fof(sos_12,axiom,
! [A] : '+'(A,'1') = '1',
file('theBenchmark.p',sos_12) ).
fof(sos_13,axiom,
! [A,B] : '==>'('==>'(A,B),B) = '==>'('==>'(B,A),A),
file('theBenchmark.p',sos_13) ).
fof(goals_14,conjecture,
! [X17,X18] : '+'(X17,'==>'(X17,X18)) = '+'(X18,'==>'(X18,X17)),
file('theBenchmark.p',goals_14) ).
fof(goals_14_neg,negated_conjecture,
~ ! [X17,X18] : '+'(X17,'==>'(X17,X18)) = '+'(X18,'==>'(X18,X17)),
inference(assume_negation,[status(cth)],[goals_14]) ).
cnf(c_15,plain,
'+'('+'(A,B),C) = '+'(A,'+'(B,C)),
inference(clausify,[status(thm)],[sos_01]) ).
cnf(c_16,plain,
'+'(A,B) = '+'(B,A),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_17,plain,
'+'(A,'0') = A,
inference(clausify,[status(thm)],[sos_03]) ).
cnf(c_18,plain,
'>='(A,A),
inference(clausify,[status(thm)],[sos_04]) ).
cnf(c_19,plain,
( '>='(A,C)
| ~ '>='(B,C)
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_05]) ).
cnf(c_20,plain,
( B = A
| ~ '>='(B,A)
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_06]) ).
cnf(c_21,plain,
( '>='(B,'==>'(A,C))
| ~ '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_22,plain,
( ~ '>='(B,'==>'(A,C))
| '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_23,plain,
'>='(A,'0'),
inference(clausify,[status(thm)],[sos_08]) ).
cnf(c_24,plain,
( '>='('+'(A,C),'+'(B,C))
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_09]) ).
cnf(c_26,plain,
( '>='('==>'(C,A),'==>'(C,B))
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_11]) ).
cnf(c_27,plain,
'+'(A,'1') = '1',
inference(clausify,[status(thm)],[sos_12]) ).
cnf(c_28,plain,
'==>'('==>'(A,B),B) = '==>'('==>'(B,A),A),
inference(clausify,[status(thm)],[sos_13]) ).
fof(nnf_14,plain,
? [X17,X18] : '+'(X18,'==>'(X18,X17)) != '+'(X17,'==>'(X17,X18)),
inference(fof_nnf,[status(thm)],[goals_14_neg]) ).
fof(sk_goals_14_neg,plain,
'+'(sK0,'==>'(sK0,sK1)) != '+'(sK1,'==>'(sK1,sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X17,sK1),skolemize(X18,sK0)],[nnf_14]) ).
cnf(c_29,negated_conjecture,
'+'(sK0,'==>'(sK0,sK1)) != '+'(sK1,'==>'(sK1,sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_14_neg]) ).
cnf(c_26708,plain,
'+'('+'(A,B),C) = '+'(B,'+'(A,C)),
inference(paramod,[status(thm)],[c_16,c_15]) ).
cnf(c_30,plain,
'+'(A,'+'(B,C)) = '+'(B,'+'(A,C)),
inference(paramod,[status(thm)],[c_15,c_26708]) ).
cnf(c_26709,plain,
A = '+'('0',A),
inference(paramod,[status(thm)],[c_17,c_16]) ).
cnf(c_33,plain,
'+'('0',A) = A,
inference(copy,[status(thm)],[c_26709]) ).
cnf(c_34,plain,
'>='(A,'==>'(B,'+'(B,A))),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_35,plain,
( '>='(C,'==>'('+'(A,B),D))
| ~ '>='('+'(A,'+'(B,C)),D) ),
inference(paramod,[status(thm)],[c_15,c_21]) ).
cnf(c_36,plain,
( '>='(A,'==>'(B,C))
| ~ '>='('+'(A,B),C) ),
inference(paramod,[status(thm)],[c_16,c_21]) ).
cnf(c_38,plain,
'>='('+'(A,'==>'(A,B)),B),
inference(resolve,[status(thm)],[c_22,c_18]) ).
cnf(c_26710,plain,
'>='('+'(A,B),'+'('0',B)),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_40,plain,
'>='('+'(A,B),B),
inference(paramod,[status(thm)],[c_33,c_26710]) ).
cnf(c_26711,plain,
'1' = '+'('1',A),
inference(paramod,[status(thm)],[c_27,c_16]) ).
cnf(c_44,plain,
'+'('1',A) = '1',
inference(copy,[status(thm)],[c_26711]) ).
cnf(c_47,plain,
'==>'('==>'('==>'(A,B),B),A) = '==>'('==>'(A,'==>'(B,A)),'==>'(B,A)),
inference(paramod,[status(thm)],[c_28,c_28]) ).
cnf(c_48,plain,
( '>='('+'(A,C),'==>'(B,D))
| ~ '>='('+'(A,'+'(B,C)),D) ),
inference(paramod,[status(thm)],[c_30,c_21]) ).
cnf(c_60,plain,
'>='(A,'==>'(B,A)),
inference(resolve,[status(thm)],[c_21,c_40]) ).
cnf(c_62,plain,
'>='('+'(A,B),A),
inference(paramod,[status(thm)],[c_16,c_40]) ).
cnf(c_65,plain,
'>='('1',A),
inference(paramod,[status(thm)],[c_44,c_40]) ).
cnf(c_69,plain,
'>='(A,'==>'(B,'==>'(C,'+'(C,'+'(B,A))))),
inference(resolve,[status(thm)],[c_21,c_34]) ).
cnf(c_26712,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_26713,plain,
'0' = '==>'(A,'+'(A,'0')),
inference(resolve,[status(thm)],[c_26712,c_34]) ).
cnf(c_26714,plain,
'0' = '==>'(A,A),
inference(paramod,[status(thm)],[c_17,c_26713]) ).
cnf(c_70,plain,
'==>'(A,A) = '0',
inference(copy,[status(thm)],[c_26714]) ).
cnf(c_76,plain,
'>='('==>'(A,'1'),'==>'(A,B)),
inference(resolve,[status(thm)],[c_26,c_65]) ).
cnf(c_26715,plain,
( '>='('+'(C,A),B)
| ~ '>='(A,B) ),
inference(resolve,[status(thm)],[c_19,c_40]) ).
cnf(c_84,plain,
'>='('+'(A,B),'==>'(C,B)),
inference(resolve,[status(thm)],[c_26715,c_60]) ).
cnf(c_90,plain,
'>='('+'(A,'+'('==>'(A,B),C)),B),
inference(resolve,[status(thm)],[c_22,c_62]) ).
cnf(c_95,plain,
'>='(A,'==>'('+'(B,C),B)),
inference(resolve,[status(thm)],[c_35,c_62]) ).
cnf(c_103,plain,
( '>='(C,'==>'('+'(B,A),D))
| ~ '>='('+'(A,'+'(B,C)),D) ),
inference(paramod,[status(thm)],[c_30,c_35]) ).
cnf(c_107,plain,
'>='('+'(A,'+'(B,'==>'(B,'==>'(A,C)))),C),
inference(resolve,[status(thm)],[c_22,c_38]) ).
cnf(c_26716,plain,
( A = '1'
| ~ '>='(A,'1') ),
inference(resolve,[status(thm)],[c_20,c_65]) ).
cnf(c_108,plain,
'+'(A,'==>'(A,'1')) = '1',
inference(resolve,[status(thm)],[c_26716,c_38]) ).
cnf(c_115,plain,
'>='('+'(A,'+'(B,'==>'('+'(A,B),C))),C),
inference(paramod,[status(thm)],[c_15,c_38]) ).
cnf(c_117,plain,
'>='('==>'('0',A),A),
inference(paramod,[status(thm)],[c_33,c_38]) ).
cnf(c_26717,plain,
( '==>'(A,B) = B
| ~ '>='('==>'(A,B),B) ),
inference(resolve,[status(thm)],[c_20,c_60]) ).
cnf(c_123,plain,
'==>'('0',A) = A,
inference(resolve,[status(thm)],[c_26717,c_117]) ).
cnf(c_169,plain,
'>='('0','==>'('1',A)),
inference(paramod,[status(thm)],[c_70,c_76]) ).
cnf(c_26718,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_26719,plain,
'0' = '==>'('1',A),
inference(resolve,[status(thm)],[c_26718,c_169]) ).
cnf(c_173,plain,
'==>'('1',A) = '0',
inference(copy,[status(thm)],[c_26719]) ).
cnf(c_26720,plain,
'==>'('0',A) = '==>'('==>'(A,'1'),'1'),
inference(paramod,[status(thm)],[c_173,c_28]) ).
cnf(c_26721,plain,
A = '==>'('==>'(A,'1'),'1'),
inference(paramod,[status(thm)],[c_123,c_26720]) ).
cnf(c_181,plain,
'==>'('==>'(A,'1'),'1') = A,
inference(copy,[status(thm)],[c_26721]) ).
cnf(c_203,plain,
'>='(A,'==>'(B,'==>'(C,B))),
inference(resolve,[status(thm)],[c_36,c_84]) ).
cnf(c_26722,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_26723,plain,
'0' = '==>'('+'(A,B),A),
inference(resolve,[status(thm)],[c_26722,c_95]) ).
cnf(c_279,plain,
'==>'('+'(A,B),A) = '0',
inference(copy,[status(thm)],[c_26723]) ).
cnf(c_26724,plain,
'+'('1',A) = '+'(B,'+'('==>'(B,'1'),A)),
inference(paramod,[status(thm)],[c_108,c_15]) ).
cnf(c_26725,plain,
'1' = '+'(B,'+'('==>'(B,'1'),A)),
inference(paramod,[status(thm)],[c_44,c_26724]) ).
cnf(c_282,plain,
'+'(A,'+'('==>'(A,'1'),B)) = '1',
inference(copy,[status(thm)],[c_26725]) ).
cnf(c_26726,plain,
'1' = '+'(A,'+'(B,'==>'('+'(A,B),'1'))),
inference(paramod,[status(thm)],[c_108,c_15]) ).
cnf(c_283,plain,
'+'(A,'+'(B,'==>'('+'(A,B),'1'))) = '1',
inference(copy,[status(thm)],[c_26726]) ).
cnf(c_26727,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_26728,plain,
'0' = '==>'(A,'==>'(B,A)),
inference(resolve,[status(thm)],[c_26727,c_203]) ).
cnf(c_375,plain,
'==>'(A,'==>'(B,A)) = '0',
inference(copy,[status(thm)],[c_26728]) ).
cnf(c_26729,plain,
'==>'('==>'('==>'(A,B),B),A) = '==>'('0','==>'(B,A)),
inference(paramod,[status(thm)],[c_375,c_47]) ).
cnf(c_384,plain,
'==>'('==>'('==>'(A,B),B),A) = '==>'(B,A),
inference(paramod,[status(thm)],[c_123,c_26729]) ).
cnf(c_26730,plain,
'==>'('0',A) = '==>'('==>'(A,'+'(A,B)),'+'(A,B)),
inference(paramod,[status(thm)],[c_279,c_28]) ).
cnf(c_26731,plain,
A = '==>'('==>'(A,'+'(A,B)),'+'(A,B)),
inference(paramod,[status(thm)],[c_123,c_26730]) ).
cnf(c_386,plain,
'==>'('==>'(A,'+'(A,B)),'+'(A,B)) = A,
inference(copy,[status(thm)],[c_26731]) ).
cnf(c_393,plain,
'==>'(A,'==>'('==>'(A,B),B)) = '0',
inference(paramod,[status(thm)],[c_28,c_375]) ).
cnf(c_847,plain,
'>='(A,'==>'('+'(B,'==>'(B,C)),C)),
inference(resolve,[status(thm)],[c_35,c_90]) ).
cnf(c_4859,plain,
'>='('==>'(A,'==>'(B,C)),'==>'('+'(A,B),C)),
inference(resolve,[status(thm)],[c_103,c_107]) ).
cnf(c_4861,plain,
'>='('+'(A,'==>'(B,'==>'(A,C))),'==>'(B,C)),
inference(resolve,[status(thm)],[c_48,c_107]) ).
cnf(c_4864,plain,
'>='('==>'(A,'==>'(B,C)),'==>'('+'(B,A),C)),
inference(resolve,[status(thm)],[c_35,c_107]) ).
cnf(c_26732,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_26733,plain,
'0' = '==>'('+'(A,'==>'(A,B)),B),
inference(resolve,[status(thm)],[c_26732,c_847]) ).
cnf(c_5768,plain,
'==>'('+'(A,'==>'(A,B)),B) = '0',
inference(copy,[status(thm)],[c_26733]) ).
cnf(c_5937,plain,
'>='('+'(A,'==>'('+'(A,B),C)),'==>'(B,C)),
inference(resolve,[status(thm)],[c_48,c_115]) ).
cnf(c_26734,plain,
'==>'('0',A) = '==>'('==>'(A,'+'(B,'==>'(B,A))),'+'(B,'==>'(B,A))),
inference(paramod,[status(thm)],[c_5768,c_28]) ).
cnf(c_26735,plain,
A = '==>'('==>'(A,'+'(B,'==>'(B,A))),'+'(B,'==>'(B,A))),
inference(paramod,[status(thm)],[c_123,c_26734]) ).
cnf(c_6070,plain,
'==>'('==>'(A,'+'(B,'==>'(B,A))),'+'(B,'==>'(B,A))) = A,
inference(copy,[status(thm)],[c_26735]) ).
cnf(c_14532,plain,
'>='('==>'('+'(A,B),'1'),'==>'(B,'==>'(A,'1'))),
inference(paramod,[status(thm)],[c_283,c_69]) ).
cnf(c_15631,plain,
'==>'('==>'(A,'+'(B,A)),'+'(A,B)) = A,
inference(paramod,[status(thm)],[c_16,c_386]) ).
cnf(c_19042,plain,
'>='('==>'(A,'==>'(B,C)),'==>'(B,'==>'(A,C))),
inference(resolve,[status(thm)],[c_21,c_4861]) ).
cnf(c_19233,plain,
'>='('==>'('+'(A,B),C),'==>'(A,'==>'(B,C))),
inference(resolve,[status(thm)],[c_21,c_5937]) ).
cnf(c_26736,plain,
( '==>'('+'(A,B),C) = '==>'(B,'==>'(A,C))
| ~ '>='('==>'('+'(A,B),C),'==>'(B,'==>'(A,C))) ),
inference(resolve,[status(thm)],[c_20,c_4864]) ).
cnf(c_19571,plain,
'==>'('+'(A,B),'1') = '==>'(B,'==>'(A,'1')),
inference(resolve,[status(thm)],[c_26736,c_14532]) ).
cnf(c_26737,plain,
'==>'('==>'('+'('==>'(A,'1'),B),'1'),'+'('+'('==>'(A,'1'),B),A)) = '+'('==>'(A,'1'),B),
inference(paramod,[status(thm)],[c_282,c_15631]) ).
cnf(c_26738,plain,
'==>'('==>'(B,'==>'('==>'(A,'1'),'1')),'+'('+'('==>'(A,'1'),B),A)) = '+'('==>'(A,'1'),B),
inference(paramod,[status(thm)],[c_19571,c_26737]) ).
cnf(c_26739,plain,
'==>'('==>'(B,A),'+'('+'('==>'(A,'1'),B),A)) = '+'('==>'(A,'1'),B),
inference(paramod,[status(thm)],[c_181,c_26738]) ).
cnf(c_26740,plain,
'==>'('==>'(B,A),'+'(A,'+'('==>'(A,'1'),B))) = '+'('==>'(A,'1'),B),
inference(paramod,[status(thm)],[c_16,c_26739]) ).
cnf(c_19719,plain,
'==>'('==>'(A,B),'1') = '+'('==>'(B,'1'),A),
inference(paramod,[status(thm)],[c_282,c_26740]) ).
cnf(c_26741,plain,
( '==>'(A,'==>'(B,C)) = '==>'(B,'==>'(A,C))
| ~ '>='('==>'(A,'==>'(B,C)),'==>'(B,'==>'(A,C))) ),
inference(resolve,[status(thm)],[c_20,c_19042]) ).
cnf(c_21891,plain,
'==>'(A,'==>'(B,C)) = '==>'(B,'==>'(A,C)),
inference(resolve,[status(thm)],[c_26741,c_19042]) ).
cnf(c_26742,plain,
( '==>'('+'(A,B),C) = '==>'(A,'==>'(B,C))
| ~ '>='('==>'('+'(A,B),C),'==>'(A,'==>'(B,C))) ),
inference(resolve,[status(thm)],[c_20,c_4859]) ).
cnf(c_22016,plain,
'==>'('+'(A,B),C) = '==>'(A,'==>'(B,C)),
inference(resolve,[status(thm)],[c_26742,c_19233]) ).
cnf(c_26743,plain,
'==>'('+'('==>'(A,'1'),B),'1') = '==>'('==>'('1','==>'(B,A)),'==>'(B,A)),
inference(paramod,[status(thm)],[c_19719,c_28]) ).
cnf(c_26744,plain,
'==>'('==>'(A,'1'),'==>'(B,'1')) = '==>'('==>'('1','==>'(B,A)),'==>'(B,A)),
inference(paramod,[status(thm)],[c_22016,c_26743]) ).
cnf(c_26745,plain,
'==>'('==>'(A,'1'),'==>'(B,'1')) = '==>'('0','==>'(B,A)),
inference(paramod,[status(thm)],[c_173,c_26744]) ).
cnf(c_24454,plain,
'==>'('==>'(A,'1'),'==>'(B,'1')) = '==>'(B,A),
inference(paramod,[status(thm)],[c_123,c_26745]) ).
cnf(c_26746,plain,
'==>'('==>'('==>'('==>'(A,'1'),'==>'(B,'1')),'==>'(B,'1')),'==>'(A,'1')) = '==>'(A,B),
inference(paramod,[status(thm)],[c_24454,c_384]) ).
cnf(c_26747,plain,
'==>'('==>'(B,'==>'('==>'('==>'(A,'1'),'==>'(B,'1')),'1')),'==>'(A,'1')) = '==>'(A,B),
inference(paramod,[status(thm)],[c_21891,c_26746]) ).
cnf(c_26748,plain,
'==>'('==>'(B,'+'('==>'('==>'(B,'1'),'1'),'==>'(A,'1'))),'==>'(A,'1')) = '==>'(A,B),
inference(paramod,[status(thm)],[c_19719,c_26747]) ).
cnf(c_26749,plain,
'==>'('==>'(B,'+'('+'('==>'('1','1'),B),'==>'(A,'1'))),'==>'(A,'1')) = '==>'(A,B),
inference(paramod,[status(thm)],[c_19719,c_26748]) ).
cnf(c_26750,plain,
'==>'('==>'(B,'+'('+'('0',B),'==>'(A,'1'))),'==>'(A,'1')) = '==>'(A,B),
inference(paramod,[status(thm)],[c_70,c_26749]) ).
cnf(c_26751,plain,
'==>'('==>'(B,'+'(B,'==>'(A,'1'))),'==>'(A,'1')) = '==>'(A,B),
inference(paramod,[status(thm)],[c_33,c_26750]) ).
cnf(c_26752,plain,
'==>'(A,'==>'('==>'(B,'+'(B,'==>'(A,'1'))),'1')) = '==>'(A,B),
inference(paramod,[status(thm)],[c_21891,c_26751]) ).
cnf(c_26753,plain,
'==>'(A,'+'('==>'('+'(B,'==>'(A,'1')),'1'),B)) = '==>'(A,B),
inference(paramod,[status(thm)],[c_19719,c_26752]) ).
cnf(c_26754,plain,
'==>'(A,'+'('==>'(B,'==>'('==>'(A,'1'),'1')),B)) = '==>'(A,B),
inference(paramod,[status(thm)],[c_22016,c_26753]) ).
cnf(c_26755,plain,
'==>'(A,'+'('==>'(B,'+'('==>'('1','1'),A)),B)) = '==>'(A,B),
inference(paramod,[status(thm)],[c_19719,c_26754]) ).
cnf(c_26756,plain,
'==>'(A,'+'('==>'(B,'+'('0',A)),B)) = '==>'(A,B),
inference(paramod,[status(thm)],[c_70,c_26755]) ).
cnf(c_26757,plain,
'==>'(A,'+'('==>'(B,A),B)) = '==>'(A,B),
inference(paramod,[status(thm)],[c_33,c_26756]) ).
cnf(c_26268,plain,
'==>'(A,'+'(B,'==>'(B,A))) = '==>'(A,B),
inference(paramod,[status(thm)],[c_16,c_26757]) ).
cnf(c_26408,plain,
'==>'('==>'(A,B),'+'(B,'==>'(B,A))) = A,
inference(paramod,[status(thm)],[c_26268,c_6070]) ).
cnf(c_26758,plain,
'==>'('==>'('+'(A,'==>'(A,B)),B),'+'(B,'==>'(B,A))) = '+'(A,'==>'(A,B)),
inference(paramod,[status(thm)],[c_26268,c_26408]) ).
cnf(c_26759,plain,
'==>'('==>'(A,'==>'('==>'(A,B),B)),'+'(B,'==>'(B,A))) = '+'(A,'==>'(A,B)),
inference(paramod,[status(thm)],[c_22016,c_26758]) ).
cnf(c_26760,plain,
'==>'('0','+'(B,'==>'(B,A))) = '+'(A,'==>'(A,B)),
inference(paramod,[status(thm)],[c_393,c_26759]) ).
cnf(c_26706,plain,
'+'(A,'==>'(A,B)) = '+'(B,'==>'(B,A)),
inference(paramod,[status(thm)],[c_123,c_26760]) ).
cnf(c_26707,plain,
$false,
inference(resolve,[status(thm)],[c_26706,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL900+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n016.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Fri Sep 25 23:51:16 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 3600081 was started by sandbox on n016,
% 0.10/0.35 % Fri Sep 25 23:51:16 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 81.38/10.68
% 81.38/10.68 % given #500 (T,wt=11): 2364 A + B >= ==>(==>(B,C),==>(D,C)). [hyper(19,a,214,a,b,79,a)].
% 81.38/10.68
% 81.38/10.68 % SZS status Theorem for theBenchmark
% 81.38/10.68
% 81.38/10.68 % Proof 1 at 7.05 (+ 3.18) seconds.
% 81.38/10.68 % Length of proof is 83.
% 81.38/10.68 % Level of proof is 14.
% 81.38/10.68 % Maximum clause weight is 17.000.
% 81.38/10.68 % Given clauses 960.
% 81.38/10.68
% 81.38/10.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------