%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL888+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:59:59 AM UTC 2026
% Result : Theorem 50.14s 6.98s
% Output : CNFRefutation 50.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 13
% Syntax : Number of formulae : 111 ( 83 unt; 0 def)
% Number of atoms : 147 ( 66 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 25 ~; 20 |; 8 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 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 : 142 ( 15 sgn 33 !; 3 ?)
% 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_10,axiom,
! [X11,X12,X13] :
( '>='(X11,X12)
=> '>='('==>'(X12,X13),'==>'(X11,X13)) ),
file('theBenchmark.p',sos_10) ).
fof(sos_11,axiom,
! [X14,X15,X16] :
( '>='(X14,X15)
=> '>='('==>'(X16,X14),'==>'(X16,X15)) ),
file('theBenchmark.p',sos_11) ).
fof(sos_12,axiom,
! [A,B] : '+'(A,'==>'(A,B)) = '+'(B,'==>'(B,A)),
file('theBenchmark.p',sos_12) ).
fof(goals_13,conjecture,
! [X17,X18,X19] :
( ( X19 = '==>'(X19,X18)
& X17 = '==>'(X17,X18) )
=> X17 = X19 ),
file('theBenchmark.p',goals_13) ).
fof(goals_13_neg,negated_conjecture,
~ ! [X17,X18,X19] :
( ( X19 = '==>'(X19,X18)
& X17 = '==>'(X17,X18) )
=> X17 = X19 ),
inference(assume_negation,[status(cth)],[goals_13]) ).
cnf(c_14,plain,
'+'('+'(A,B),C) = '+'(A,'+'(B,C)),
inference(clausify,[status(thm)],[sos_01]) ).
cnf(c_15,plain,
'+'(A,B) = '+'(B,A),
inference(clausify,[status(thm)],[sos_02]) ).
cnf(c_16,plain,
'+'(A,'0') = A,
inference(clausify,[status(thm)],[sos_03]) ).
cnf(c_17,plain,
'>='(A,A),
inference(clausify,[status(thm)],[sos_04]) ).
cnf(c_18,plain,
( '>='(A,C)
| ~ '>='(B,C)
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_05]) ).
cnf(c_19,plain,
( B = A
| ~ '>='(B,A)
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_06]) ).
cnf(c_20,plain,
( '>='(B,'==>'(A,C))
| ~ '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_21,plain,
( ~ '>='(B,'==>'(A,C))
| '>='('+'(A,B),C) ),
inference(clausify,[status(thm)],[sos_07]) ).
cnf(c_22,plain,
'>='(A,'0'),
inference(clausify,[status(thm)],[sos_08]) ).
cnf(c_23,plain,
( '>='('+'(A,C),'+'(B,C))
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_09]) ).
cnf(c_24,plain,
( '>='('==>'(B,C),'==>'(A,C))
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_10]) ).
cnf(c_25,plain,
( '>='('==>'(C,A),'==>'(C,B))
| ~ '>='(A,B) ),
inference(clausify,[status(thm)],[sos_11]) ).
cnf(c_26,plain,
'+'(A,'==>'(A,B)) = '+'(B,'==>'(B,A)),
inference(clausify,[status(thm)],[sos_12]) ).
fof(nnf_13,plain,
? [X17,X18,X19] :
( X19 != X17
& '==>'(X19,X18) = X19
& '==>'(X17,X18) = X17 ),
inference(fof_nnf,[status(thm)],[goals_13_neg]) ).
fof(sk_goals_13_neg,plain,
( sK2 != sK0
& '==>'(sK2,sK1) = sK2
& '==>'(sK0,sK1) = sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X17,sK0),skolemize(X18,sK1),skolemize(X19,sK2)],[nnf_13]) ).
cnf(c_27,negated_conjecture,
'==>'(sK0,sK1) = sK0,
inference(split_conjunct,[status(thm)],[sk_goals_13_neg]) ).
cnf(c_28,negated_conjecture,
'==>'(sK2,sK1) = sK2,
inference(split_conjunct,[status(thm)],[sk_goals_13_neg]) ).
cnf(c_29,negated_conjecture,
sK2 != sK0,
inference(split_conjunct,[status(thm)],[sk_goals_13_neg]) ).
cnf(c_20801,plain,
'+'('+'(A,B),C) = '+'(B,'+'(A,C)),
inference(paramod,[status(thm)],[c_15,c_14]) ).
cnf(c_30,plain,
'+'(A,'+'(B,C)) = '+'(B,'+'(A,C)),
inference(paramod,[status(thm)],[c_14,c_20801]) ).
cnf(c_20802,plain,
A = '+'('0',A),
inference(paramod,[status(thm)],[c_16,c_15]) ).
cnf(c_33,plain,
'+'('0',A) = A,
inference(copy,[status(thm)],[c_20802]) ).
cnf(c_34,plain,
'>='(A,'==>'(B,'+'(B,A))),
inference(resolve,[status(thm)],[c_20,c_17]) ).
cnf(c_36,plain,
( '>='(A,'==>'(B,C))
| ~ '>='('+'(A,B),C) ),
inference(paramod,[status(thm)],[c_15,c_20]) ).
cnf(c_37,plain,
( '>='('0','==>'(A,B))
| ~ '>='(A,B) ),
inference(paramod,[status(thm)],[c_16,c_20]) ).
cnf(c_38,plain,
'>='('+'(A,'==>'(A,B)),B),
inference(resolve,[status(thm)],[c_21,c_17]) ).
cnf(c_39,plain,
'>='(A,'==>'(B,'0')),
inference(resolve,[status(thm)],[c_20,c_22]) ).
cnf(c_20803,plain,
'>='('+'(A,B),'+'('0',B)),
inference(resolve,[status(thm)],[c_23,c_22]) ).
cnf(c_40,plain,
'>='('+'(A,B),B),
inference(paramod,[status(thm)],[c_33,c_20803]) ).
cnf(c_41,plain,
'>='('==>'('0',A),'==>'(B,A)),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_20804,plain,
'+'('+'(A,'==>'(A,B)),C) = '+'(B,'+'('==>'(B,A),C)),
inference(paramod,[status(thm)],[c_26,c_14]) ).
cnf(c_42,plain,
'+'(A,'+'('==>'(A,B),C)) = '+'(B,'+'('==>'(B,A),C)),
inference(paramod,[status(thm)],[c_14,c_20804]) ).
cnf(c_47,plain,
( ~ '>='(A,sK2)
| '>='('+'(sK2,A),sK1) ),
inference(paramod,[status(thm)],[c_28,c_21]) ).
cnf(c_49,plain,
( '>='('+'(A,C),'==>'(B,D))
| ~ '>='('+'(A,'+'(B,C)),D) ),
inference(paramod,[status(thm)],[c_30,c_20]) ).
cnf(c_52,plain,
'==>'('0',A) = '+'(A,'==>'(A,'0')),
inference(paramod,[status(thm)],[c_33,c_26]) ).
cnf(c_20805,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_20806,plain,
'0' = '==>'(A,'0'),
inference(resolve,[status(thm)],[c_20805,c_39]) ).
cnf(c_58,plain,
'==>'(A,'0') = '0',
inference(copy,[status(thm)],[c_20806]) ).
cnf(c_20807,plain,
'==>'('0',A) = '+'(A,'0'),
inference(paramod,[status(thm)],[c_58,c_52]) ).
cnf(c_59,plain,
'==>'('0',A) = A,
inference(paramod,[status(thm)],[c_16,c_20807]) ).
cnf(c_60,plain,
'>='(A,'==>'(B,A)),
inference(paramod,[status(thm)],[c_59,c_41]) ).
cnf(c_61,plain,
'>='('==>'(A,'+'(B,C)),'==>'(A,C)),
inference(resolve,[status(thm)],[c_25,c_40]) ).
cnf(c_76,plain,
'>='(A,'==>'(B,'+'(A,B))),
inference(paramod,[status(thm)],[c_15,c_34]) ).
cnf(c_87,plain,
'>='(sK1,sK0),
inference(paramod,[status(thm)],[c_27,c_60]) ).
cnf(c_88,plain,
'>='(sK1,sK2),
inference(paramod,[status(thm)],[c_28,c_60]) ).
cnf(c_20808,plain,
( '>='('+'(C,A),B)
| ~ '>='(A,B) ),
inference(resolve,[status(thm)],[c_18,c_40]) ).
cnf(c_92,plain,
'>='('+'(A,sK1),sK0),
inference(resolve,[status(thm)],[c_20808,c_87]) ).
cnf(c_95,plain,
'>='('==>'(A,sK1),'==>'(A,sK2)),
inference(resolve,[status(thm)],[c_25,c_88]) ).
cnf(c_133,plain,
'>='(A,'==>'(sK1,sK0)),
inference(resolve,[status(thm)],[c_36,c_92]) ).
cnf(c_20809,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_20810,plain,
'0' = '==>'(sK1,sK0),
inference(resolve,[status(thm)],[c_20809,c_133]) ).
cnf(c_177,plain,
'==>'(sK1,sK0) = '0',
inference(copy,[status(thm)],[c_20810]) ).
cnf(c_20811,plain,
'+'(sK1,'0') = '+'(sK0,'==>'(sK0,sK1)),
inference(paramod,[status(thm)],[c_177,c_26]) ).
cnf(c_20812,plain,
'+'('0',sK1) = '+'(sK0,'==>'(sK0,sK1)),
inference(paramod,[status(thm)],[c_15,c_20811]) ).
cnf(c_20813,plain,
sK1 = '+'(sK0,'==>'(sK0,sK1)),
inference(paramod,[status(thm)],[c_33,c_20812]) ).
cnf(c_20814,plain,
sK1 = '+'(sK0,sK0),
inference(paramod,[status(thm)],[c_27,c_20813]) ).
cnf(c_186,plain,
'+'(sK0,sK0) = sK1,
inference(copy,[status(thm)],[c_20814]) ).
cnf(c_20815,plain,
'+'('+'(A,sK0),sK0) = '+'(A,sK1),
inference(paramod,[status(thm)],[c_186,c_14]) ).
cnf(c_211,plain,
'+'(sK0,'+'(A,sK0)) = '+'(A,sK1),
inference(paramod,[status(thm)],[c_15,c_20815]) ).
cnf(c_20816,plain,
'+'(A,'+'(B,'==>'(B,'==>'(A,C)))) = '+'(C,'+'('==>'(C,A),'==>'('==>'(A,C),B))),
inference(paramod,[status(thm)],[c_26,c_42]) ).
cnf(c_277,plain,
'+'(A,'+'('==>'(A,B),'==>'('==>'(B,A),C))) = '+'(B,'+'(C,'==>'(C,'==>'(B,A)))),
inference(copy,[status(thm)],[c_20816]) ).
cnf(c_281,plain,
'>='('+'('==>'(A,B),C),'==>'(A,'+'(B,'+'('==>'(B,A),C)))),
inference(paramod,[status(thm)],[c_42,c_34]) ).
cnf(c_424,plain,
'>='(sK0,'==>'(sK0,sK2)),
inference(paramod,[status(thm)],[c_27,c_95]) ).
cnf(c_425,plain,
'>='('0','==>'(sK0,'==>'(sK0,sK2))),
inference(resolve,[status(thm)],[c_37,c_424]) ).
cnf(c_615,plain,
'>='('+'(sK2,'+'(A,'==>'(A,sK2))),sK1),
inference(resolve,[status(thm)],[c_47,c_38]) ).
cnf(c_901,plain,
'>='('==>'(sK2,'+'(A,sK1)),sK2),
inference(paramod,[status(thm)],[c_28,c_61]) ).
cnf(c_20817,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_19,c_22]) ).
cnf(c_20818,plain,
'0' = '==>'(sK0,'==>'(sK0,sK2)),
inference(resolve,[status(thm)],[c_20817,c_425]) ).
cnf(c_1002,plain,
'==>'(sK0,'==>'(sK0,sK2)) = '0',
inference(copy,[status(thm)],[c_20818]) ).
cnf(c_5226,plain,
'>='('==>'(sK2,'+'(sK0,'+'(A,sK0))),sK2),
inference(paramod,[status(thm)],[c_211,c_901]) ).
cnf(c_10404,plain,
'>='('+'(sK2,'==>'(A,sK2)),'==>'(A,sK1)),
inference(resolve,[status(thm)],[c_49,c_615]) ).
cnf(c_20819,plain,
'+'(sK2,'+'('==>'(sK2,sK0),'==>'('==>'(sK0,sK2),sK0))) = '+'(sK0,'+'(sK0,'0')),
inference(paramod,[status(thm)],[c_1002,c_277]) ).
cnf(c_20820,plain,
'+'(sK2,'+'('==>'(sK2,sK0),'==>'('==>'(sK0,sK2),sK0))) = '+'(sK0,'+'('0',sK0)),
inference(paramod,[status(thm)],[c_15,c_20819]) ).
cnf(c_20821,plain,
'+'(sK2,'+'('==>'(sK2,sK0),'==>'('==>'(sK0,sK2),sK0))) = '+'(sK0,sK0),
inference(paramod,[status(thm)],[c_33,c_20820]) ).
cnf(c_16719,plain,
'+'(sK2,'+'('==>'(sK2,sK0),'==>'('==>'(sK0,sK2),sK0))) = sK1,
inference(paramod,[status(thm)],[c_186,c_20821]) ).
cnf(c_20822,plain,
( '>='('+'('==>'(A,B),C),D)
| ~ '>='('==>'(A,'+'(B,'+'('==>'(B,A),C))),D) ),
inference(resolve,[status(thm)],[c_18,c_281]) ).
cnf(c_20823,plain,
'>='('+'('==>'(sK2,sK0),sK0),sK2),
inference(resolve,[status(thm)],[c_20822,c_5226]) ).
cnf(c_20065,plain,
'>='('+'(sK0,'==>'(sK2,sK0)),sK2),
inference(paramod,[status(thm)],[c_15,c_20823]) ).
cnf(c_20072,plain,
'>='('==>'(sK2,sK0),'==>'(sK0,sK2)),
inference(resolve,[status(thm)],[c_20,c_20065]) ).
cnf(c_20570,plain,
'>='('+'(sK2,'==>'(sK0,sK2)),sK0),
inference(paramod,[status(thm)],[c_27,c_10404]) ).
cnf(c_20576,plain,
'>='('==>'(sK0,sK2),'==>'(sK2,sK0)),
inference(resolve,[status(thm)],[c_20,c_20570]) ).
cnf(c_20824,plain,
( '==>'(sK0,sK2) = '==>'(sK2,sK0)
| ~ '>='('==>'(sK0,sK2),'==>'(sK2,sK0)) ),
inference(resolve,[status(thm)],[c_19,c_20072]) ).
cnf(c_20825,plain,
'==>'(sK0,sK2) = '==>'(sK2,sK0),
inference(resolve,[status(thm)],[c_20824,c_20576]) ).
cnf(c_20620,plain,
'==>'(sK2,sK0) = '==>'(sK0,sK2),
inference(copy,[status(thm)],[c_20825]) ).
cnf(c_20826,plain,
'+'(sK2,'+'('==>'(sK0,sK2),'==>'('==>'(sK0,sK2),sK0))) = sK1,
inference(paramod,[status(thm)],[c_20620,c_16719]) ).
cnf(c_20827,plain,
'+'(sK2,'+'(sK0,'==>'(sK0,'==>'(sK0,sK2)))) = sK1,
inference(paramod,[status(thm)],[c_26,c_20826]) ).
cnf(c_20828,plain,
'+'(sK2,'+'(sK0,'0')) = sK1,
inference(paramod,[status(thm)],[c_1002,c_20827]) ).
cnf(c_20829,plain,
'+'(sK2,'+'('0',sK0)) = sK1,
inference(paramod,[status(thm)],[c_15,c_20828]) ).
cnf(c_20830,plain,
'+'(sK2,sK0) = sK1,
inference(paramod,[status(thm)],[c_33,c_20829]) ).
cnf(c_20631,plain,
'+'(sK0,sK2) = sK1,
inference(paramod,[status(thm)],[c_15,c_20830]) ).
cnf(c_20831,plain,
'>='(sK2,'==>'(sK0,sK1)),
inference(paramod,[status(thm)],[c_20631,c_34]) ).
cnf(c_20640,plain,
'>='(sK2,sK0),
inference(paramod,[status(thm)],[c_27,c_20831]) ).
cnf(c_20832,plain,
'>='(sK0,'==>'(sK2,sK1)),
inference(paramod,[status(thm)],[c_20631,c_76]) ).
cnf(c_20643,plain,
'>='(sK0,sK2),
inference(paramod,[status(thm)],[c_28,c_20832]) ).
cnf(c_20833,plain,
( sK2 = sK0
| ~ '>='(sK0,sK2) ),
inference(resolve,[status(thm)],[c_19,c_20640]) ).
cnf(c_20799,negated_conjecture,
~ '>='(sK0,sK2),
inference(resolve,[status(thm)],[c_20833,c_29]) ).
cnf(c_20800,plain,
$false,
inference(resolve,[status(thm)],[c_20799,c_20643]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL888+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n015.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Fri Sep 25 23:49:13 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.57 % Process 2580907 was started by sandbox2 on n015,
% 0.10/0.57 % Fri Sep 25 23:49:13 2026
% 0.10/0.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.58
% 0.10/0.58 % From the command line: assign(max_seconds, 300).
% 50.14/6.98
% 50.14/6.98 % given #500 (T,wt=9): 2128 c1 >= ==>(A,==>(c1 + B,c2)). [hyper(18,a,1305,a,b,60,a)].
% 50.14/6.98
% 50.14/6.98 % SZS status Theorem for theBenchmark
% 50.14/6.98
% 50.14/6.98 % Proof 1 at 4.54 (+ 1.81) seconds.
% 50.14/6.98 % Length of proof is 75.
% 50.14/6.98 % Level of proof is 19.
% 50.14/6.98 % Maximum clause weight is 21.000.
% 50.14/6.98 % Given clauses 794.
% 50.14/6.98
% 50.14/6.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------