%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL894+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 : n020.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 35.92s 5.00s
% Output : CNFRefutation 35.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 34 unt; 0 def)
% Number of atoms : 93 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 23 ~; 23 |; 4 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 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 : 75 ( 4 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,B] : '+'(A,'==>'(A,B)) = '+'(B,'==>'(B,A)),
file('theBenchmark.p',sos_12) ).
fof(goals_13,conjecture,
( ( '>='(c,b)
& '>='(c,a) )
<=> '>='(c,'+'(a,'==>'(a,b))) ),
file('theBenchmark.p',goals_13) ).
fof(goals_13_neg,negated_conjecture,
~ ( ( '>='(c,b)
& '>='(c,a) )
<=> '>='(c,'+'(a,'==>'(a,b))) ),
inference(assume_negation,[status(cth)],[goals_13]) ).
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_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]) ).
cnf(c_27,negated_conjecture,
( '>='(c,'+'(a,'==>'(a,b)))
| '>='(c,a) ),
inference(clausify,[status(thm)],[goals_13_neg]) ).
cnf(c_28,negated_conjecture,
( '>='(c,'+'(a,'==>'(a,b)))
| '>='(c,b) ),
inference(clausify,[status(thm)],[goals_13_neg]) ).
cnf(c_29,negated_conjecture,
( ~ '>='(c,'+'(a,'==>'(a,b)))
| ~ '>='(c,b)
| ~ '>='(c,a) ),
inference(clausify,[status(thm)],[goals_13_neg]) ).
cnf(c_24037,plain,
A = '+'('0',A),
inference(paramod,[status(thm)],[c_16,c_15]) ).
cnf(c_33,plain,
'+'('0',A) = A,
inference(copy,[status(thm)],[c_24037]) ).
cnf(c_34,plain,
'>='(A,'==>'(B,'+'(B,A))),
inference(resolve,[status(thm)],[c_20,c_17]) ).
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_24038,plain,
( A = '0'
| ~ '>='('0',A) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_40,plain,
( '0' = A
| ~ '>='('0',A) ),
inference(copy,[status(thm)],[c_24038]) ).
cnf(c_24039,plain,
'>='('+'(A,B),'+'('0',B)),
inference(resolve,[status(thm)],[c_23,c_22]) ).
cnf(c_42,plain,
'>='('+'(A,B),B),
inference(paramod,[status(thm)],[c_33,c_24039]) ).
cnf(c_59,plain,
( '>='(c,A)
| ~ '>='('+'(a,'==>'(a,b)),A)
| '>='(c,a) ),
inference(resolve,[status(thm)],[c_27,c_18]) ).
cnf(c_61,plain,
( ~ '>='('+'(a,'==>'(a,b)),a)
| '>='(c,a) ),
inference(factor,[status(thm)],[c_59]) ).
cnf(c_73,plain,
( '>='(c,A)
| ~ '>='('+'(a,'==>'(a,b)),A)
| '>='(c,b) ),
inference(resolve,[status(thm)],[c_28,c_18]) ).
cnf(c_24040,plain,
( ~ '>='('+'(a,'==>'(a,b)),b)
| '>='(c,b) ),
inference(factor,[status(thm)],[c_73]) ).
cnf(c_75,plain,
'>='(c,b),
inference(resolve,[status(thm)],[c_38,c_24040]) ).
cnf(c_76,negated_conjecture,
( ~ '>='(c,'+'(a,'==>'(a,b)))
| ~ '>='(c,a) ),
inference(resolve,[status(thm)],[c_75,c_29]) ).
cnf(c_81,plain,
'>='('==>'(A,c),'==>'(A,b)),
inference(resolve,[status(thm)],[c_75,c_25]) ).
cnf(c_97,plain,
'>='(A,'==>'(B,'+'(A,B))),
inference(paramod,[status(thm)],[c_15,c_34]) ).
cnf(c_119,plain,
'>='('+'(A,B),A),
inference(paramod,[status(thm)],[c_15,c_42]) ).
cnf(c_122,plain,
'>='(c,a),
inference(resolve,[status(thm)],[c_119,c_61]) ).
cnf(c_123,negated_conjecture,
~ '>='(c,'+'(a,'==>'(a,b))),
inference(resolve,[status(thm)],[c_122,c_76]) ).
cnf(c_135,plain,
'>='('0','==>'(c,a)),
inference(resolve,[status(thm)],[c_37,c_122]) ).
cnf(c_24041,plain,
'0' = '==>'(c,a),
inference(resolve,[status(thm)],[c_135,c_40]) ).
cnf(c_240,plain,
'==>'(c,a) = '0',
inference(copy,[status(thm)],[c_24041]) ).
cnf(c_24042,plain,
'+'(c,'0') = '+'(a,'==>'(a,c)),
inference(paramod,[status(thm)],[c_240,c_26]) ).
cnf(c_24043,plain,
c = '+'(a,'==>'(a,c)),
inference(paramod,[status(thm)],[c_16,c_24042]) ).
cnf(c_355,plain,
'+'(a,'==>'(a,c)) = c,
inference(copy,[status(thm)],[c_24043]) ).
cnf(c_361,plain,
'>='('+'('==>'(A,c),B),'+'('==>'(A,b),B)),
inference(resolve,[status(thm)],[c_81,c_23]) ).
cnf(c_892,plain,
'>='('+'(A,B),'+'(B,A)),
inference(resolve,[status(thm)],[c_97,c_21]) ).
cnf(c_951,plain,
( '>='('+'(B,A),C)
| ~ '>='('+'(A,B),C) ),
inference(resolve,[status(thm)],[c_892,c_18]) ).
cnf(c_14465,plain,
'>='('+'(A,'==>'(B,c)),'+'('==>'(B,b),A)),
inference(resolve,[status(thm)],[c_361,c_951]) ).
cnf(c_24044,plain,
'>='(c,'+'('==>'(a,b),a)),
inference(paramod,[status(thm)],[c_355,c_14465]) ).
cnf(c_24045,plain,
'>='(c,'+'(a,'==>'(a,b))),
inference(paramod,[status(thm)],[c_15,c_24044]) ).
cnf(c_24036,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_123,c_24045]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL894+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 23:47:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 4113586 was started by sandbox on n020,
% 0.08/0.35 % Fri Sep 25 23:47:49 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 35.92/5.00
% 35.92/5.00 % given #500 (T,wt=15): 1256 c >= ==>(A + B,B + a). [resolve(111,a,125,a)].
% 35.92/5.00
% 35.92/5.00 % given #1000 (A,wt=19): 411 A + (B + ==>(B,c)) >= a. [para(78(a,2),220(a,1))].
% 35.92/5.00
% 35.92/5.00 % SZS status Theorem for theBenchmark
% 35.92/5.00
% 35.92/5.00 % Proof 1 at 3.32 (+ 1.28) seconds.
% 35.92/5.00 % Length of proof is 49.
% 35.92/5.00 % Level of proof is 9.
% 35.92/5.00 % Maximum clause weight is 19.000.
% 35.92/5.00 % Given clauses 1391.
% 35.92/5.00
% 35.92/5.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------