%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 : Thu Sep 24 01:09:03 PM UTC 2026
% Result : Theorem 0.12s 0.48s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 39 unt; 0 def)
% Number of atoms : 94 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 29 ~; 24 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 107 ( 106 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : '+'(A,B) = '+'(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : '+'(A,'0') = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : '>='(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X3,X4] :
( ( '>='(X4,X3)
& '>='(X3,X4) )
=> X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X5,X6,X7] :
( '>='('+'(X5,X6),X7)
<=> '>='(X6,'==>'(X5,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : '>='(A,'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X11,X12,X13] :
( '>='(X11,X12)
=> '>='('==>'(X12,X13),'==>'(X11,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X14,X15,X16] :
( '>='(X14,X15)
=> '>='('==>'(X16,X14),'==>'(X16,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : '+'(A,'1') = '1',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : '==>'('==>'('==>'(A,'1'),A),A) = '0',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [X17] : '==>'('==>'(X17,'1'),'1') = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X17] : '==>'('==>'(X17,'1'),'1') = X17,
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f17,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0] : '+'(X0,'0') = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0] : '>='(X0,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X3,X4] :
( X3 = X4
| ~ '>='(X4,X3)
| ~ '>='(X3,X4) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = X1
| ~ '>='(X1,X0)
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X5,X6,X7] :
( ( ~ '>='(X6,'==>'(X5,X7))
| '>='('+'(X5,X6),X7) )
& ( '>='(X6,'==>'(X5,X7))
| ~ '>='('+'(X5,X6),X7) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
( ! [X5,X6,X7] :
( ~ '>='(X6,'==>'(X5,X7))
| '>='('+'(X5,X6),X7) )
& ! [X5,X6,X7] :
( '>='(X6,'==>'(X5,X7))
| ~ '>='('+'(X5,X6),X7) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( '>='(X1,'==>'(X0,X2))
| ~ '>='('+'(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ '>='(X1,'==>'(X0,X2))
| '>='('+'(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
! [X0] : '>='(X0,'0'),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
! [X11,X12,X13] :
( '>='('==>'(X12,X13),'==>'(X11,X13))
| ~ '>='(X11,X12) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f34,plain,
! [X11,X12] :
( ! [X13] : '>='('==>'(X12,X13),'==>'(X11,X13))
| ~ '>='(X11,X12) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( '>='('==>'(X1,X2),'==>'(X0,X2))
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X14,X15,X16] :
( '>='('==>'(X16,X14),'==>'(X16,X15))
| ~ '>='(X14,X15) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
! [X14,X15] :
( ! [X16] : '>='('==>'(X16,X14),'==>'(X16,X15))
| ~ '>='(X14,X15) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( '>='('==>'(X2,X0),'==>'(X2,X1))
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0] : '+'(X0,'1') = '1',
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
! [X0] : '==>'('==>'('==>'(X0,'1'),X0),X0) = '0',
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f41,plain,
? [X17] : '==>'('==>'(X17,'1'),'1') != X17,
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f42,plain,
'==>'('==>'(sK0_skl,'1'),'1') != sK0_skl,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X17,sK0_skl)],[f41]) ).
fof(f43,plain,
'==>'('==>'(sK0_skl,'1'),'1') != sK0_skl,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( '>='('1','==>'(X1,X0))
| ~ '>='('1',X0) ),
inference(paramodulation,[status(thm)],[f39,f27]) ).
fof(f45,plain,
! [X0] : '>='('1','==>'(X0,'1')),
inference(resolution,[status(thm)],[f19,f44]) ).
fof(f46,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'+'(X1,X0))),
inference(resolution,[status(thm)],[f19,f27]) ).
fof(f47,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(resolution,[status(thm)],[f19,f28]) ).
fof(f53,plain,
! [X0,X1] : '>='('==>'('==>'(X0,'1'),X1),'==>'('1',X1)),
inference(resolution,[status(thm)],[f45,f35]) ).
fof(f74,plain,
! [X0,X1] : '>='('+'('1','==>'('==>'(X0,'1'),X1)),X1),
inference(resolution,[status(thm)],[f53,f28]) ).
fof(f112,plain,
! [X0] : '>='('0','==>'(X0,X0)),
inference(paramodulation,[status(thm)],[f18,f46]) ).
fof(f115,plain,
! [X0] : '1' = '+'('1',X0),
inference(paramodulation,[status(thm)],[f39,f17]) ).
fof(f129,plain,
! [X0,X1,X2] :
( '>='(X0,'==>'(X1,X2))
| ~ '>='('+'(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f17,f27]) ).
fof(f155,plain,
! [X0] : '>='('1',X0),
inference(backward_demodulation,[status(thm)],[f115,f74]) ).
fof(f176,plain,
! [X0,X1] : '>='('==>'(X0,'1'),'==>'(X0,X1)),
inference(resolution,[status(thm)],[f155,f38]) ).
fof(f248,plain,
! [X0] :
( '==>'(X0,X0) = '0'
| ~ '>='('==>'(X0,X0),'0') ),
inference(resolution,[status(thm)],[f24,f112]) ).
fof(f256,plain,
! [X0] :
( X0 = '1'
| ~ '>='(X0,'1') ),
inference(resolution,[status(thm)],[f24,f155]) ).
fof(f264,plain,
! [X0] : '==>'(X0,X0) = '0',
inference(forward_subsumption_resolution,[status(thm)],[f248,f29]) ).
fof(f284,plain,
! [X0,X1] :
( ~ '>='(X1,'0')
| '>='('+'(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f264,f28]) ).
fof(f289,plain,
! [X0,X1] : '>='('+'(X0,X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[f284,f29]) ).
fof(f334,plain,
! [X0,X1] : '>='('+'(X0,X1),X1),
inference(paramodulation,[status(thm)],[f17,f289]) ).
fof(f337,plain,
! [X0,X1] : '>='(X0,'==>'(X1,X0)),
inference(resolution,[status(thm)],[f334,f27]) ).
fof(f359,plain,
! [X0] : '+'(X0,'==>'(X0,'1')) = '1',
inference(resolution,[status(thm)],[f256,f47]) ).
fof(f769,plain,
! [X0] : '>='('+'('==>'('==>'(X0,'1'),X0),'0'),X0),
inference(paramodulation,[status(thm)],[f40,f47]) ).
fof(f780,plain,
! [X0] : '>='('==>'('==>'(X0,'1'),X0),X0),
inference(forward_demodulation,[status(thm)],[f18,f769]) ).
fof(f801,plain,
! [X0,X1] :
( '>='(X1,'==>'('==>'(X1,'1'),X0))
| ~ '>='('1',X0) ),
inference(paramodulation,[status(thm)],[f359,f129]) ).
fof(f810,plain,
! [X0,X1] : '>='(X0,'==>'('==>'(X0,'1'),X1)),
inference(forward_subsumption_resolution,[status(thm)],[f801,f155]) ).
fof(f1181,plain,
! [X0] :
( X0 = '==>'('==>'(X0,'1'),X0)
| ~ '>='(X0,'==>'('==>'(X0,'1'),X0)) ),
inference(resolution,[status(thm)],[f780,f24]) ).
fof(f1196,plain,
! [X0] : X0 = '==>'('==>'(X0,'1'),X0),
inference(forward_subsumption_resolution,[status(thm)],[f1181,f337]) ).
fof(f1229,plain,
! [X0] : '>='('==>'('==>'(X0,'1'),'1'),X0),
inference(paramodulation,[status(thm)],[f1196,f176]) ).
fof(f1837,plain,
! [X0] :
( X0 = '==>'('==>'(X0,'1'),'1')
| ~ '>='(X0,'==>'('==>'(X0,'1'),'1')) ),
inference(resolution,[status(thm)],[f1229,f24]) ).
fof(f1851,plain,
! [X0] : X0 = '==>'('==>'(X0,'1'),'1'),
inference(forward_subsumption_resolution,[status(thm)],[f1837,f810]) ).
fof(f1864,plain,
sK0_skl != sK0_skl,
inference(backward_demodulation,[status(thm)],[f1851,f43]) ).
fof(f1896,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.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 : Mon Sep 21 01:10:23 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.48 % Refutation found
% 0.12/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.52/0.52 % Elapsed time: 0.145865 seconds
% 0.52/0.52 % CPU time: 0.960101 seconds
% 0.52/0.52 % Total memory used: 78.628 MB
% 0.52/0.52 % Net memory used: 76.969 MB
%------------------------------------------------------------------------------