%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL903+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 : n008.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 01:09:04 PM UTC 2026
% Result : Theorem 5.95s 1.28s
% Output : CNFRefutation 5.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 47 unt; 0 def)
% Number of atoms : 121 ( 45 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 85 ( 41 ~; 36 |; 4 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 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 : 139 ( 138 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : '+'('+'(A,B),C) = '+'(A,'+'(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f5,axiom,
! [X0,X1,X2] :
( ( '>='(X1,X2)
& '>='(X0,X1) )
=> '>='(X0,X2) ),
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(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,X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X17] : '+'(X17,X17) = X17,
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
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(f20,plain,
! [X0,X1,X2] :
( '>='(X0,X2)
| ~ '>='(X1,X2)
| ~ '>='(X0,X1) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0,X2] :
( '>='(X0,X2)
| ! [X1] :
( ~ '>='(X1,X2)
| ~ '>='(X0,X1) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( '>='(X0,X2)
| ~ '>='(X1,X2)
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
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(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,X17) != X17,
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f42,plain,
'+'(sK0_skl,sK0_skl) != sK0_skl,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X17,sK0_skl)],[f41]) ).
fof(f43,plain,
'+'(sK0_skl,sK0_skl) != sK0_skl,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0] : '1' = '+'('1',X0),
inference(paramodulation,[status(thm)],[f39,f17]) ).
fof(f94,plain,
! [X0] :
( '0' = X0
| ~ '>='('0',X0) ),
inference(resolution,[status(thm)],[f24,f29]) ).
fof(f102,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'+'(X1,X0))),
inference(resolution,[status(thm)],[f27,f19]) ).
fof(f119,plain,
! [X0,X1,X2] : '>='(X0,'==>'(X1,'==>'(X2,'+'(X2,'+'(X1,X0))))),
inference(resolution,[status(thm)],[f102,f27]) ).
fof(f120,plain,
! [X0] : '0' = '==>'(X0,'+'(X0,'0')),
inference(resolution,[status(thm)],[f102,f94]) ).
fof(f130,plain,
! [X0] : '0' = '==>'(X0,X0),
inference(forward_demodulation,[status(thm)],[f18,f120]) ).
fof(f143,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(resolution,[status(thm)],[f28,f19]) ).
fof(f146,plain,
! [X0,X1] :
( ~ '>='(X1,'0')
| '>='('+'(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f130,f28]) ).
fof(f149,plain,
! [X0,X1] : '>='('+'(X0,X1),X0),
inference(forward_subsumption_resolution,[status(thm)],[f146,f29]) ).
fof(f153,plain,
! [X0,X1,X2] :
( '>='(X0,X1)
| ~ '>='(X0,'+'(X1,X2)) ),
inference(resolution,[status(thm)],[f149,f22]) ).
fof(f157,plain,
! [X0] : '>='('1',X0),
inference(paramodulation,[status(thm)],[f39,f149]) ).
fof(f159,plain,
! [X0,X1] : '>='('+'(X0,X1),X1),
inference(paramodulation,[status(thm)],[f17,f149]) ).
fof(f163,plain,
! [X0] :
( X0 = '1'
| ~ '>='(X0,'1') ),
inference(resolution,[status(thm)],[f157,f24]) ).
fof(f166,plain,
! [X0,X1] : '>='(X0,'==>'(X1,X0)),
inference(resolution,[status(thm)],[f159,f27]) ).
fof(f233,plain,
! [X0] : '+'(X0,'==>'(X0,'1')) = '1',
inference(resolution,[status(thm)],[f143,f163]) ).
fof(f235,plain,
! [X0,X1] :
( X0 = '+'(X1,'==>'(X1,X0))
| ~ '>='(X0,'+'(X1,'==>'(X1,X0))) ),
inference(resolution,[status(thm)],[f143,f24]) ).
fof(f240,plain,
! [X0] : '>='('+'('==>'('==>'(X0,'1'),X0),'0'),X0),
inference(paramodulation,[status(thm)],[f40,f143]) ).
fof(f243,plain,
! [X0] : '>='('==>'('==>'(X0,'1'),X0),X0),
inference(forward_demodulation,[status(thm)],[f18,f240]) ).
fof(f247,plain,
! [X0,X1,X2] :
( '==>'(X0,X2) = '==>'(X1,X2)
| ~ '>='('==>'(X0,X2),'==>'(X1,X2))
| ~ '>='(X0,X1) ),
inference(resolution,[status(thm)],[f35,f24]) ).
fof(f363,plain,
! [X0,X1] : '+'('1',X0) = '+'(X1,'+'('==>'(X1,'1'),X0)),
inference(paramodulation,[status(thm)],[f233,f16]) ).
fof(f367,plain,
! [X0,X1] : '1' = '+'(X0,'+'('==>'(X0,'1'),X1)),
inference(forward_demodulation,[status(thm)],[f44,f363]) ).
fof(f598,plain,
! [X0,X1,X2] : '>='('+'(X0,'==>'(X0,'+'(X1,X2))),X1),
inference(resolution,[status(thm)],[f153,f143]) ).
fof(f653,plain,
! [X0] :
( X0 = '==>'('==>'(X0,'1'),X0)
| ~ '>='(X0,'==>'('==>'(X0,'1'),X0)) ),
inference(resolution,[status(thm)],[f243,f24]) ).
fof(f662,plain,
! [X0] : X0 = '==>'('==>'(X0,'1'),X0),
inference(forward_subsumption_resolution,[status(thm)],[f653,f166]) ).
fof(f3341,plain,
! [X0,X1,X2] : '>='('==>'(X0,'+'(X1,X2)),'==>'(X0,X1)),
inference(resolution,[status(thm)],[f598,f27]) ).
fof(f3731,plain,
! [X0,X1] :
( '==>'('==>'(X0,'1'),X0) = '==>'(X1,X0)
| ~ '>='(X0,'==>'(X1,X0))
| ~ '>='('==>'(X0,'1'),X1) ),
inference(paramodulation,[status(thm)],[f662,f247]) ).
fof(f3752,plain,
! [X0,X1] :
( X0 = '==>'(X1,X0)
| ~ '>='(X0,'==>'(X1,X0))
| ~ '>='('==>'(X0,'1'),X1) ),
inference(forward_demodulation,[status(thm)],[f662,f3731]) ).
fof(f3753,plain,
! [X0,X1] :
( X0 = '==>'(X1,X0)
| ~ '>='('==>'(X0,'1'),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3752,f166]) ).
fof(f5200,plain,
! [X0,X1] : '0' = '==>'(X0,'==>'(X1,'+'(X1,'+'(X0,'0')))),
inference(resolution,[status(thm)],[f119,f94]) ).
fof(f5245,plain,
! [X0,X1] : '0' = '==>'(X0,'==>'(X1,'+'(X1,X0))),
inference(forward_demodulation,[status(thm)],[f18,f5200]) ).
fof(f5423,plain,
! [X0,X1] : '0' = '==>'(X0,'==>'(X1,'+'(X0,X1))),
inference(paramodulation,[status(thm)],[f17,f5245]) ).
fof(f10459,plain,
! [X0,X1] : '>='('==>'(X0,'1'),'==>'(X0,X1)),
inference(paramodulation,[status(thm)],[f367,f3341]) ).
fof(f11501,plain,
! [X0,X1] : X0 = '==>'('==>'(X0,X1),X0),
inference(resolution,[status(thm)],[f3753,f10459]) ).
fof(f11578,plain,
! [X0,X1] : '==>'(X0,X1) = '==>'(X0,'==>'(X0,X1)),
inference(paramodulation,[status(thm)],[f11501,f11501]) ).
fof(f11745,plain,
! [X0] : '==>'(X0,'+'(X0,X0)) = '0',
inference(paramodulation,[status(thm)],[f5423,f11578]) ).
fof(f11920,plain,
! [X0] :
( '+'(X0,X0) = '+'(X0,'==>'(X0,'+'(X0,X0)))
| ~ '>='('+'(X0,X0),'+'(X0,'0')) ),
inference(paramodulation,[status(thm)],[f11745,f235]) ).
fof(f12000,plain,
! [X0] :
( '+'(X0,X0) = '+'(X0,'==>'(X0,'+'(X0,X0)))
| ~ '>='('+'(X0,X0),X0) ),
inference(forward_demodulation,[status(thm)],[f18,f11920]) ).
fof(f12001,plain,
! [X0] :
( '+'(X0,X0) = '+'(X0,'0')
| ~ '>='('+'(X0,X0),X0) ),
inference(forward_demodulation,[status(thm)],[f11745,f12000]) ).
fof(f12002,plain,
! [X0] :
( '+'(X0,X0) = X0
| ~ '>='('+'(X0,X0),X0) ),
inference(forward_demodulation,[status(thm)],[f18,f12001]) ).
fof(f12003,plain,
! [X0] : '+'(X0,X0) = X0,
inference(forward_subsumption_resolution,[status(thm)],[f12002,f159]) ).
fof(f12042,plain,
sK0_skl != sK0_skl,
inference(backward_demodulation,[status(thm)],[f12003,f43]) ).
fof(f12227,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f12042]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL903+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n008.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 01:11:39 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Drodi V4.1.1
% 5.95/1.28 % Refutation found
% 5.95/1.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.95/1.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.95/1.31 % Elapsed time: 0.873930 seconds
% 5.95/1.31 % CPU time: 6.586660 seconds
% 5.95/1.31 % Total memory used: 91.666 MB
% 5.95/1.31 % Net memory used: 88.907 MB
%------------------------------------------------------------------------------