%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL899+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 : 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 : Thu Sep 24 01:09:03 PM UTC 2026
% Result : Theorem 0.21s 10.54s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 32 unt; 0 def)
% Number of atoms : 69 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 22 ~; 16 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 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 : 76 ( 75 !; 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(f9,axiom,
! [X8,X9,X10] :
( '>='(X8,X9)
=> '>='('+'(X8,X10),'+'(X9,X10)) ),
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,B] : '==>'('==>'(A,B),B) = '==>'('==>'(B,A),A),
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(f30,plain,
! [X8,X9,X10] :
( '>='('+'(X8,X10),'+'(X9,X10))
| ~ '>='(X8,X9) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
! [X8,X9] :
( ! [X10] : '>='('+'(X8,X10),'+'(X9,X10))
| ~ '>='(X8,X9) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( '>='('+'(X0,X2),'+'(X1,X2))
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f39,plain,
! [X0] : '+'(X0,'1') = '1',
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
! [X0,X1] : '==>'('==>'(X0,X1),X1) = '==>'('==>'(X1,X0),X0),
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(f58,plain,
! [X0] : '+'('0',X0) = X0,
inference(paramodulation,[status(thm)],[f17,f18]) ).
fof(f78,plain,
! [X0] :
( X0 = '0'
| ~ '>='('0',X0) ),
inference(resolution,[status(thm)],[f24,f29]) ).
fof(f85,plain,
! [X0] : '+'('1',X0) = '1',
inference(paramodulation,[status(thm)],[f17,f39]) ).
fof(f110,plain,
! [X0,X1] :
( '>='(X1,'==>'('1',X0))
| ~ '>='('1',X0) ),
inference(paramodulation,[status(thm)],[f85,f27]) ).
fof(f115,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(resolution,[status(thm)],[f28,f19]) ).
fof(f118,plain,
! [X0,X1] : '>='('+'(X0,X1),'+'('0',X1)),
inference(resolution,[status(thm)],[f32,f29]) ).
fof(f120,plain,
! [X0,X1] : '>='('+'(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f58,f118]) ).
fof(f121,plain,
! [X0,X1] : '>='(X0,'==>'(X1,X0)),
inference(resolution,[status(thm)],[f120,f27]) ).
fof(f128,plain,
! [X0] : '>='('1',X0),
inference(paramodulation,[status(thm)],[f85,f120]) ).
fof(f136,plain,
! [X0,X1] : '>='(X0,'==>'('1',X1)),
inference(backward_subsumption_resolution,[status(thm)],[f110,f128]) ).
fof(f377,plain,
! [X0] : '==>'('1',X0) = '0',
inference(resolution,[status(thm)],[f136,f78]) ).
fof(f443,plain,
! [X0] : '==>'('==>'(X0,'1'),'1') = '==>'('0',X0),
inference(paramodulation,[status(thm)],[f377,f40]) ).
fof(f447,plain,
'==>'('0',sK0_skl) != sK0_skl,
inference(backward_demodulation,[status(thm)],[f443,f43]) ).
fof(f519,plain,
! [X0] : '>='('==>'('0',X0),X0),
inference(paramodulation,[status(thm)],[f58,f115]) ).
fof(f560,plain,
! [X0] :
( X0 = '==>'('0',X0)
| ~ '>='(X0,'==>'('0',X0)) ),
inference(resolution,[status(thm)],[f519,f24]) ).
fof(f568,plain,
sK0_skl != sK0_skl,
inference(backward_demodulation,[status(thm)],[f578,f447]) ).
fof(f578,plain,
! [X0] : X0 = '==>'('0',X0),
inference(forward_subsumption_resolution,[status(thm)],[f560,f121]) ).
fof(f580,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f568]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL899+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/10.49 % Computer : n020.cluster.edu
% 0.17/10.49 % Model : x86_64 x86_64
% 0.17/10.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.49 % Memory : 8046.5625MB
% 0.17/10.49 % OS : Linux 6.8.0-71-generic
% 0.17/10.49 % CPULimit : 300
% 0.17/10.49 % WCLimit : 300
% 0.17/10.49 % DateTime : Mon Sep 21 01:11:28 UTC 2026
% 0.17/10.49 % CPUTime :
% 0.21/10.50 % Drodi V4.1.1
% 0.21/10.54 % Refutation found
% 0.21/10.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/10.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/10.56 % Elapsed time: 0.060815 seconds
% 0.21/10.56 % CPU time: 0.267454 seconds
% 0.21/10.56 % Total memory used: 69.208 MB
% 0.21/10.56 % Net memory used: 68.631 MB
%------------------------------------------------------------------------------