%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL893+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 : n001.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 01:09:02 PM UTC 2026
% Result : Theorem 0.15s 0.80s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 48 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 14 ~; 10 |; 5 &)
% ( 1 <=>; 3 =>; 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; 2 con; 0-2 aty)
% Number of variables : 37 ( 36 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] : '+'(A,'0') = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : '>='(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X3,X4] :
( ( '>='(X4,X3)
& '>='(X3,X4) )
=> X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X5,X6,X7] :
( '>='('+'(X5,X6),X7)
<=> '>='(X6,'==>'(X5,X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : '>='(A,'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : h(A) = '==>'(h(A),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [X17] :
( h(X17) = X17
=> X17 = '0' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [X17] :
( h(X17) = X17
=> X17 = '0' ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f19,plain,
! [X0] : '+'(X0,'0') = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0] : '>='(X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f25,plain,
! [X3,X4] :
( X3 = X4
| ~ '>='(X4,X3)
| ~ '>='(X3,X4) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ~ '>='(X1,X0)
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X5,X6,X7] :
( ( ~ '>='(X6,'==>'(X5,X7))
| '>='('+'(X5,X6),X7) )
& ( '>='(X6,'==>'(X5,X7))
| ~ '>='('+'(X5,X6),X7) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f28,plain,
( ! [X5,X6,X7] :
( ~ '>='(X6,'==>'(X5,X7))
| '>='('+'(X5,X6),X7) )
& ! [X5,X6,X7] :
( '>='(X6,'==>'(X5,X7))
| ~ '>='('+'(X5,X6),X7) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( '>='(X1,'==>'(X0,X2))
| ~ '>='('+'(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,plain,
! [X0] : '>='(X0,'0'),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
! [X0] : h(X0) = '==>'(h(X0),X0),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f43,plain,
? [X17] :
( X17 != '0'
& h(X17) = X17 ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f44,plain,
( sK0_skl != '0'
& h(sK0_skl) = sK0_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X17,sK0_skl)],[f43]) ).
fof(f45,plain,
h(sK0_skl) = sK0_skl,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
sK0_skl != '0',
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f97,plain,
h(sK0_skl) = '==>'(sK0_skl,sK0_skl),
inference(paramodulation,[status(thm)],[f45,f42]) ).
fof(f98,plain,
sK0_skl = '==>'(sK0_skl,sK0_skl),
inference(forward_demodulation,[status(thm)],[f45,f97]) ).
fof(f99,plain,
! [X0] :
( '0' = X0
| ~ '>='('0',X0) ),
inference(resolution,[status(thm)],[f26,f31]) ).
fof(f102,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'+'(X1,X0))),
inference(resolution,[status(thm)],[f29,f21]) ).
fof(f127,plain,
! [X0] : '0' = '==>'(X0,'+'(X0,'0')),
inference(resolution,[status(thm)],[f102,f99]) ).
fof(f139,plain,
! [X0] : '0' = '==>'(X0,X0),
inference(forward_demodulation,[status(thm)],[f19,f127]) ).
fof(f140,plain,
sK0_skl = '0',
inference(backward_demodulation,[status(thm)],[f139,f98]) ).
fof(f144,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f140,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL893+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.75 % Computer : n001.cluster.edu
% 0.11/0.75 % Model : x86_64 x86_64
% 0.11/0.75 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.75 % Memory : 8046.5625MB
% 0.11/0.75 % OS : Linux 6.8.0-71-generic
% 0.11/0.75 % CPULimit : 300
% 0.11/0.75 % WCLimit : 300
% 0.11/0.75 % DateTime : Mon Sep 21 01:16:00 UTC 2026
% 0.11/0.75 % CPUTime :
% 0.11/0.76 % Drodi V4.1.1
% 0.15/0.80 % Refutation found
% 0.15/0.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.83 % Elapsed time: 0.059859 seconds
% 0.15/0.83 % CPU time: 0.158957 seconds
% 0.15/0.83 % Total memory used: 66.717 MB
% 0.15/0.83 % Net memory used: 66.341 MB
%------------------------------------------------------------------------------