%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL138-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 01:06:54 PM UTC 2026
% Result : Unsatisfiable 103.95s 13.70s
% Output : CNFRefutation 81.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 4
% Syntax : Number of formulae : 73 ( 73 unt; 0 def)
% Number of atoms : 73 ( 72 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 188 ( 188 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : implies(truth,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
implies(x,implies(y,z)) != implies(y,implies(x,z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0] : implies(truth,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
implies(x,implies(y,z)) != implies(y,implies(x,z)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(paramodulation,[status(thm)],[f6,f8]) ).
fof(f825,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f857,plain,
! [X0,X1] : implies(implies(X0,truth),implies(X1,implies(X0,X1))) = truth,
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f877,plain,
! [X0,X1,X2] : implies(implies(X0,implies(X1,X2)),implies(implies(implies(X2,X1),X1),implies(X0,X2))) = truth,
inference(paramodulation,[status(thm)],[f8,f7]) ).
fof(f903,plain,
! [X0,X1,X2] : implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X0)),implies(X2,X0)) = implies(truth,implies(implies(X0,X1),implies(X2,X1))),
inference(paramodulation,[status(thm)],[f7,f8]) ).
fof(f905,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f6,f825]) ).
fof(f930,plain,
! [X0,X1,X2] : implies(implies(implies(implies(X0,X1),implies(X2,X1)),implies(X2,X0)),implies(X2,X0)) = implies(implies(X0,X1),implies(X2,X1)),
inference(forward_demodulation,[status(thm)],[f6,f903]) ).
fof(f969,plain,
! [X0] : implies(implies(truth,X0),X0) = truth,
inference(paramodulation,[status(thm)],[f6,f905]) ).
fof(f977,plain,
! [X0] : implies(X0,implies(X0,X0)) = truth,
inference(paramodulation,[status(thm)],[f20,f905]) ).
fof(f1009,plain,
! [X0,X1,X2] : implies(truth,implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))) = truth,
inference(paramodulation,[status(thm)],[f905,f7]) ).
fof(f1124,plain,
! [X0] : implies(X0,X0) = truth,
inference(forward_demodulation,[status(thm)],[f6,f969]) ).
fof(f1146,plain,
! [X0,X1] : implies(truth,implies(X0,implies(X1,X0))) = truth,
inference(backward_demodulation,[status(thm)],[f1147,f857]) ).
fof(f1147,plain,
! [X0] : implies(X0,truth) = truth,
inference(forward_demodulation,[status(thm)],[f1124,f977]) ).
fof(f1209,plain,
! [X0,X1,X2] : implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2)) = truth,
inference(forward_demodulation,[status(thm)],[f6,f1009]) ).
fof(f1645,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = truth,
inference(forward_demodulation,[status(thm)],[f6,f1146]) ).
fof(f1702,plain,
! [X0,X1] : implies(implies(implies(X0,X1),X1),X1) = implies(truth,implies(X0,X1)),
inference(paramodulation,[status(thm)],[f1645,f8]) ).
fof(f1708,plain,
! [X0,X1] : implies(implies(implies(X0,X1),X1),X1) = implies(X0,X1),
inference(forward_demodulation,[status(thm)],[f6,f1702]) ).
fof(f1864,plain,
! [X0,X1,X2] : implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(X2,implies(X1,X0))),implies(X2,implies(X1,X0))) = implies(implies(implies(X1,X0),X0),implies(X2,X0)),
inference(paramodulation,[status(thm)],[f8,f930]) ).
fof(f1868,plain,
! [X0,X1,X2] : implies(implies(implies(truth,implies(X0,implies(X1,X2))),implies(X0,X2)),implies(X0,X2)) = implies(implies(X2,implies(X1,X2)),implies(X0,implies(X1,X2))),
inference(paramodulation,[status(thm)],[f1645,f930]) ).
fof(f1975,plain,
! [X0,X1,X2] : implies(implies(implies(X0,implies(X1,X2)),implies(X0,X2)),implies(X0,X2)) = implies(implies(X2,implies(X1,X2)),implies(X0,implies(X1,X2))),
inference(forward_demodulation,[status(thm)],[f6,f1868]) ).
fof(f1976,plain,
! [X0,X1,X2] : implies(implies(implies(X0,implies(X1,X2)),implies(X0,X2)),implies(X0,X2)) = implies(truth,implies(X0,implies(X1,X2))),
inference(forward_demodulation,[status(thm)],[f1645,f1975]) ).
fof(f1977,plain,
! [X0,X1,X2] : implies(implies(implies(X0,implies(X1,X2)),implies(X0,X2)),implies(X0,X2)) = implies(X0,implies(X1,X2)),
inference(forward_demodulation,[status(thm)],[f6,f1976]) ).
fof(f3001,plain,
! [X0,X1,X2] : implies(implies(implies(X0,implies(X1,implies(X2,X0))),truth),implies(X0,implies(X2,X0))) = implies(X0,implies(X1,implies(X2,X0))),
inference(paramodulation,[status(thm)],[f1645,f1977]) ).
fof(f3194,plain,
! [X0,X1,X2] : implies(truth,implies(X0,implies(X1,X0))) = implies(X0,implies(X2,implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f1147,f3001]) ).
fof(f3195,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X0)) = implies(X0,implies(X2,implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f6,f3194]) ).
fof(f3196,plain,
! [X0,X1,X2] : truth = implies(X0,implies(X1,implies(X2,X0))),
inference(forward_demodulation,[status(thm)],[f1645,f3195]) ).
fof(f3984,plain,
! [X0,X1,X2] : implies(implies(implies(implies(X0,X1),X1),implies(X2,X1)),implies(implies(implies(X1,X2),X2),implies(X0,X1))) = truth,
inference(paramodulation,[status(thm)],[f1708,f877]) ).
fof(f3988,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),implies(X2,X1)),implies(implies(implies(X1,X2),X2),implies(implies(X1,X0),X0))) = truth,
inference(paramodulation,[status(thm)],[f8,f877]) ).
fof(f4046,plain,
! [X0,X1,X2] : implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X0)),implies(X2,implies(X1,X0))),implies(X2,implies(X1,X0))) = implies(truth,implies(implies(implies(X0,X1),X1),implies(X2,X0))),
inference(paramodulation,[status(thm)],[f877,f8]) ).
fof(f4287,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),X1),implies(X2,X1)) = implies(truth,implies(implies(implies(X1,X0),X0),implies(X2,X1))),
inference(forward_demodulation,[status(thm)],[f1864,f4046]) ).
fof(f4288,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),X1),implies(X2,X1)) = implies(implies(implies(X1,X0),X0),implies(X2,X1)),
inference(forward_demodulation,[status(thm)],[f6,f4287]) ).
fof(f4345,plain,
! [X0,X1,X2] : implies(implies(implies(implies(X0,X1),X1),implies(implies(X1,X2),X2)),implies(implies(implies(X1,implies(X2,X1)),implies(X2,X1)),implies(X0,X1))) = truth,
inference(paramodulation,[status(thm)],[f8,f3984]) ).
fof(f4589,plain,
! [X0,X1,X2] : implies(implies(implies(implies(X0,X1),X1),implies(implies(X1,X2),X2)),implies(implies(implies(implies(X2,X1),X1),X1),implies(X0,X1))) = truth,
inference(forward_demodulation,[status(thm)],[f4288,f4345]) ).
fof(f4590,plain,
! [X0,X1,X2] : implies(implies(implies(implies(X0,X1),X1),implies(implies(X1,X2),X2)),implies(implies(X2,X1),implies(X0,X1))) = truth,
inference(forward_demodulation,[status(thm)],[f1708,f4589]) ).
fof(f5616,plain,
! [X0,X1,X2] : implies(implies(implies(implies(implies(X0,X1),X1),implies(implies(X0,X2),X2)),implies(implies(X2,X0),implies(X1,X0))),implies(implies(X2,X0),implies(X1,X0))) = implies(truth,implies(implies(implies(X0,X1),X1),implies(implies(X0,X2),X2))),
inference(paramodulation,[status(thm)],[f3988,f8]) ).
fof(f6024,plain,
! [X0,X1,X2] : implies(implies(implies(implies(implies(X0,X1),X1),implies(implies(X0,X2),X2)),implies(implies(X2,X0),implies(X1,X0))),implies(implies(X2,X0),implies(X1,X0))) = implies(implies(implies(X0,X1),X1),implies(implies(X0,X2),X2)),
inference(forward_demodulation,[status(thm)],[f6,f5616]) ).
fof(f6036,plain,
! [X0,X1,X2] : implies(implies(implies(implies(X0,X1),X1),implies(implies(X0,X2),X2)),implies(implies(X2,X0),implies(X1,X0))) = truth,
inference(paramodulation,[status(thm)],[f8,f4590]) ).
fof(f6239,plain,
! [X0,X1,X2] : implies(truth,implies(implies(X0,X1),implies(X2,X1))) = implies(implies(implies(X1,X2),X2),implies(implies(X1,X0),X0)),
inference(backward_demodulation,[status(thm)],[f6036,f6024]) ).
fof(f6685,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(X2,X1)) = implies(implies(implies(X1,X2),X2),implies(implies(X1,X0),X0)),
inference(forward_demodulation,[status(thm)],[f6,f6239]) ).
fof(f6713,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(X2,X1)) = implies(implies(implies(X2,X1),X1),implies(implies(X1,X0),X0)),
inference(paramodulation,[status(thm)],[f8,f6685]) ).
fof(f6739,plain,
! [X0,X1,X2,X3] : implies(implies(X0,X1),implies(implies(X2,implies(X3,X1)),X1)) = implies(implies(truth,implies(X2,implies(X3,X1))),implies(implies(X1,X0),X0)),
inference(paramodulation,[status(thm)],[f3196,f6685]) ).
fof(f6748,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(X2,X1)) = implies(implies(implies(X1,X2),X2),implies(implies(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f8,f6685]) ).
fof(f6956,plain,
! [X0,X1,X2,X3] : implies(implies(X0,X1),implies(implies(X2,implies(X3,X1)),X1)) = implies(implies(X2,implies(X3,X1)),implies(implies(X1,X0),X0)),
inference(forward_demodulation,[status(thm)],[f6,f6739]) ).
fof(f7257,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),X1),implies(X2,X1)) = implies(implies(implies(X2,X1),X1),implies(truth,implies(X0,X1))),
inference(paramodulation,[status(thm)],[f1645,f6713]) ).
fof(f7497,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),X1),implies(X2,X1)) = implies(implies(implies(X2,X1),X1),implies(X0,X1)),
inference(forward_demodulation,[status(thm)],[f6,f7257]) ).
fof(f7600,plain,
! [X0,X1,X2,X3] : implies(implies(X0,X1),implies(implies(X2,implies(X3,X1)),X1)) = implies(implies(truth,implies(X2,implies(X3,X1))),implies(implies(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f3196,f6748]) ).
fof(f7601,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(implies(X2,X1),X1)) = implies(implies(truth,implies(X2,X1)),implies(implies(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f1645,f6748]) ).
fof(f7842,plain,
! [X0,X1,X2,X3] : implies(implies(X0,X1),implies(implies(X2,implies(X3,X1)),X1)) = implies(implies(X2,implies(X3,X1)),implies(implies(X0,X1),X1)),
inference(forward_demodulation,[status(thm)],[f6,f7600]) ).
fof(f7843,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(implies(X2,X1),X1)) = implies(implies(X2,X1),implies(implies(X0,X1),X1)),
inference(forward_demodulation,[status(thm)],[f6,f7601]) ).
fof(f11180,plain,
! [X0,X1,X2] : implies(truth,implies(implies(X0,implies(X1,X2)),implies(X1,X2))) = implies(implies(X0,implies(X1,X2)),implies(implies(X2,implies(X1,X2)),implies(X1,X2))),
inference(paramodulation,[status(thm)],[f1645,f7843]) ).
fof(f11603,plain,
! [X0,X1,X2] : implies(implies(X0,implies(X1,X2)),implies(X1,X2)) = implies(implies(X0,implies(X1,X2)),implies(implies(X2,implies(X1,X2)),implies(X1,X2))),
inference(forward_demodulation,[status(thm)],[f6,f11180]) ).
fof(f11606,plain,
! [X0,X1,X2] : implies(implies(X0,implies(X1,X2)),implies(X1,X2)) = implies(implies(implies(X1,X2),X2),implies(implies(X0,implies(X1,X2)),X2)),
inference(forward_demodulation,[status(thm)],[f6956,f11603]) ).
fof(f12171,plain,
! [X0,X1,X2] : implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X1)),implies(X0,implies(X2,X1))),implies(X0,implies(X2,X1))) = implies(implies(implies(X2,X1),X1),implies(X0,X1)),
inference(paramodulation,[status(thm)],[f7497,f930]) ).
fof(f12180,plain,
! [X0,X1,X2] : implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X1)),implies(implies(implies(X2,X1),X1),X1)),implies(implies(implies(X2,X1),X1),X1)) = implies(implies(implies(X2,X1),X1),implies(X0,X1)),
inference(paramodulation,[status(thm)],[f7497,f1977]) ).
fof(f12779,plain,
! [X0,X1,X2] : implies(truth,implies(X0,implies(X1,X2))) = implies(implies(implies(X1,X2),X2),implies(X0,X2)),
inference(forward_demodulation,[status(thm)],[f1209,f12171]) ).
fof(f12873,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(implies(implies(X1,X2),X2),implies(X0,X2)),
inference(forward_demodulation,[status(thm)],[f6,f12779]) ).
fof(f12902,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),X1),implies(implies(implies(implies(implies(X2,X1),X1),implies(X0,X1)),implies(implies(implies(X0,X1),X1),X1)),X1)) = implies(implies(implies(X0,X1),X1),implies(X2,X1)),
inference(forward_demodulation,[status(thm)],[f7842,f12180]) ).
fof(f12903,plain,
! [X0,X1,X2] : implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X1)),implies(implies(implies(X2,X1),X1),X1)),implies(X2,X1)) = implies(implies(implies(X2,X1),X1),implies(X0,X1)),
inference(forward_demodulation,[status(thm)],[f12873,f12902]) ).
fof(f12904,plain,
! [X0,X1,X2] : implies(implies(implies(implies(X0,X1),X1),implies(implies(implies(implies(X2,X1),X1),implies(X0,X1)),X1)),implies(X0,X1)) = implies(implies(implies(X0,X1),X1),implies(X2,X1)),
inference(forward_demodulation,[status(thm)],[f7842,f12903]) ).
fof(f12905,plain,
! [X0,X1,X2] : implies(implies(implies(implies(implies(X0,X1),X1),implies(X2,X1)),implies(X2,X1)),implies(X2,X1)) = implies(implies(implies(X2,X1),X1),implies(X0,X1)),
inference(forward_demodulation,[status(thm)],[f11606,f12904]) ).
fof(f12906,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),X1),implies(X2,X1)) = implies(implies(implies(X2,X1),X1),implies(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1708,f12905]) ).
fof(f12907,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(implies(implies(X0,X2),X2),implies(X1,X2)),
inference(forward_demodulation,[status(thm)],[f12873,f12906]) ).
fof(f12917,plain,
implies(x,implies(y,z)) != implies(x,implies(y,z)),
inference(backward_demodulation,[status(thm)],[f13586,f10]) ).
fof(f13586,plain,
! [X0,X1,X2] : implies(X0,implies(X1,X2)) = implies(X1,implies(X0,X2)),
inference(forward_demodulation,[status(thm)],[f12873,f12907]) ).
fof(f14316,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f12917]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL138-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n005.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 00:07:03 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.46 % Drodi V4.1.1
% 103.95/13.70 % Refutation found
% 103.95/13.70 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 103.95/13.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.13/17.24 % Elapsed time: 16.780043 seconds
% 11.13/17.24 % CPU time: 122.586768 seconds
% 11.13/17.24 % Total memory used: 18.702 GB
% 11.13/17.24 % Net memory used: 18.687 GB
%------------------------------------------------------------------------------