%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO072-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 12:06:38 PM UTC 2026
% Result : Unsatisfiable 77.80s 10.34s
% Output : CNFRefutation 49.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 49 unt; 2 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,D)))))))) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
add(b,a) != add(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2,X3] : inverse(add(inverse(add(inverse(add(X0,X1)),X2)),inverse(add(X0,inverse(add(inverse(X2),inverse(add(X2,X3)))))))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
add(b,a) != add(a,b),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF0_fnc = add(b,a),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f6,definition,
sF1_fnc = add(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f7,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f4,f6,f5]) ).
fof(f10,plain,
! [X0,X1] : inverse(add(inverse(add(inverse(sF1_fnc),X0)),inverse(add(a,inverse(add(inverse(X0),inverse(add(X0,X1)))))))) = X0,
inference(paramodulation,[status(thm)],[f6,f3]) ).
fof(f12,plain,
! [X0,X1,X2] : inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(X0)),X1)),X0)),X2)),inverse(X0))),X0)) = inverse(X0),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f16,plain,
! [X0,X1] : inverse(add(inverse(add(inverse(add(X0,X1)),b)),inverse(add(X0,inverse(add(inverse(b),inverse(sF0_fnc))))))) = b,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f25,plain,
! [X0,X1,X2] : inverse(add(inverse(add(X0,X1)),inverse(add(inverse(add(inverse(sF1_fnc),X0)),inverse(add(inverse(X1),inverse(add(X1,X2)))))))) = X1,
inference(paramodulation,[status(thm)],[f10,f3]) ).
fof(f1180,plain,
! [X0] : inverse(add(inverse(add(X0,inverse(X0))),X0)) = inverse(X0),
inference(paramodulation,[status(thm)],[f3,f12]) ).
fof(f1412,plain,
! [X0,X1] : inverse(add(inverse(X0),inverse(add(X0,inverse(add(inverse(X0),inverse(add(X0,X1)))))))) = X0,
inference(paramodulation,[status(thm)],[f1180,f3]) ).
fof(f1596,plain,
! [X0,X1,X2] : inverse(add(inverse(add(inverse(add(X0,X1)),X2)),inverse(add(X0,X2)))) = X2,
inference(paramodulation,[status(thm)],[f1412,f3]) ).
fof(f6535,plain,
! [X0,X1] : inverse(add(inverse(add(X0,X1)),inverse(add(inverse(X0),X1)))) = X1,
inference(paramodulation,[status(thm)],[f1412,f1596]) ).
fof(f6828,plain,
! [X0] : inverse(add(inverse(add(add(X0,inverse(X0)),X0)),inverse(X0))) = X0,
inference(paramodulation,[status(thm)],[f1180,f6535]) ).
fof(f7130,plain,
! [X0] : inverse(add(X0,inverse(add(add(X0,inverse(X0)),inverse(X0))))) = inverse(X0),
inference(paramodulation,[status(thm)],[f6828,f1596]) ).
fof(f7634,plain,
! [X0,X1] : inverse(add(inverse(add(inverse(X0),X1)),inverse(add(X0,X1)))) = X1,
inference(paramodulation,[status(thm)],[f7130,f1596]) ).
fof(f8107,plain,
inverse(add(inverse(add(inverse(b),a)),inverse(sF0_fnc))) = a,
inference(paramodulation,[status(thm)],[f5,f7634]) ).
fof(f8807,plain,
inverse(add(a,inverse(add(inverse(b),inverse(sF0_fnc))))) = inverse(sF0_fnc),
inference(paramodulation,[status(thm)],[f8107,f1596]) ).
fof(f11176,plain,
! [X0,X1,X2] : inverse(add(inverse(add(X0,X1)),inverse(add(inverse(add(X2,X0)),X1)))) = X1,
inference(paramodulation,[status(thm)],[f25,f1596]) ).
fof(f12037,plain,
inverse(add(inverse(add(inverse(sF0_fnc),b)),inverse(add(a,inverse(add(inverse(b),inverse(sF0_fnc))))))) = b,
inference(paramodulation,[status(thm)],[f8807,f16]) ).
fof(f12111,plain,
inverse(add(inverse(add(inverse(sF0_fnc),b)),inverse(sF0_fnc))) = b,
inference(forward_demodulation,[status(thm)],[f8807,f12037]) ).
fof(f13992,plain,
! [X0] : inverse(add(inverse(add(inverse(X0),X0)),inverse(X0))) = X0,
inference(paramodulation,[status(thm)],[f12,f11176]) ).
fof(f14436,plain,
! [X0] : inverse(add(X0,inverse(add(inverse(X0),inverse(X0))))) = inverse(X0),
inference(paramodulation,[status(thm)],[f13992,f1596]) ).
fof(f14998,plain,
! [X0] : inverse(add(inverse(X0),inverse(add(X0,inverse(add(inverse(X0),inverse(X0))))))) = X0,
inference(paramodulation,[status(thm)],[f14436,f1412]) ).
fof(f15388,plain,
! [X0] : inverse(add(inverse(X0),inverse(X0))) = X0,
inference(forward_demodulation,[status(thm)],[f14436,f14998]) ).
fof(f15444,plain,
! [X0] : inverse(add(X0,X0)) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f15388,f14436]) ).
fof(f15447,plain,
inverse(add(inverse(sF0_fnc),inverse(add(a,inverse(add(inverse(b),inverse(sF0_fnc))))))) = add(a,inverse(add(inverse(b),inverse(sF0_fnc)))),
inference(paramodulation,[status(thm)],[f8807,f15388]) ).
fof(f15716,plain,
inverse(add(inverse(sF0_fnc),inverse(sF0_fnc))) = add(a,inverse(add(inverse(b),inverse(sF0_fnc)))),
inference(forward_demodulation,[status(thm)],[f8807,f15447]) ).
fof(f15717,plain,
sF0_fnc = add(a,inverse(add(inverse(b),inverse(sF0_fnc)))),
inference(forward_demodulation,[status(thm)],[f15388,f15716]) ).
fof(f15995,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f15444,f15388]) ).
fof(f16076,plain,
! [X0,X1] : inverse(add(inverse(add(inverse(add(X0,X1)),X0)),inverse(X0))) = X0,
inference(paramodulation,[status(thm)],[f15444,f1596]) ).
fof(f16376,plain,
! [X0,X1] : inverse(X0) = add(inverse(add(inverse(X1),X0)),inverse(add(X1,X0))),
inference(paramodulation,[status(thm)],[f7634,f15995]) ).
fof(f32246,plain,
! [X0,X1] : inverse(add(X0,inverse(inverse(add(X1,X0))))) = inverse(add(X1,X0)),
inference(paramodulation,[status(thm)],[f1596,f16076]) ).
fof(f32511,plain,
! [X0,X1] : inverse(add(X0,add(X1,X0))) = inverse(add(X1,X0)),
inference(forward_demodulation,[status(thm)],[f15995,f32246]) ).
fof(f33598,plain,
! [X0,X1] : inverse(inverse(add(X0,X1))) = add(X1,add(X0,X1)),
inference(paramodulation,[status(thm)],[f32511,f15995]) ).
fof(f33749,plain,
! [X0,X1] : add(X0,X1) = add(X1,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f15995,f33598]) ).
fof(f36707,plain,
! [X0,X1] : add(inverse(add(inverse(X0),X1)),inverse(add(X0,X1))) = add(inverse(add(X0,X1)),inverse(X1)),
inference(paramodulation,[status(thm)],[f16376,f33749]) ).
fof(f37106,plain,
! [X0,X1] : inverse(X0) = add(inverse(add(X1,X0)),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f16376,f36707]) ).
fof(f37397,plain,
! [X0,X1] : inverse(inverse(X0)) = add(inverse(add(X1,inverse(X0))),X0),
inference(paramodulation,[status(thm)],[f15995,f37106]) ).
fof(f37666,plain,
! [X0,X1] : X0 = add(inverse(add(X1,inverse(X0))),X0),
inference(forward_demodulation,[status(thm)],[f15995,f37397]) ).
fof(f38191,plain,
! [X0,X1] : inverse(add(inverse(X0),inverse(add(X1,X0)))) = X0,
inference(paramodulation,[status(thm)],[f37666,f1596]) ).
fof(f42846,plain,
inverse(add(inverse(inverse(sF0_fnc)),b)) = inverse(sF0_fnc),
inference(paramodulation,[status(thm)],[f12111,f38191]) ).
fof(f43101,plain,
inverse(add(sF0_fnc,b)) = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f15995,f42846]) ).
fof(f45499,plain,
inverse(add(inverse(b),inverse(sF0_fnc))) = b,
inference(paramodulation,[status(thm)],[f43101,f38191]) ).
fof(f53469,plain,
sF0_fnc = add(a,b),
inference(backward_demodulation,[status(thm)],[f45499,f15717]) ).
fof(f53567,plain,
sF0_fnc = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f6,f53469]) ).
fof(f53568,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f53567,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO072-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 13:49:50 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 77.80/10.34 % Refutation found
% 77.80/10.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 77.80/10.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 67.39/10.70 % Elapsed time: 10.220139 seconds
% 67.39/10.70 % CPU time: 79.424130 seconds
% 67.39/10.70 % Total memory used: 1.449 GB
% 67.39/10.70 % Net memory used: 1.398 GB
%------------------------------------------------------------------------------