%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP710-11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:35:12 PM UTC 2026
% Result : Unsatisfiable 1.40s 0.65s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 69 unt; 1 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 113 ( 113 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : mult(A,i(A)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(i(A),A) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [X5] : mult(X5,x4) != x3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X1,X2))) = mult(mult(mult(X0,X1),X1),X2),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0] : mult(X0,i(X0)) = unit,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0] : mult(i(X0),X0) = unit,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0] : mult(X0,x4) != x3,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,definition,
! [X0] : sF0_fnc(X0) = mult(X0,x4),
introduced(definition,[new_symbols(definition,[sF0_fnc(X0)])],[function_definition]) ).
fof(f14,plain,
! [X0] : sF0_fnc(X0) != x3,
inference(definition_folding,[],[f12,f13]) ).
fof(f15,plain,
! [X0,X1] : mult(X0,mult(X1,mult(X1,x4))) = sF0_fnc(mult(mult(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f13,f9]) ).
fof(f17,plain,
! [X0,X1] : mult(X0,mult(x4,mult(x4,X1))) = mult(sF0_fnc(mult(X0,x4)),X1),
inference(paramodulation,[status(thm)],[f13,f9]) ).
fof(f21,plain,
! [X0,X1] : mult(X0,mult(X1,sF0_fnc(X1))) = sF0_fnc(mult(mult(X0,X1),X1)),
inference(forward_demodulation,[status(thm)],[f13,f15]) ).
fof(f22,plain,
! [X0,X1] : mult(X0,mult(x4,mult(x4,X1))) = mult(sF0_fnc(sF0_fnc(X0)),X1),
inference(forward_demodulation,[status(thm)],[f13,f17]) ).
fof(f28,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X1,mult(X2,sF0_fnc(X2))))) = sF0_fnc(mult(mult(mult(mult(X0,X1),X1),X2),X2)),
inference(paramodulation,[status(thm)],[f21,f9]) ).
fof(f33,plain,
! [X0,X1,X2] : mult(X0,mult(X1,sF0_fnc(mult(mult(X1,X2),X2)))) = sF0_fnc(mult(mult(mult(mult(X0,X1),X1),X2),X2)),
inference(forward_demodulation,[status(thm)],[f21,f28]) ).
fof(f34,plain,
! [X0,X1,X2] : mult(X0,mult(X1,sF0_fnc(mult(mult(X1,X2),X2)))) = sF0_fnc(mult(mult(X0,mult(X1,mult(X1,X2))),X2)),
inference(forward_demodulation,[status(thm)],[f9,f33]) ).
fof(f345,plain,
! [X0,X1] : mult(X0,mult(X1,mult(X1,unit))) = mult(mult(X0,X1),X1),
inference(paramodulation,[status(thm)],[f9,f7]) ).
fof(f360,plain,
! [X0,X1] : mult(X0,mult(X1,X1)) = mult(mult(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f7,f345]) ).
fof(f387,plain,
! [X0] : sF0_fnc(mult(mult(unit,X0),X0)) = mult(X0,sF0_fnc(X0)),
inference(paramodulation,[status(thm)],[f21,f8]) ).
fof(f403,plain,
! [X0,X1] : mult(unit,mult(X0,mult(X0,X1))) = mult(mult(X0,X0),X1),
inference(paramodulation,[status(thm)],[f8,f9]) ).
fof(f405,plain,
! [X0] : sF0_fnc(mult(X0,X0)) = mult(X0,sF0_fnc(X0)),
inference(forward_demodulation,[status(thm)],[f8,f387]) ).
fof(f432,plain,
! [X0,X1] : mult(X0,mult(X0,X1)) = mult(mult(X0,X0),X1),
inference(forward_demodulation,[status(thm)],[f8,f403]) ).
fof(f454,plain,
! [X0,X1] : mult(X0,mult(i(X0),mult(i(X0),X1))) = mult(mult(unit,i(X0)),X1),
inference(paramodulation,[status(thm)],[f10,f9]) ).
fof(f462,plain,
! [X0,X1] : mult(X0,mult(i(X0),mult(i(X0),X1))) = mult(i(X0),X1),
inference(forward_demodulation,[status(thm)],[f8,f454]) ).
fof(f479,plain,
! [X0,X1] : mult(i(X0),mult(X0,mult(X0,X1))) = mult(mult(unit,X0),X1),
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f486,plain,
! [X0,X1] : mult(i(X0),mult(X0,mult(X0,X1))) = mult(X0,X1),
inference(forward_demodulation,[status(thm)],[f8,f479]) ).
fof(f489,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X1,X2))) = mult(mult(X0,mult(X1,X1)),X2),
inference(backward_demodulation,[status(thm)],[f360,f9]) ).
fof(f495,plain,
! [X0] : mult(i(X0),mult(X0,X0)) = mult(unit,X0),
inference(paramodulation,[status(thm)],[f11,f360]) ).
fof(f518,plain,
! [X0] : mult(i(X0),mult(X0,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f495]) ).
fof(f536,plain,
! [X0,X1] : mult(X0,mult(X1,mult(X1,x4))) = sF0_fnc(mult(X0,mult(X1,X1))),
inference(paramodulation,[status(thm)],[f13,f489]) ).
fof(f537,plain,
! [X0,X1] : mult(i(mult(X0,X0)),mult(X0,mult(X0,X1))) = mult(unit,X1),
inference(paramodulation,[status(thm)],[f11,f489]) ).
fof(f565,plain,
! [X0,X1] : mult(X0,mult(X1,sF0_fnc(X1))) = sF0_fnc(mult(X0,mult(X1,X1))),
inference(forward_demodulation,[status(thm)],[f13,f536]) ).
fof(f566,plain,
! [X0,X1] : mult(i(mult(X0,X0)),mult(X0,mult(X0,X1))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f537]) ).
fof(f785,plain,
! [X0] : mult(X0,mult(X0,i(mult(X0,X0)))) = unit,
inference(paramodulation,[status(thm)],[f10,f432]) ).
fof(f1090,plain,
! [X0,X1] : mult(X0,sF0_fnc(mult(X1,X1))) = sF0_fnc(mult(X0,mult(X1,X1))),
inference(forward_demodulation,[status(thm)],[f405,f565]) ).
fof(f1251,plain,
! [X0] : mult(X0,unit) = mult(sF0_fnc(sF0_fnc(X0)),i(mult(x4,x4))),
inference(paramodulation,[status(thm)],[f785,f22]) ).
fof(f1298,plain,
! [X0] : X0 = mult(sF0_fnc(sF0_fnc(X0)),i(mult(x4,x4))),
inference(forward_demodulation,[status(thm)],[f7,f1251]) ).
fof(f1299,plain,
! [X0] : X0 = mult(sF0_fnc(sF0_fnc(X0)),i(sF0_fnc(x4))),
inference(forward_demodulation,[status(thm)],[f13,f1298]) ).
fof(f1580,plain,
! [X0] : mult(i(mult(i(X0),i(X0))),mult(i(X0),X0)) = mult(X0,X0),
inference(paramodulation,[status(thm)],[f518,f566]) ).
fof(f1644,plain,
! [X0] : mult(i(mult(i(X0),i(X0))),unit) = mult(X0,X0),
inference(forward_demodulation,[status(thm)],[f11,f1580]) ).
fof(f1645,plain,
! [X0] : i(mult(i(X0),i(X0))) = mult(X0,X0),
inference(forward_demodulation,[status(thm)],[f7,f1644]) ).
fof(f2564,plain,
! [X0,X1] : mult(mult(X0,X0),mult(i(X0),mult(i(X0),X1))) = X1,
inference(paramodulation,[status(thm)],[f1645,f566]) ).
fof(f2590,plain,
! [X0,X1] : mult(X0,mult(X0,mult(i(X0),mult(i(X0),X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f432,f2564]) ).
fof(f2591,plain,
! [X0,X1] : mult(X0,mult(i(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f462,f2590]) ).
fof(f2655,plain,
! [X0] : mult(X0,sF0_fnc(i(X0))) = x4,
inference(paramodulation,[status(thm)],[f13,f2591]) ).
fof(f2656,plain,
! [X0,X1] : mult(mult(i(X0),i(X0)),mult(mult(X0,X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f1645,f2591]) ).
fof(f2691,plain,
! [X0,X1] : mult(i(X0),mult(i(X0),mult(mult(X0,X0),X1))) = X1,
inference(forward_demodulation,[status(thm)],[f432,f2656]) ).
fof(f2692,plain,
! [X0,X1] : mult(i(X0),mult(i(X0),mult(X0,mult(X0,X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f432,f2691]) ).
fof(f2693,plain,
! [X0,X1] : mult(i(X0),mult(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f486,f2692]) ).
fof(f2726,plain,
! [X0] : mult(mult(i(X0),i(X0)),sF0_fnc(mult(X0,X0))) = x4,
inference(paramodulation,[status(thm)],[f1645,f2655]) ).
fof(f2744,plain,
! [X0] : mult(i(X0),mult(i(X0),sF0_fnc(mult(X0,X0)))) = x4,
inference(forward_demodulation,[status(thm)],[f432,f2726]) ).
fof(f2745,plain,
! [X0] : mult(i(X0),sF0_fnc(mult(i(X0),mult(X0,X0)))) = x4,
inference(forward_demodulation,[status(thm)],[f1090,f2744]) ).
fof(f2746,plain,
! [X0] : mult(i(X0),sF0_fnc(X0)) = x4,
inference(forward_demodulation,[status(thm)],[f518,f2745]) ).
fof(f3366,plain,
! [X0,X1,X2] : mult(X0,mult(X1,sF0_fnc(mult(X1,mult(X2,X2))))) = sF0_fnc(mult(mult(X0,mult(X1,mult(X1,X2))),X2)),
inference(forward_demodulation,[status(thm)],[f360,f34]) ).
fof(f3389,plain,
! [X0,X1] : mult(X0,mult(i(X1),sF0_fnc(X1))) = sF0_fnc(mult(mult(X0,mult(i(X1),mult(i(X1),X1))),X1)),
inference(paramodulation,[status(thm)],[f2693,f3366]) ).
fof(f3502,plain,
! [X0,X1] : mult(X0,x4) = sF0_fnc(mult(mult(X0,mult(i(X1),mult(i(X1),X1))),X1)),
inference(forward_demodulation,[status(thm)],[f2746,f3389]) ).
fof(f3503,plain,
! [X0,X1] : sF0_fnc(X0) = sF0_fnc(mult(mult(X0,mult(i(X1),mult(i(X1),X1))),X1)),
inference(forward_demodulation,[status(thm)],[f13,f3502]) ).
fof(f3504,plain,
! [X0,X1] : sF0_fnc(X0) = sF0_fnc(mult(mult(X0,mult(i(X1),unit)),X1)),
inference(forward_demodulation,[status(thm)],[f11,f3503]) ).
fof(f3505,plain,
! [X0,X1] : sF0_fnc(X0) = sF0_fnc(mult(mult(X0,i(X1)),X1)),
inference(forward_demodulation,[status(thm)],[f7,f3504]) ).
fof(f3708,plain,
! [X0,X1] : mult(mult(X0,i(X1)),X1) = mult(sF0_fnc(sF0_fnc(X0)),i(sF0_fnc(x4))),
inference(paramodulation,[status(thm)],[f3505,f1299]) ).
fof(f3725,plain,
! [X0,X1] : mult(mult(X0,i(X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f1299,f3708]) ).
fof(f4146,plain,
! [X0] : sF0_fnc(mult(X0,i(x4))) = X0,
inference(paramodulation,[status(thm)],[f13,f3725]) ).
fof(f4231,plain,
! [X0] : X0 != x3,
inference(paramodulation,[status(thm)],[f4146,f14]) ).
fof(f4243,plain,
$false,
inference(destructive_equality_resolution,[status(thm)],[f4231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP710-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:37:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 1.40/0.65 % Refutation found
% 1.40/0.65 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.40/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.40/0.67 % Elapsed time: 0.295656 seconds
% 1.40/0.67 % CPU time: 2.216895 seconds
% 1.40/0.67 % Total memory used: 68.338 MB
% 1.40/0.67 % Net memory used: 66.818 MB
%------------------------------------------------------------------------------