%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP660-12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:35:02 PM UTC 2026
% Result : Unsatisfiable 8.93s 2.19s
% Output : CNFRefutation 13.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 8
% Syntax : Number of formulae : 81 ( 81 unt; 2 def)
% Number of atoms : 81 ( 80 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 101 ( 101 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
mult(rd(x1,x1),x0) != x0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),X2),X0) = mult(X0,mult(X1,mult(X2,X0))),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
mult(rd(x1,x1),x0) != x0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,definition,
sF1_fnc = rd(x1,x1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f14,definition,
sF0_fnc = mult(sF1_fnc,x0),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f15,plain,
sF0_fnc != x0,
inference(definition_folding,[],[f12,f14,f13]) ).
fof(f16,plain,
mult(sF1_fnc,x1) = x1,
inference(paramodulation,[status(thm)],[f13,f9]) ).
fof(f27,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,mult(X2,X0))),X0) = mult(mult(X0,X1),X2),
inference(paramodulation,[status(thm)],[f11,f10]) ).
fof(f29,plain,
! [X0,X1,X2] : rd(mult(X0,X1),X0) = mult(mult(X0,rd(X1,mult(X2,X0))),X2),
inference(paramodulation,[status(thm)],[f9,f27]) ).
fof(f31,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),X0) = mult(mult(X0,X1),rd(X2,X0)),
inference(paramodulation,[status(thm)],[f9,f27]) ).
fof(f44,plain,
! [X0,X1,X2] : rd(mult(X0,X1),X0) = mult(mult(X0,rd(X1,X2)),rd(X2,X0)),
inference(paramodulation,[status(thm)],[f9,f31]) ).
fof(f45,plain,
! [X0] : rd(mult(X0,x1),X0) = mult(mult(X0,sF1_fnc),rd(x1,X0)),
inference(paramodulation,[status(thm)],[f16,f31]) ).
fof(f67,plain,
rd(mult(x1,x1),x1) = mult(mult(x1,sF1_fnc),sF1_fnc),
inference(paramodulation,[status(thm)],[f13,f45]) ).
fof(f71,plain,
! [X0] : rd(rd(mult(X0,x1),X0),rd(x1,X0)) = mult(X0,sF1_fnc),
inference(paramodulation,[status(thm)],[f45,f10]) ).
fof(f72,plain,
x1 = mult(mult(x1,sF1_fnc),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f10,f67]) ).
fof(f80,plain,
rd(x1,sF1_fnc) = mult(x1,sF1_fnc),
inference(paramodulation,[status(thm)],[f72,f10]) ).
fof(f238,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f260,plain,
! [X0,X1,X2] : rd(mult(X0,X1),X0) = mult(mult(X0,X2),rd(ld(X2,X1),X0)),
inference(paramodulation,[status(thm)],[f7,f31]) ).
fof(f261,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(X2,mult(ld(X2,X0),mult(X1,X2))),
inference(paramodulation,[status(thm)],[f7,f11]) ).
fof(f262,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f7,f10]) ).
fof(f290,plain,
rd(rd(x1,sF1_fnc),rd(x1,sF1_fnc)) = mult(sF1_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f16,f71]) ).
fof(f297,plain,
rd(mult(x1,sF1_fnc),rd(x1,sF1_fnc)) = mult(sF1_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f80,f290]) ).
fof(f298,plain,
rd(mult(x1,sF1_fnc),mult(x1,sF1_fnc)) = mult(sF1_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f80,f297]) ).
fof(f390,plain,
! [X0,X1,X2] : rd(rd(mult(X0,X1),X0),rd(X2,X0)) = mult(X0,rd(X1,X2)),
inference(paramodulation,[status(thm)],[f44,f10]) ).
fof(f507,plain,
! [X0,X1,X2] : rd(mult(X0,X1),X0) = mult(X2,rd(ld(ld(X0,X2),X1),X0)),
inference(paramodulation,[status(thm)],[f7,f260]) ).
fof(f870,plain,
! [X0,X1] : rd(X0,rd(X1,X0)) = mult(X0,rd(X0,X1)),
inference(paramodulation,[status(thm)],[f10,f390]) ).
fof(f888,plain,
! [X0,X1,X2] : rd(rd(X0,X1),rd(X2,X1)) = mult(X1,rd(ld(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f7,f390]) ).
fof(f948,plain,
rd(sF1_fnc,mult(x1,sF1_fnc)) = mult(sF1_fnc,rd(sF1_fnc,x1)),
inference(paramodulation,[status(thm)],[f80,f870]) ).
fof(f959,plain,
! [X0,X1] : ld(mult(X0,rd(X0,X1)),X0) = rd(X1,X0),
inference(paramodulation,[status(thm)],[f870,f238]) ).
fof(f980,plain,
! [X0,X1] : ld(mult(mult(X0,X1),X0),mult(X0,X1)) = rd(X1,mult(X0,X1)),
inference(paramodulation,[status(thm)],[f10,f959]) ).
fof(f984,plain,
! [X0,X1] : ld(mult(X0,X1),X0) = rd(ld(X1,X0),X0),
inference(paramodulation,[status(thm)],[f262,f959]) ).
fof(f1012,plain,
! [X0,X1] : ld(ld(mult(X0,X1),X0),ld(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f984,f238]) ).
fof(f1089,plain,
ld(ld(x1,sF1_fnc),ld(x1,sF1_fnc)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f16,f1012]) ).
fof(f1091,plain,
! [X0,X1] : ld(ld(X0,X1),ld(ld(X1,X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f7,f1012]) ).
fof(f1171,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,X2)),X2) = mult(X2,mult(ld(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f9,f261]) ).
fof(f1373,plain,
! [X0,X1] : ld(X0,ld(ld(X1,rd(X1,X0)),X1)) = X1,
inference(paramodulation,[status(thm)],[f238,f1091]) ).
fof(f1434,plain,
! [X0,X1] : ld(mult(ld(ld(X0,rd(X0,X1)),X0),X1),ld(ld(X0,rd(X0,X1)),X0)) = rd(X0,ld(ld(X0,rd(X0,X1)),X0)),
inference(paramodulation,[status(thm)],[f1373,f984]) ).
fof(f1437,plain,
! [X0,X1] : mult(X0,X1) = ld(ld(X1,rd(X1,X0)),X1),
inference(paramodulation,[status(thm)],[f1373,f7]) ).
fof(f1449,plain,
! [X0,X1] : ld(mult(ld(ld(X0,rd(X0,X1)),X0),X1),ld(ld(X0,rd(X0,X1)),X0)) = ld(X0,rd(X0,X1)),
inference(forward_demodulation,[status(thm)],[f262,f1434]) ).
fof(f1454,plain,
! [X0,X1] : ld(mult(ld(ld(X0,rd(X0,X1)),X0),X1),mult(X1,X0)) = ld(X0,rd(X0,X1)),
inference(backward_demodulation,[status(thm)],[f1437,f1449]) ).
fof(f1457,plain,
! [X0,X1] : ld(mult(mult(X0,X1),X0),mult(X0,X1)) = ld(X1,rd(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1437,f1454]) ).
fof(f1458,plain,
ld(sF1_fnc,rd(sF1_fnc,x1)) = mult(sF1_fnc,rd(sF1_fnc,x1)),
inference(backward_demodulation,[status(thm)],[f1462,f948]) ).
fof(f1462,plain,
! [X0,X1] : rd(X0,mult(X1,X0)) = ld(X0,rd(X0,X1)),
inference(forward_demodulation,[status(thm)],[f980,f1457]) ).
fof(f1865,plain,
rd(mult(x1,ld(x1,sF1_fnc)),x1) = mult(sF1_fnc,rd(sF1_fnc,x1)),
inference(paramodulation,[status(thm)],[f1089,f507]) ).
fof(f1919,plain,
rd(sF1_fnc,x1) = mult(sF1_fnc,rd(sF1_fnc,x1)),
inference(forward_demodulation,[status(thm)],[f7,f1865]) ).
fof(f1922,plain,
rd(sF1_fnc,x1) = ld(sF1_fnc,rd(sF1_fnc,x1)),
inference(forward_demodulation,[status(thm)],[f1458,f1919]) ).
fof(f1989,plain,
mult(x1,sF1_fnc) = ld(rd(sF1_fnc,x1),sF1_fnc),
inference(paramodulation,[status(thm)],[f1922,f1437]) ).
fof(f1999,plain,
rd(mult(x1,sF1_fnc),x1) = mult(sF1_fnc,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f2045,f298]) ).
fof(f2045,plain,
mult(x1,sF1_fnc) = x1,
inference(forward_demodulation,[status(thm)],[f238,f1989]) ).
fof(f2058,plain,
rd(x1,x1) = mult(sF1_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f2045,f1999]) ).
fof(f2060,plain,
sF1_fnc = mult(sF1_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f13,f2058]) ).
fof(f3546,plain,
! [X0] : rd(mult(sF1_fnc,X0),sF1_fnc) = mult(mult(sF1_fnc,rd(X0,sF1_fnc)),sF1_fnc),
inference(paramodulation,[status(thm)],[f2060,f29]) ).
fof(f3551,plain,
ld(sF1_fnc,sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f2060,f8]) ).
fof(f3558,plain,
rd(sF1_fnc,sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f2060,f10]) ).
fof(f3591,plain,
! [X0] : rd(mult(sF1_fnc,X0),sF1_fnc) = mult(sF1_fnc,mult(ld(sF1_fnc,sF1_fnc),X0)),
inference(forward_demodulation,[status(thm)],[f1171,f3546]) ).
fof(f3593,plain,
! [X0] : rd(mult(sF1_fnc,X0),sF1_fnc) = mult(sF1_fnc,mult(sF1_fnc,X0)),
inference(backward_demodulation,[status(thm)],[f3551,f3591]) ).
fof(f3683,plain,
! [X0] : rd(rd(X0,sF1_fnc),sF1_fnc) = mult(sF1_fnc,rd(ld(sF1_fnc,X0),sF1_fnc)),
inference(paramodulation,[status(thm)],[f3558,f888]) ).
fof(f5407,plain,
! [X0] : rd(X0,sF1_fnc) = mult(sF1_fnc,mult(sF1_fnc,ld(sF1_fnc,X0))),
inference(paramodulation,[status(thm)],[f7,f3593]) ).
fof(f5417,plain,
! [X0] : mult(sF1_fnc,mult(sF1_fnc,X0)) = ld(ld(mult(sF1_fnc,X0),mult(sF1_fnc,mult(sF1_fnc,X0))),mult(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f3593,f1437]) ).
fof(f5424,plain,
! [X0] : ld(mult(sF1_fnc,mult(sF1_fnc,X0)),mult(sF1_fnc,X0)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f3593,f238]) ).
fof(f5472,plain,
! [X0] : rd(rd(X0,sF1_fnc),sF1_fnc) = mult(sF1_fnc,mult(sF1_fnc,ld(sF1_fnc,X0))),
inference(backward_demodulation,[status(thm)],[f5536,f3683]) ).
fof(f5536,plain,
! [X0] : rd(X0,sF1_fnc) = mult(sF1_fnc,X0),
inference(forward_demodulation,[status(thm)],[f7,f5407]) ).
fof(f5582,plain,
! [X0] : mult(sF1_fnc,rd(X0,sF1_fnc)) = mult(sF1_fnc,mult(sF1_fnc,ld(sF1_fnc,X0))),
inference(forward_demodulation,[status(thm)],[f5536,f5472]) ).
fof(f5583,plain,
! [X0] : mult(sF1_fnc,mult(sF1_fnc,X0)) = mult(sF1_fnc,mult(sF1_fnc,ld(sF1_fnc,X0))),
inference(forward_demodulation,[status(thm)],[f5536,f5582]) ).
fof(f5598,plain,
! [X0] : ld(mult(sF1_fnc,X0),mult(sF1_fnc,X0)) = sF1_fnc,
inference(backward_demodulation,[status(thm)],[f5617,f5424]) ).
fof(f5604,plain,
! [X0] : mult(sF1_fnc,mult(sF1_fnc,X0)) = ld(ld(mult(sF1_fnc,X0),mult(sF1_fnc,X0)),mult(sF1_fnc,X0)),
inference(backward_demodulation,[status(thm)],[f5617,f5417]) ).
fof(f5617,plain,
! [X0] : mult(sF1_fnc,mult(sF1_fnc,X0)) = mult(sF1_fnc,X0),
inference(forward_demodulation,[status(thm)],[f7,f5583]) ).
fof(f5805,plain,
! [X0] : mult(sF1_fnc,X0) = ld(ld(mult(sF1_fnc,X0),mult(sF1_fnc,X0)),mult(sF1_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f5617,f5604]) ).
fof(f5806,plain,
! [X0] : mult(sF1_fnc,X0) = ld(sF1_fnc,mult(sF1_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f5598,f5805]) ).
fof(f5813,plain,
sF0_fnc = x0,
inference(backward_demodulation,[status(thm)],[f5917,f14]) ).
fof(f5917,plain,
! [X0] : mult(sF1_fnc,X0) = X0,
inference(forward_demodulation,[status(thm)],[f8,f5806]) ).
fof(f6127,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5813,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP660-12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.45 % Computer : n002.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Sun Sep 20 20:32:33 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.48 % Drodi V4.1.1
% 8.93/2.19 % Refutation found
% 8.93/2.19 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.93/2.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.63/16.41 % Elapsed time: 15.931745 seconds
% 14.63/16.41 % CPU time: 92.349180 seconds
% 14.63/16.41 % Total memory used: 42.678 GB
% 14.63/16.41 % Net memory used: 42.676 GB
%------------------------------------------------------------------------------