%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP660-13 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 2.14s 0.69s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 8
% Syntax : Number of formulae : 85 ( 85 unt; 2 def)
% Number of atoms : 85 ( 84 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 : 92 ( 92 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
mult(x0,ld(x1,x1)) != x0,
file('/export/starexec/sandbox/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(x0,ld(x1,x1)) != x0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,definition,
sF1_fnc = ld(x1,x1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f14,definition,
sF0_fnc = mult(x0,sF1_fnc),
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(x1,sF1_fnc) = x1,
inference(paramodulation,[status(thm)],[f13,f7]) ).
fof(f18,plain,
ld(x0,sF0_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f14,f8]) ).
fof(f23,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(X1,mult(X2,mult(ld(mult(X1,X2),X0),X1))),
inference(paramodulation,[status(thm)],[f7,f11]) ).
fof(f27,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(f37,plain,
! [X0,X1,X2] : ld(X0,mult(X1,X0)) = mult(X2,mult(ld(mult(X0,X2),X1),X0)),
inference(paramodulation,[status(thm)],[f23,f8]) ).
fof(f43,plain,
! [X0] : mult(mult(X0,x1),sF1_fnc) = mult(sF1_fnc,mult(ld(sF1_fnc,X0),x1)),
inference(paramodulation,[status(thm)],[f16,f27]) ).
fof(f47,plain,
! [X0,X1,X2] : mult(mult(X0,X1),ld(X1,X2)) = mult(ld(X1,X2),mult(ld(ld(X1,X2),X0),X2)),
inference(paramodulation,[status(thm)],[f7,f27]) ).
fof(f52,plain,
! [X0,X1,X2] : ld(X0,mult(mult(X1,X2),X0)) = mult(ld(X0,X1),mult(X2,X0)),
inference(paramodulation,[status(thm)],[f27,f8]) ).
fof(f102,plain,
! [X0,X1,X2] : ld(X0,ld(X1,mult(X2,X1))) = mult(ld(mult(X1,X0),X2),X1),
inference(paramodulation,[status(thm)],[f37,f8]) ).
fof(f141,plain,
! [X0,X1,X2] : ld(ld(X0,X1),ld(X0,mult(X2,X0))) = mult(ld(X1,X2),X0),
inference(paramodulation,[status(thm)],[f7,f102]) ).
fof(f147,plain,
! [X0,X1,X2] : ld(ld(mult(X0,X1),X2),ld(X1,ld(X0,mult(X2,X0)))) = X0,
inference(paramodulation,[status(thm)],[f102,f8]) ).
fof(f282,plain,
! [X0,X1,X2] : ld(X0,mult(mult(X1,rd(X2,X0)),X0)) = mult(ld(X0,X1),X2),
inference(paramodulation,[status(thm)],[f9,f52]) ).
fof(f286,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f297,plain,
rd(x1,sF1_fnc) = x1,
inference(paramodulation,[status(thm)],[f16,f10]) ).
fof(f299,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f7,f10]) ).
fof(f354,plain,
! [X0,X1] : ld(ld(X0,X1),X0) = mult(ld(X1,X0),X0),
inference(paramodulation,[status(thm)],[f8,f141]) ).
fof(f374,plain,
! [X0,X1] : ld(ld(X0,rd(X0,X1)),X0) = mult(X1,X0),
inference(paramodulation,[status(thm)],[f286,f354]) ).
fof(f376,plain,
ld(ld(sF0_fnc,x0),sF0_fnc) = mult(sF1_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f18,f354]) ).
fof(f377,plain,
ld(ld(x1,x1),x1) = mult(sF1_fnc,x1),
inference(paramodulation,[status(thm)],[f13,f354]) ).
fof(f385,plain,
! [X0,X1] : rd(ld(ld(X0,X1),X0),X0) = ld(X1,X0),
inference(paramodulation,[status(thm)],[f354,f10]) ).
fof(f395,plain,
! [X0,X1] : ld(ld(X0,X1),ld(ld(X1,X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f354,f8]) ).
fof(f397,plain,
ld(sF1_fnc,x1) = mult(sF1_fnc,x1),
inference(forward_demodulation,[status(thm)],[f13,f377]) ).
fof(f434,plain,
! [X0,X1] : rd(X0,mult(X1,X0)) = ld(X0,rd(X0,X1)),
inference(paramodulation,[status(thm)],[f374,f299]) ).
fof(f446,plain,
rd(ld(sF1_fnc,x0),x0) = ld(sF0_fnc,x0),
inference(paramodulation,[status(thm)],[f18,f385]) ).
fof(f608,plain,
ld(ld(sF0_fnc,x0),ld(sF1_fnc,x0)) = x0,
inference(paramodulation,[status(thm)],[f446,f286]) ).
fof(f695,plain,
! [X0,X1] : ld(ld(mult(X0,X1),X0),ld(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f8,f395]) ).
fof(f711,plain,
! [X0,X1] : rd(X0,X1) = ld(X0,rd(X0,rd(X1,X0))),
inference(paramodulation,[status(thm)],[f9,f434]) ).
fof(f828,plain,
! [X0,X1] : mult(X0,rd(X0,X1)) = rd(X0,rd(X1,X0)),
inference(paramodulation,[status(thm)],[f711,f7]) ).
fof(f1179,plain,
mult(sF1_fnc,rd(sF1_fnc,x1)) = rd(sF1_fnc,x1),
inference(paramodulation,[status(thm)],[f297,f828]) ).
fof(f1719,plain,
ld(x1,mult(rd(sF1_fnc,x1),x1)) = mult(ld(x1,sF1_fnc),sF1_fnc),
inference(paramodulation,[status(thm)],[f1179,f282]) ).
fof(f1756,plain,
ld(x1,sF1_fnc) = mult(ld(x1,sF1_fnc),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f9,f1719]) ).
fof(f1757,plain,
ld(x1,sF1_fnc) = ld(ld(sF1_fnc,x1),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f354,f1756]) ).
fof(f1772,plain,
rd(sF1_fnc,ld(x1,sF1_fnc)) = ld(sF1_fnc,x1),
inference(paramodulation,[status(thm)],[f1757,f299]) ).
fof(f1783,plain,
x1 = ld(sF1_fnc,x1),
inference(forward_demodulation,[status(thm)],[f299,f1772]) ).
fof(f1786,plain,
x1 = mult(sF1_fnc,x1),
inference(backward_demodulation,[status(thm)],[f1783,f397]) ).
fof(f1811,plain,
! [X0] : ld(ld(x1,X0),ld(x1,x1)) = mult(ld(X0,sF1_fnc),x1),
inference(paramodulation,[status(thm)],[f1786,f141]) ).
fof(f1831,plain,
! [X0] : ld(ld(x1,X0),sF1_fnc) = mult(ld(X0,sF1_fnc),x1),
inference(forward_demodulation,[status(thm)],[f13,f1811]) ).
fof(f2220,plain,
mult(mult(sF1_fnc,x1),sF1_fnc) = mult(sF1_fnc,ld(ld(x1,sF1_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f1831,f43]) ).
fof(f2248,plain,
mult(x1,sF1_fnc) = mult(sF1_fnc,ld(ld(x1,sF1_fnc),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f1786,f2220]) ).
fof(f2249,plain,
x1 = mult(sF1_fnc,ld(ld(x1,sF1_fnc),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f16,f2248]) ).
fof(f3214,plain,
ld(sF1_fnc,x1) = ld(ld(x1,sF1_fnc),sF1_fnc),
inference(paramodulation,[status(thm)],[f2249,f8]) ).
fof(f3234,plain,
x1 = ld(ld(x1,sF1_fnc),sF1_fnc),
inference(forward_demodulation,[status(thm)],[f1783,f3214]) ).
fof(f3247,plain,
mult(ld(x1,sF1_fnc),x1) = sF1_fnc,
inference(paramodulation,[status(thm)],[f3234,f7]) ).
fof(f3251,plain,
ld(ld(x1,x1),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f1831,f3247]) ).
fof(f3252,plain,
ld(sF1_fnc,sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f13,f3251]) ).
fof(f3484,plain,
! [X0] : mult(mult(X0,sF1_fnc),ld(sF1_fnc,sF1_fnc)) = mult(ld(sF1_fnc,sF1_fnc),mult(ld(sF1_fnc,X0),sF1_fnc)),
inference(paramodulation,[status(thm)],[f3252,f47]) ).
fof(f3614,plain,
! [X0] : mult(mult(X0,sF1_fnc),sF1_fnc) = mult(ld(sF1_fnc,sF1_fnc),mult(ld(sF1_fnc,X0),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f3252,f3484]) ).
fof(f3615,plain,
! [X0] : mult(mult(X0,sF1_fnc),sF1_fnc) = ld(sF1_fnc,mult(mult(sF1_fnc,ld(sF1_fnc,X0)),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f52,f3614]) ).
fof(f3616,plain,
! [X0] : mult(mult(X0,sF1_fnc),sF1_fnc) = ld(sF1_fnc,mult(X0,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f7,f3615]) ).
fof(f4368,plain,
! [X0] : mult(X0,sF1_fnc) = ld(sF1_fnc,mult(rd(X0,sF1_fnc),sF1_fnc)),
inference(paramodulation,[status(thm)],[f9,f3616]) ).
fof(f4409,plain,
! [X0] : mult(X0,sF1_fnc) = ld(sF1_fnc,X0),
inference(forward_demodulation,[status(thm)],[f9,f4368]) ).
fof(f4819,plain,
sF0_fnc = ld(sF1_fnc,x0),
inference(backward_demodulation,[status(thm)],[f4409,f14]) ).
fof(f4820,plain,
! [X0] : X0 = ld(sF1_fnc,rd(X0,sF1_fnc)),
inference(paramodulation,[status(thm)],[f9,f4409]) ).
fof(f4869,plain,
! [X0] : ld(X0,ld(sF1_fnc,X0)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f4409,f8]) ).
fof(f4905,plain,
ld(ld(sF0_fnc,x0),sF0_fnc) = x0,
inference(backward_demodulation,[status(thm)],[f4819,f608]) ).
fof(f4918,plain,
mult(sF1_fnc,sF0_fnc) = x0,
inference(forward_demodulation,[status(thm)],[f376,f4905]) ).
fof(f5047,plain,
! [X0] : ld(ld(mult(rd(X0,sF1_fnc),sF1_fnc),rd(X0,sF1_fnc)),X0) = rd(X0,sF1_fnc),
inference(paramodulation,[status(thm)],[f4820,f695]) ).
fof(f5067,plain,
! [X0] : ld(ld(X0,rd(X0,sF1_fnc)),X0) = rd(X0,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f9,f5047]) ).
fof(f5068,plain,
! [X0] : mult(sF1_fnc,X0) = rd(X0,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f374,f5067]) ).
fof(f5124,plain,
! [X0] : ld(ld(mult(sF1_fnc,mult(X0,sF1_fnc)),X0),sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f4869,f147]) ).
fof(f5142,plain,
! [X0] : ld(ld(mult(sF1_fnc,ld(sF1_fnc,X0)),X0),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f4409,f5124]) ).
fof(f5143,plain,
! [X0] : ld(ld(X0,X0),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f7,f5142]) ).
fof(f5282,plain,
! [X0] : rd(sF1_fnc,sF1_fnc) = ld(X0,X0),
inference(paramodulation,[status(thm)],[f5143,f299]) ).
fof(f5305,plain,
! [X0] : mult(sF1_fnc,sF1_fnc) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f5068,f5282]) ).
fof(f5306,plain,
! [X0] : ld(sF1_fnc,sF1_fnc) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f4409,f5305]) ).
fof(f5307,plain,
! [X0] : sF1_fnc = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f3252,f5306]) ).
fof(f5335,plain,
! [X0] : rd(X0,sF1_fnc) = X0,
inference(paramodulation,[status(thm)],[f5307,f299]) ).
fof(f5355,plain,
! [X0] : mult(sF1_fnc,X0) = X0,
inference(forward_demodulation,[status(thm)],[f5068,f5335]) ).
fof(f5360,plain,
sF0_fnc = x0,
inference(backward_demodulation,[status(thm)],[f5355,f4918]) ).
fof(f5427,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5360,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660-13 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:29:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 2.14/0.69 % Refutation found
% 2.14/0.69 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.14/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.33/1.91 % Elapsed time: 1.320130 seconds
% 8.33/1.91 % CPU time: 2.104967 seconds
% 8.33/1.91 % Total memory used: 89.304 MB
% 8.33/1.91 % Net memory used: 88.374 MB
%------------------------------------------------------------------------------