%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP700+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:35:09 PM UTC 2026
% Result : Theorem 0.17s 0.71s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 28 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 47 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [C,B,A] : mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [X0] :
? [X1] :
( mult(X0,X1) = unit
& mult(X1,X0) = unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [X0] :
? [X1] :
( mult(X0,X1) = unit
& mult(X1,X0) = unit ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),X0),mult(X0,X2)) = mult(X0,mult(mult(mult(X1,X0),X0),X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
? [X0] :
! [X1] :
( mult(X0,X1) != unit
| mult(X1,X0) != unit ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f20,plain,
! [X1] :
( mult(sK0_skl,X1) != unit
| mult(X1,sK0_skl) != unit ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f19]) ).
fof(f21,plain,
! [X0] :
( mult(sK0_skl,X0) != unit
| mult(X0,sK0_skl) != unit ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f35,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f13,f12]) ).
fof(f42,plain,
! [X0] : rd(X0,X0) = unit,
inference(paramodulation,[status(thm)],[f16,f14]) ).
fof(f65,plain,
! [X0,X1] : mult(mult(mult(X0,X1),X0),X0) = mult(X0,mult(mult(mult(X1,X0),X0),unit)),
inference(paramodulation,[status(thm)],[f15,f17]) ).
fof(f81,plain,
! [X0,X1] : mult(mult(mult(X0,X1),X0),X0) = mult(X0,mult(mult(X1,X0),X0)),
inference(forward_demodulation,[status(thm)],[f15,f65]) ).
fof(f88,plain,
mult(ld(sK0_skl,unit),sK0_skl) != unit,
inference(resolution,[status(thm)],[f21,f11]) ).
fof(f280,plain,
! [X0,X1] : mult(mult(X0,X1),X1) = mult(X1,mult(mult(ld(X1,X0),X1),X1)),
inference(paramodulation,[status(thm)],[f11,f81]) ).
fof(f861,plain,
! [X0,X1] : rd(mult(mult(X0,X1),X1),mult(mult(ld(X1,X0),X1),X1)) = X1,
inference(paramodulation,[status(thm)],[f280,f14]) ).
fof(f4354,plain,
! [X0] : rd(mult(X0,X0),mult(mult(ld(X0,unit),X0),X0)) = X0,
inference(paramodulation,[status(thm)],[f16,f861]) ).
fof(f4455,plain,
! [X0] : ld(X0,mult(X0,X0)) = mult(mult(ld(X0,unit),X0),X0),
inference(paramodulation,[status(thm)],[f4354,f35]) ).
fof(f4524,plain,
! [X0] : X0 = mult(mult(ld(X0,unit),X0),X0),
inference(forward_demodulation,[status(thm)],[f12,f4455]) ).
fof(f4576,plain,
! [X0] : rd(X0,X0) = mult(ld(X0,unit),X0),
inference(paramodulation,[status(thm)],[f4524,f14]) ).
fof(f4676,plain,
! [X0] : unit = mult(ld(X0,unit),X0),
inference(forward_demodulation,[status(thm)],[f42,f4576]) ).
fof(f4677,plain,
unit != unit,
inference(backward_demodulation,[status(thm)],[f4676,f88]) ).
fof(f4722,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f4677]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP700+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n009.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 20 20:33:57 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.71 % Refutation found
% 0.17/0.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.46/0.76 % Elapsed time: 0.307430 seconds
% 0.46/0.76 % CPU time: 2.074490 seconds
% 0.46/0.76 % Total memory used: 116.179 MB
% 0.46/0.76 % Net memory used: 115.805 MB
%------------------------------------------------------------------------------