%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP665+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 : n010.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 12:35:04 PM UTC 2026
% Result : Theorem 0.21s 0.52s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 36 unt; 0 def)
% Number of atoms : 68 ( 67 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 28 ~; 17 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 77 ( 69 !; 8 ?)
% 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(f7,axiom,
! [C,B,A] : mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [C,B,A] : mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : mult(op_c,A) = mult(A,op_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [X0,X1] :
( mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c))
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c))
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f15,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
! [X0,X1,X2] : mult(X0,mult(X1,X2)) = mult(rd(mult(X0,X1),X0),mult(X0,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,X2),ld(X2,mult(X1,X2))),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
! [X0] : mult(op_c,X0) = mult(X0,op_c),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f21,plain,
? [X0,X1] :
( mult(mult(X0,X1),op_c) != mult(X0,mult(X1,op_c))
| mult(mult(X0,op_c),X1) != mult(X0,mult(op_c,X1))
| mult(op_c,mult(X0,X1)) != mult(mult(op_c,X0),X1) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f22,plain,
( ? [X0,X1] : mult(mult(X0,X1),op_c) != mult(X0,mult(X1,op_c))
| ? [X0,X1] : mult(mult(X0,op_c),X1) != mult(X0,mult(op_c,X1))
| ? [X0,X1] : mult(op_c,mult(X0,X1)) != mult(mult(op_c,X0),X1) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
( mult(mult(sK4_skl,sK5_skl),op_c) != mult(sK4_skl,mult(sK5_skl,op_c))
| mult(mult(sK2_skl,op_c),sK3_skl) != mult(sK2_skl,mult(op_c,sK3_skl))
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(mult(op_c,sK0_skl),sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X1,sK3_skl),skolemize(X0,sK4_skl),skolemize(X1,sK5_skl)],[f22]) ).
fof(f24,plain,
( mult(mult(sK4_skl,sK5_skl),op_c) != mult(sK4_skl,mult(sK5_skl,op_c))
| mult(mult(sK2_skl,op_c),sK3_skl) != mult(sK2_skl,mult(op_c,sK3_skl))
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(mult(op_c,sK0_skl),sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f27,plain,
( mult(mult(sK4_skl,sK5_skl),op_c) != mult(sK4_skl,mult(sK5_skl,op_c))
| mult(mult(sK2_skl,op_c),sK3_skl) != mult(sK2_skl,mult(op_c,sK3_skl))
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(mult(sK0_skl,op_c),sK1_skl) ),
inference(paramodulation,[status(thm)],[f20,f24]) ).
fof(f28,plain,
( mult(op_c,mult(sK4_skl,sK5_skl)) != mult(sK4_skl,mult(sK5_skl,op_c))
| mult(mult(sK2_skl,op_c),sK3_skl) != mult(sK2_skl,mult(op_c,sK3_skl))
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(mult(sK0_skl,op_c),sK1_skl) ),
inference(paramodulation,[status(thm)],[f20,f27]) ).
fof(f36,plain,
! [X0] : ld(op_c,mult(X0,op_c)) = X0,
inference(paramodulation,[status(thm)],[f20,f13]) ).
fof(f39,plain,
! [X0] : ld(X0,mult(op_c,X0)) = op_c,
inference(paramodulation,[status(thm)],[f20,f13]) ).
fof(f49,plain,
! [X0] : ld(ld(op_c,X0),X0) = op_c,
inference(paramodulation,[status(thm)],[f12,f39]) ).
fof(f57,plain,
! [X0] : mult(ld(op_c,X0),op_c) = X0,
inference(paramodulation,[status(thm)],[f49,f12]) ).
fof(f71,plain,
! [X0] : ld(op_c,X0) = rd(X0,op_c),
inference(paramodulation,[status(thm)],[f14,f36]) ).
fof(f87,plain,
! [X0,X1] : mult(mult(ld(op_c,X0),X1),op_c) = mult(X0,ld(op_c,mult(X1,op_c))),
inference(paramodulation,[status(thm)],[f57,f19]) ).
fof(f92,plain,
! [X0,X1] : mult(mult(X0,X1),op_c) = mult(mult(op_c,X0),ld(op_c,mult(X1,op_c))),
inference(paramodulation,[status(thm)],[f20,f19]) ).
fof(f93,plain,
! [X0,X1] : mult(mult(X0,X1),op_c) = mult(mult(X0,op_c),X1),
inference(paramodulation,[status(thm)],[f36,f19]) ).
fof(f106,plain,
! [X0,X1] : mult(mult(ld(op_c,X0),X1),op_c) = mult(X0,X1),
inference(forward_demodulation,[status(thm)],[f36,f87]) ).
fof(f110,plain,
! [X0,X1] : mult(mult(X0,X1),op_c) = mult(mult(op_c,X0),X1),
inference(forward_demodulation,[status(thm)],[f36,f92]) ).
fof(f126,plain,
! [X0,X1] : ld(op_c,mult(X0,X1)) = mult(ld(op_c,X0),X1),
inference(paramodulation,[status(thm)],[f106,f36]) ).
fof(f144,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1),
inference(paramodulation,[status(thm)],[f20,f110]) ).
fof(f211,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(X0,op_c),X1),
inference(paramodulation,[status(thm)],[f20,f93]) ).
fof(f236,plain,
( mult(op_c,mult(sK4_skl,sK5_skl)) != mult(sK4_skl,mult(sK5_skl,op_c))
| mult(mult(sK2_skl,op_c),sK3_skl) != mult(sK2_skl,mult(op_c,sK3_skl))
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(backward_demodulation,[status(thm)],[f211,f28]) ).
fof(f272,plain,
( mult(op_c,mult(sK4_skl,sK5_skl)) != mult(sK4_skl,mult(sK5_skl,op_c))
| mult(op_c,mult(sK2_skl,sK3_skl)) != mult(sK2_skl,mult(op_c,sK3_skl))
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f211,f236]) ).
fof(f273,plain,
( mult(op_c,mult(sK4_skl,sK5_skl)) != mult(sK4_skl,mult(sK5_skl,op_c))
| mult(op_c,mult(sK2_skl,sK3_skl)) != mult(sK2_skl,mult(op_c,sK3_skl)) ),
inference(trivial_equality_resolution,[status(thm)],[f272]) ).
fof(f303,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(rd(mult(X0,op_c),op_c),mult(op_c,X1)),
inference(paramodulation,[status(thm)],[f20,f18]) ).
fof(f312,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(rd(mult(op_c,X0),op_c),mult(X1,op_c)),
inference(paramodulation,[status(thm)],[f20,f18]) ).
fof(f325,plain,
mult(op_c,mult(sK4_skl,sK5_skl)) != mult(sK4_skl,mult(sK5_skl,op_c)),
inference(backward_subsumption_resolution,[status(thm)],[f273,f326]) ).
fof(f326,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(X0,mult(op_c,X1)),
inference(forward_demodulation,[status(thm)],[f15,f303]) ).
fof(f339,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(ld(op_c,mult(op_c,X0)),mult(X1,op_c)),
inference(forward_demodulation,[status(thm)],[f71,f312]) ).
fof(f340,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = ld(op_c,mult(mult(op_c,X0),mult(X1,op_c))),
inference(forward_demodulation,[status(thm)],[f126,f339]) ).
fof(f341,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = ld(op_c,mult(op_c,mult(X0,mult(X1,op_c)))),
inference(forward_demodulation,[status(thm)],[f144,f340]) ).
fof(f343,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(X0,mult(X1,op_c)),
inference(forward_demodulation,[status(thm)],[f13,f341]) ).
fof(f350,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f325,f343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP665+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n010.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % 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 20:30:56 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.50 % Drodi V4.1.1
% 0.21/0.52 % Refutation found
% 0.21/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.60 % Elapsed time: 0.106446 seconds
% 0.25/0.60 % CPU time: 0.196713 seconds
% 0.25/0.60 % Total memory used: 30.522 MB
% 0.25/0.60 % Net memory used: 30.458 MB
%------------------------------------------------------------------------------