%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP657+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:35:01 PM UTC 2026
% Result : Theorem 0.20s 0.55s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 19 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 4 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 51 ( 46 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [C,B,A] : mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0,X1,X2] : mult(mult(X0,X1),mult(X2,X0)) = mult(X0,mult(mult(X1,X2),X0)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0] :
? [X1] :
( mult(X0,X1) != X1
| mult(X1,X0) != X1 ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f14,plain,
! [X0] :
( ? [X1] : mult(X0,X1) != X1
| ? [X1] : mult(X1,X0) != X1 ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0] :
( mult(X0,sK1_skl(X0)) != sK1_skl(X0)
| mult(sK0_skl(X0),X0) != sK0_skl(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X1,sK0_skl(X0)),skolemize(X1,sK1_skl(X0))],[f14]) ).
fof(f16,plain,
! [X0] :
( mult(X0,sK1_skl(X0)) != sK1_skl(X0)
| mult(sK0_skl(X0),X0) != sK0_skl(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f31,plain,
! [X0,X1,X2] : mult(X0,mult(X1,X2)) = mult(X2,mult(mult(ld(X2,X0),X1),X2)),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f35,plain,
! [X0,X1,X2] : rd(mult(X0,mult(mult(X1,X2),X0)),mult(X2,X0)) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f12,f11]) ).
fof(f44,plain,
! [X0,X1,X2] : ld(X0,mult(X1,mult(X2,X0))) = mult(mult(ld(X0,X1),X2),X0),
inference(paramodulation,[status(thm)],[f31,f9]) ).
fof(f214,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(ld(X1,X1),X0),X1),
inference(paramodulation,[status(thm)],[f9,f44]) ).
fof(f266,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(ld(X1,X1),X0),
inference(paramodulation,[status(thm)],[f214,f11]) ).
fof(f283,plain,
! [X0,X1] : X0 = mult(ld(X1,X1),X0),
inference(forward_demodulation,[status(thm)],[f11,f266]) ).
fof(f310,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X0)),mult(X1,X0)) = mult(X0,ld(X2,X2)),
inference(paramodulation,[status(thm)],[f283,f35]) ).
fof(f327,plain,
! [X0,X1] : X0 = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f11,f310]) ).
fof(f411,plain,
! [X0] : mult(ld(X0,X0),sK1_skl(ld(X0,X0))) != sK1_skl(ld(X0,X0)),
inference(resolution,[status(thm)],[f327,f16]) ).
fof(f442,plain,
! [X0] : sK1_skl(ld(X0,X0)) != sK1_skl(ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f283,f411]) ).
fof(f443,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP657+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 % Computer : n010.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Sun Sep 20 20:30:10 UTC 2026
% 0.20/0.48 % CPUTime :
% 0.20/0.51 % Drodi V4.1.1
% 0.20/0.55 % Refutation found
% 0.20/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.58 % Elapsed time: 0.077743 seconds
% 0.20/0.58 % CPU time: 0.202856 seconds
% 0.20/0.58 % Total memory used: 33.655 MB
% 0.20/0.58 % Net memory used: 33.611 MB
%------------------------------------------------------------------------------