%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP656+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 : n008.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 0.09s 1.00s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 30 unt; 0 def)
% Number of atoms : 42 ( 41 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 : 82 ( 77 !; 5 ?)
% 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,
! [C,B,A] : mult(mult(A,B),mult(C,A)) = mult(mult(A,mult(B,C)),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
file('/export/starexec/sandbox2/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(f10,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
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(mult(X0,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(f32,plain,
! [X0,X1,X2] : mult(mult(X0,rd(X1,X2)),mult(X2,X0)) = mult(mult(X0,X1),X0),
inference(paramodulation,[status(thm)],[f10,f12]) ).
fof(f33,plain,
! [X0,X1,X2] : mult(mult(X0,X1),mult(ld(X1,X2),X0)) = mult(mult(X0,X2),X0),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f34,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),mult(X2,X0)),X0) = mult(X0,mult(X1,X2)),
inference(paramodulation,[status(thm)],[f12,f11]) ).
fof(f35,plain,
! [X0,X1,X2] : ld(mult(X0,mult(X1,X2)),mult(mult(X0,X1),mult(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f12,f9]) ).
fof(f62,plain,
! [X0,X1,X2] : ld(mult(X0,X1),mult(mult(X0,X2),X0)) = mult(ld(X1,X2),X0),
inference(paramodulation,[status(thm)],[f33,f9]) ).
fof(f73,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),X2) = mult(X2,mult(ld(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f8,f34]) ).
fof(f96,plain,
! [X0,X1,X2] : ld(mult(X0,mult(rd(X1,X2),X2)),mult(mult(X0,X1),X0)) = X0,
inference(paramodulation,[status(thm)],[f32,f35]) ).
fof(f119,plain,
! [X0,X1,X2] : mult(ld(mult(rd(X0,X1),X1),X0),X2) = X2,
inference(forward_demodulation,[status(thm)],[f62,f96]) ).
fof(f120,plain,
! [X0,X1] : mult(ld(X0,X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f10,f119]) ).
fof(f126,plain,
! [X0] : mult(sK0_skl(ld(X0,X0)),ld(X0,X0)) != sK0_skl(ld(X0,X0)),
inference(resolution,[status(thm)],[f120,f16]) ).
fof(f132,plain,
! [X0,X1,X2] : mult(mult(ld(X0,X0),X1),mult(X2,ld(X0,X0))) = mult(mult(X1,X2),ld(X0,X0)),
inference(paramodulation,[status(thm)],[f120,f12]) ).
fof(f139,plain,
! [X0,X1,X2] : mult(X0,mult(ld(X0,X1),ld(X2,X2))) = mult(mult(ld(X2,X2),X1),ld(X2,X2)),
inference(paramodulation,[status(thm)],[f120,f33]) ).
fof(f147,plain,
! [X0,X1,X2] : mult(X0,mult(X1,ld(X2,X2))) = mult(mult(X0,X1),ld(X2,X2)),
inference(forward_demodulation,[status(thm)],[f120,f132]) ).
fof(f156,plain,
! [X0,X1,X2] : rd(mult(X0,mult(ld(X1,X1),X2)),X2) = mult(mult(ld(X1,X1),X0),ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f73,f139]) ).
fof(f157,plain,
! [X0,X1,X2] : rd(mult(X0,X1),X1) = mult(mult(ld(X2,X2),X0),ld(X2,X2)),
inference(forward_demodulation,[status(thm)],[f120,f156]) ).
fof(f158,plain,
! [X0,X1] : X0 = mult(mult(ld(X1,X1),X0),ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f11,f157]) ).
fof(f159,plain,
! [X0,X1] : X0 = mult(ld(X1,X1),mult(X0,ld(X1,X1))),
inference(forward_demodulation,[status(thm)],[f147,f158]) ).
fof(f160,plain,
! [X0] : sK0_skl(ld(X0,X0)) != sK0_skl(ld(X0,X0)),
inference(backward_demodulation,[status(thm)],[f164,f126]) ).
fof(f164,plain,
! [X0,X1] : X0 = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f120,f159]) ).
fof(f194,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP656+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.92 % Computer : n008.cluster.edu
% 0.09/0.92 % Model : x86_64 x86_64
% 0.09/0.92 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.92 % Memory : 8046.5625MB
% 0.09/0.92 % OS : Linux 6.8.0-71-generic
% 0.09/0.92 % CPULimit : 300
% 0.09/0.92 % WCLimit : 300
% 0.09/0.92 % DateTime : Sun Sep 20 20:30:13 UTC 2026
% 0.09/0.92 % CPUTime :
% 0.09/0.93 % Drodi V4.1.1
% 0.09/1.00 % Refutation found
% 0.09/1.00 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/1.03 % Elapsed time: 0.093177 seconds
% 0.09/1.03 % CPU time: 0.539087 seconds
% 0.09/1.03 % Total memory used: 86.113 MB
% 0.09/1.03 % Net memory used: 85.803 MB
%------------------------------------------------------------------------------