%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP715+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 : n011.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 12:35:13 PM UTC 2026
% Result : Theorem 0.15s 10.78s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 62 ( 55 unt; 0 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 67 ( 64 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [C,B,A] : mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A] : mult(A,mult(B,B)) = mult(mult(A,B),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
mult(op_a,op_b) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
mult(op_b,op_a) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [X0] :
( mult(mult(X0,op_b),op_a) = X0
& mult(mult(X0,op_a),op_b) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [X0] :
( mult(mult(X0,op_b),op_a) = X0
& mult(mult(X0,op_a),op_b) = X0 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f19,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),X2),X1) = mult(X0,mult(mult(X1,X2),X1)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
! [X0,X1] : mult(X0,mult(X1,X1)) = mult(mult(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
mult(op_a,op_b) = unit,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f24,plain,
mult(op_b,op_a) = unit,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f25,plain,
? [X0] :
( mult(mult(X0,op_b),op_a) != X0
| mult(mult(X0,op_a),op_b) != X0 ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f26,plain,
( ? [X0] : mult(mult(X0,op_b),op_a) != X0
| ? [X0] : mult(mult(X0,op_a),op_b) != X0 ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
( mult(mult(sK1_skl,op_b),op_a) != sK1_skl
| mult(mult(sK0_skl,op_a),op_b) != sK0_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f26]) ).
fof(f28,plain,
( mult(mult(sK1_skl,op_b),op_a) != sK1_skl
| mult(mult(sK0_skl,op_a),op_b) != sK0_skl ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] : mult(mult(X0,mult(mult(X1,X2),X1)),X2) = mult(mult(X0,X1),mult(mult(X2,X1),X2)),
inference(paramodulation,[status(thm)],[f19,f19]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : mult(mult(mult(X0,mult(mult(X1,X2),X1)),X3),X1) = mult(mult(mult(X0,X1),X2),mult(mult(X1,X3),X1)),
inference(paramodulation,[status(thm)],[f19,f19]) ).
fof(f31,plain,
! [X0] : mult(mult(unit,X0),op_a) = mult(op_b,mult(mult(op_a,X0),op_a)),
inference(paramodulation,[status(thm)],[f24,f19]) ).
fof(f32,plain,
! [X0] : mult(mult(unit,X0),op_b) = mult(op_a,mult(mult(op_b,X0),op_b)),
inference(paramodulation,[status(thm)],[f23,f19]) ).
fof(f33,plain,
! [X0] : mult(X0,op_a) = mult(op_b,mult(mult(op_a,X0),op_a)),
inference(forward_demodulation,[status(thm)],[f22,f31]) ).
fof(f34,plain,
! [X0] : mult(X0,op_b) = mult(op_a,mult(mult(op_b,X0),op_b)),
inference(forward_demodulation,[status(thm)],[f22,f32]) ).
fof(f35,plain,
! [X0,X1] : mult(mult(X0,X1),mult(X1,X1)) = mult(X0,mult(mult(X1,X1),X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f38,plain,
mult(op_b,mult(op_a,op_a)) = mult(unit,op_a),
inference(paramodulation,[status(thm)],[f24,f20]) ).
fof(f43,plain,
! [X0,X1] : mult(mult(X0,X1),mult(X1,X1)) = mult(X0,mult(X1,mult(X1,X1))),
inference(forward_demodulation,[status(thm)],[f20,f35]) ).
fof(f45,plain,
mult(op_b,mult(op_a,op_a)) = op_a,
inference(forward_demodulation,[status(thm)],[f22,f38]) ).
fof(f55,plain,
mult(op_a,op_a) = mult(op_b,mult(op_a,mult(op_a,op_a))),
inference(paramodulation,[status(thm)],[f20,f33]) ).
fof(f91,plain,
! [X0] : mult(mult(X0,mult(op_a,op_b)),mult(op_a,op_a)) = mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))),
inference(paramodulation,[status(thm)],[f45,f29]) ).
fof(f111,plain,
! [X0] : mult(mult(X0,unit),mult(op_a,op_a)) = mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))),
inference(forward_demodulation,[status(thm)],[f23,f91]) ).
fof(f112,plain,
! [X0] : mult(X0,mult(op_a,op_a)) = mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))),
inference(forward_demodulation,[status(thm)],[f21,f111]) ).
fof(f145,plain,
! [X0,X1] : mult(mult(mult(X0,mult(op_a,op_b)),X1),op_b) = mult(mult(mult(X0,op_b),mult(op_a,op_a)),mult(mult(op_b,X1),op_b)),
inference(paramodulation,[status(thm)],[f45,f30]) ).
fof(f175,plain,
! [X0,X1] : mult(mult(mult(X0,unit),X1),op_b) = mult(mult(mult(X0,op_b),mult(op_a,op_a)),mult(mult(op_b,X1),op_b)),
inference(forward_demodulation,[status(thm)],[f23,f145]) ).
fof(f176,plain,
! [X0,X1] : mult(mult(X0,X1),op_b) = mult(mult(mult(X0,op_b),mult(op_a,op_a)),mult(mult(op_b,X1),op_b)),
inference(forward_demodulation,[status(thm)],[f21,f175]) ).
fof(f385,plain,
mult(mult(op_a,op_a),op_b) = mult(op_a,mult(op_a,op_b)),
inference(paramodulation,[status(thm)],[f45,f34]) ).
fof(f400,plain,
mult(mult(op_a,op_a),op_b) = mult(op_a,unit),
inference(forward_demodulation,[status(thm)],[f23,f385]) ).
fof(f401,plain,
! [X0] : mult(X0,mult(op_a,op_a)) = mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))),
inference(backward_demodulation,[status(thm)],[f402,f112]) ).
fof(f402,plain,
mult(mult(op_a,op_a),op_b) = op_a,
inference(forward_demodulation,[status(thm)],[f21,f400]) ).
fof(f416,plain,
! [X0] : mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b) = mult(mult(X0,mult(op_a,op_a)),mult(mult(op_b,mult(op_a,op_a)),op_b)),
inference(paramodulation,[status(thm)],[f402,f29]) ).
fof(f420,plain,
! [X0] : mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b) = mult(mult(X0,mult(op_a,op_a)),mult(op_a,op_b)),
inference(forward_demodulation,[status(thm)],[f45,f416]) ).
fof(f421,plain,
! [X0] : mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b) = mult(mult(X0,mult(op_a,op_a)),unit),
inference(forward_demodulation,[status(thm)],[f23,f420]) ).
fof(f422,plain,
! [X0] : mult(mult(X0,mult(op_a,mult(op_a,op_a))),op_b) = mult(X0,mult(op_a,op_a)),
inference(forward_demodulation,[status(thm)],[f21,f421]) ).
fof(f677,plain,
! [X0,X1] : mult(mult(mult(X0,mult(mult(op_a,op_a),op_b)),X1),op_b) = mult(mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))),mult(mult(op_b,X1),op_b)),
inference(paramodulation,[status(thm)],[f55,f30]) ).
fof(f684,plain,
! [X0,X1] : mult(mult(mult(X0,op_a),X1),op_b) = mult(mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))),mult(mult(op_b,X1),op_b)),
inference(forward_demodulation,[status(thm)],[f402,f677]) ).
fof(f685,plain,
! [X0,X1] : mult(mult(X0,X1),op_b) = mult(mult(mult(mult(X0,op_b),op_a),X1),op_b),
inference(backward_demodulation,[status(thm)],[f686,f176]) ).
fof(f686,plain,
! [X0,X1] : mult(mult(mult(X0,op_a),X1),op_b) = mult(mult(X0,mult(op_a,op_a)),mult(mult(op_b,X1),op_b)),
inference(forward_demodulation,[status(thm)],[f401,f684]) ).
fof(f942,plain,
! [X0] : mult(mult(X0,mult(op_a,op_a)),op_b) = mult(mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))),op_b),
inference(paramodulation,[status(thm)],[f43,f685]) ).
fof(f943,plain,
! [X0] : mult(mult(X0,op_a),op_b) = mult(mult(mult(X0,op_b),mult(op_a,op_a)),op_b),
inference(paramodulation,[status(thm)],[f20,f685]) ).
fof(f984,plain,
! [X0] : mult(mult(X0,mult(op_a,op_a)),op_b) = mult(X0,mult(mult(op_b,mult(op_a,mult(op_a,op_a))),op_b)),
inference(forward_demodulation,[status(thm)],[f19,f942]) ).
fof(f985,plain,
! [X0] : mult(mult(X0,mult(op_a,op_a)),op_b) = mult(X0,mult(op_b,mult(op_a,op_a))),
inference(forward_demodulation,[status(thm)],[f422,f984]) ).
fof(f988,plain,
! [X0] : mult(mult(X0,mult(op_a,op_a)),op_b) = mult(X0,op_a),
inference(forward_demodulation,[status(thm)],[f45,f985]) ).
fof(f989,plain,
! [X0] : mult(mult(X0,op_a),op_b) = mult(X0,mult(mult(op_b,mult(op_a,op_a)),op_b)),
inference(forward_demodulation,[status(thm)],[f19,f943]) ).
fof(f990,plain,
! [X0] : mult(mult(X0,op_a),op_b) = mult(X0,mult(op_b,op_a)),
inference(forward_demodulation,[status(thm)],[f988,f989]) ).
fof(f991,plain,
! [X0] : mult(mult(X0,op_a),op_b) = mult(X0,unit),
inference(forward_demodulation,[status(thm)],[f24,f990]) ).
fof(f993,plain,
( mult(mult(sK1_skl,op_b),op_a) != sK1_skl
| sK0_skl != sK0_skl ),
inference(backward_demodulation,[status(thm)],[f1004,f28]) ).
fof(f1004,plain,
! [X0] : mult(mult(X0,op_a),op_b) = X0,
inference(forward_demodulation,[status(thm)],[f21,f991]) ).
fof(f1035,plain,
mult(mult(sK1_skl,op_b),op_a) != sK1_skl,
inference(trivial_equality_resolution,[status(thm)],[f993]) ).
fof(f1039,plain,
! [X0] : mult(mult(X0,op_a),op_b) = mult(mult(X0,op_b),op_a),
inference(paramodulation,[status(thm)],[f685,f1004]) ).
fof(f1072,plain,
sK1_skl != sK1_skl,
inference(backward_demodulation,[status(thm)],[f1093,f1035]) ).
fof(f1093,plain,
! [X0] : X0 = mult(mult(X0,op_b),op_a),
inference(forward_demodulation,[status(thm)],[f1004,f1039]) ).
fof(f1106,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1072]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.59 % Computer : n011.cluster.edu
% 0.10/10.59 % Model : x86_64 x86_64
% 0.10/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.59 % Memory : 8046.5625MB
% 0.10/10.59 % OS : Linux 6.8.0-71-generic
% 0.10/10.59 % CPULimit : 300
% 0.10/10.59 % WCLimit : 300
% 0.10/10.59 % DateTime : Sun Sep 20 20:35:06 UTC 2026
% 0.10/10.59 % CPUTime :
% 0.10/10.60 % Drodi V4.1.1
% 0.15/10.78 % Refutation found
% 0.15/10.78 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/10.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/10.80 % Elapsed time: 0.195350 seconds
% 0.15/10.80 % CPU time: 1.401987 seconds
% 0.15/10.80 % Total memory used: 101.926 MB
% 0.15/10.80 % Net memory used: 101.250 MB
%------------------------------------------------------------------------------