%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP754-1 : 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 12:35:17 PM UTC 2026
% Result : Unsatisfiable 35.45s 5.04s
% Output : CNFRefutation 35.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 46 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 118 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : mult(A,mult(B,C)) = mult(mult(rd(A,A),B),mult(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] : mult(mult(A,B),C) = mult(mult(A,C),mult(B,ld(C,C))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(X0,mult(X1,X2)) = mult(mult(rd(X0,X0),X1),mult(X0,X2)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,X2),mult(X1,ld(X2,X2))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f14,plain,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,c)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f10,f9]) ).
fof(f31,plain,
! [X0,X1,X2] : mult(X0,mult(ld(rd(X0,X0),X1),X2)) = mult(X1,mult(X0,X2)),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f34,plain,
! [X0,X1,X2] : mult(X0,mult(X1,ld(X0,X2))) = mult(mult(rd(X0,X0),X1),X2),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f35,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),mult(X0,X2)) = mult(rd(X0,X0),X1),
inference(paramodulation,[status(thm)],[f12,f11]) ).
fof(f47,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(X2,mult(X0,ld(ld(rd(X0,X0),X2),X1))),
inference(paramodulation,[status(thm)],[f8,f31]) ).
fof(f62,plain,
! [X0,X1,X2] : ld(X0,mult(X1,X2)) = mult(X1,ld(ld(rd(X1,X1),X0),X2)),
inference(paramodulation,[status(thm)],[f47,f9]) ).
fof(f74,plain,
! [X0,X1,X2] : ld(mult(X0,X1),mult(mult(X0,X2),X1)) = mult(X2,ld(X1,X1)),
inference(paramodulation,[status(thm)],[f13,f9]) ).
fof(f77,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X0),X1),mult(X0,X2)) = mult(X0,ld(X1,X2)),
inference(paramodulation,[status(thm)],[f9,f62]) ).
fof(f124,plain,
! [X0,X1,X2] : mult(X0,mult(X1,ld(X0,mult(X2,ld(X1,X1))))) = mult(mult(rd(X0,X0),X2),X1),
inference(paramodulation,[status(thm)],[f13,f34]) ).
fof(f137,plain,
! [X0,X1,X2] : mult(X0,mult(X1,ld(X0,mult(X2,ld(X1,X1))))) = mult(X0,mult(X2,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f34,f124]) ).
fof(f153,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X0),X1),X2) = mult(X0,ld(X1,ld(X0,X2))),
inference(paramodulation,[status(thm)],[f8,f77]) ).
fof(f239,plain,
! [X0,X1,X2] : rd(mult(X0,X1),mult(X0,X2)) = mult(rd(X0,X0),rd(X1,X2)),
inference(paramodulation,[status(thm)],[f10,f35]) ).
fof(f558,plain,
! [X0,X1,X2] : ld(X0,mult(mult(X1,X2),ld(X1,X0))) = mult(X2,ld(ld(X1,X0),ld(X1,X0))),
inference(paramodulation,[status(thm)],[f8,f74]) ).
fof(f560,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X0),X1),mult(X0,mult(X2,ld(X0,X1)))) = mult(X2,ld(X1,X1)),
inference(paramodulation,[status(thm)],[f34,f74]) ).
fof(f569,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X1),X2),mult(X0,X2)) = mult(X1,ld(X2,X2)),
inference(paramodulation,[status(thm)],[f10,f74]) ).
fof(f591,plain,
! [X0,X1,X2] : mult(X0,ld(X1,mult(X2,ld(X0,X1)))) = mult(X2,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f77,f560]) ).
fof(f1175,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X1),ld(X0,X2)),X2) = mult(X1,ld(ld(X0,X2),ld(X0,X2))),
inference(paramodulation,[status(thm)],[f8,f569]) ).
fof(f1192,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X1),ld(X0,X2)),X2) = ld(X2,mult(mult(X0,X1),ld(X0,X2))),
inference(forward_demodulation,[status(thm)],[f558,f1175]) ).
fof(f2305,plain,
! [X0,X1,X2] : ld(X0,mult(X0,mult(X1,ld(X0,X2)))) = mult(X2,ld(X0,mult(X1,ld(X2,X2)))),
inference(paramodulation,[status(thm)],[f137,f9]) ).
fof(f2394,plain,
! [X0,X1,X2] : mult(X0,ld(X1,X2)) = mult(X2,ld(X1,mult(X0,ld(X2,X2)))),
inference(forward_demodulation,[status(thm)],[f9,f2305]) ).
fof(f3610,plain,
! [X0,X1,X2] : mult(X0,ld(rd(mult(X0,ld(X1,X1)),X2),X1)) = mult(X1,X2),
inference(paramodulation,[status(thm)],[f22,f2394]) ).
fof(f5910,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X0),rd(mult(X0,ld(ld(X0,X1),ld(X0,X1))),X2)),X1) = mult(ld(X0,X1),X2),
inference(paramodulation,[status(thm)],[f153,f3610]) ).
fof(f5978,plain,
! [X0,X1,X2] : ld(X0,mult(X1,X2)) = ld(rd(mult(X0,ld(X1,X1)),X2),X1),
inference(paramodulation,[status(thm)],[f3610,f9]) ).
fof(f5983,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X0),rd(ld(mult(rd(X0,X0),ld(X0,X1)),X1),X2)),X1) = mult(ld(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f153,f5910]) ).
fof(f5984,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X0),rd(ld(X1,mult(mult(X0,X0),ld(X0,X1))),X2)),X1) = mult(ld(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f1192,f5983]) ).
fof(f6195,plain,
! [X0,X1,X2,X3] : rd(mult(X0,ld(X1,X1)),mult(X2,X3)) = mult(rd(X2,X2),rd(ld(X1,mult(X0,ld(X2,X1))),X3)),
inference(paramodulation,[status(thm)],[f591,f239]) ).
fof(f6271,plain,
! [X0,X1,X2] : ld(rd(mult(mult(X0,X0),ld(X1,X1)),mult(X0,X2)),X1) = mult(ld(X0,X1),X2),
inference(backward_demodulation,[status(thm)],[f6195,f5984]) ).
fof(f6288,plain,
! [X0,X1,X2] : ld(mult(X0,X0),mult(X1,mult(X0,X2))) = mult(ld(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f5978,f6271]) ).
fof(f12024,plain,
! [X0,X1,X2] : mult(mult(X0,X0),mult(ld(X0,X1),X2)) = mult(X1,mult(X0,X2)),
inference(paramodulation,[status(thm)],[f6288,f8]) ).
fof(f18129,plain,
! [X0,X1,X2] : mult(mult(X0,X0),mult(X1,X2)) = mult(mult(X0,X1),mult(X0,X2)),
inference(paramodulation,[status(thm)],[f9,f12024]) ).
fof(f18250,plain,
mult(mult(a,a),mult(b,c)) != mult(mult(a,a),mult(b,c)),
inference(backward_demodulation,[status(thm)],[f18129,f14]) ).
fof(f18374,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f18250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP754-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n011.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 20 20:37:55 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Drodi V4.1.1
% 35.45/5.04 % Refutation found
% 35.45/5.04 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 35.45/5.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 35.45/5.21 % Elapsed time: 4.765615 seconds
% 35.45/5.21 % CPU time: 37.150891 seconds
% 35.45/5.21 % Total memory used: 444.781 MB
% 35.45/5.21 % Net memory used: 440.298 MB
%------------------------------------------------------------------------------