%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP731-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:35:14 PM UTC 2026
% Result : Unsatisfiable 1.19s 0.83s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 58 unt; 0 def)
% Number of atoms : 58 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 113 ( 113 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : mult(A,i(A)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : mult(i(A),A) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] : i(mult(A,B)) = mult(i(A),i(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] : mult(i(A),mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C] : mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] : mult(A,B) = mult(mult(B,A),op_k(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B,C,D,E] : asoc(asoc(A,B,C),D,E) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B,C,D,E] : asoc(A,B,asoc(C,D,E)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
op_k(asoc(a,b,c),d) != unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0] : mult(X0,i(X0)) = unit,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
! [X0] : mult(i(X0),X0) = unit,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0,X1] : i(mult(X0,X1)) = mult(i(X0),i(X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0,X1] : mult(i(X0),mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f30,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f33,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,mult(X1,X2)),asoc(X0,X1,X2)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f34,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(X1,X0),op_k(X0,X1)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] : asoc(asoc(X0,X1,X2),X3,X4) = unit,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] : asoc(X0,X1,asoc(X2,X3,X4)) = unit,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f46,plain,
op_k(asoc(a,b,c),d) != unit,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f52,plain,
i(unit) = unit,
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f58,plain,
! [X0,X1] : mult(mult(i(mult(X0,X1)),X0),X1) = mult(unit,asoc(i(mult(X0,X1)),X0,X1)),
inference(paramodulation,[status(thm)],[f27,f33]) ).
fof(f65,plain,
! [X0,X1] : mult(mult(i(mult(X0,X1)),X0),X1) = asoc(i(mult(X0,X1)),X0,X1),
inference(forward_demodulation,[status(thm)],[f24,f58]) ).
fof(f273,plain,
! [X0] : rd(unit,X0) = i(X0),
inference(paramodulation,[status(thm)],[f27,f30]) ).
fof(f275,plain,
! [X0] : rd(unit,i(X0)) = X0,
inference(paramodulation,[status(thm)],[f26,f30]) ).
fof(f279,plain,
! [X0] : i(i(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f273,f275]) ).
fof(f296,plain,
! [X0,X1] : mult(X0,mult(i(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f279,f29]) ).
fof(f299,plain,
! [X0,X1] : mult(i(mult(X0,X1)),mult(X1,X0)) = op_k(X1,X0),
inference(paramodulation,[status(thm)],[f34,f29]) ).
fof(f366,plain,
! [X0,X1] : i(mult(i(X0),X1)) = mult(X0,i(X1)),
inference(paramodulation,[status(thm)],[f279,f28]) ).
fof(f368,plain,
! [X0,X1] : i(mult(X0,i(X1))) = mult(i(X0),X1),
inference(paramodulation,[status(thm)],[f279,f28]) ).
fof(f370,plain,
! [X0,X1] : mult(X0,i(mult(X0,X1))) = i(X1),
inference(paramodulation,[status(thm)],[f28,f296]) ).
fof(f390,plain,
! [X0,X1] : mult(mult(X0,X1),i(mult(X1,X0))) = i(op_k(X1,X0)),
inference(paramodulation,[status(thm)],[f34,f370]) ).
fof(f1084,plain,
! [X0,X1] : mult(mult(i(mult(X0,X1)),mult(X1,X0)),op_k(X0,X1)) = asoc(i(mult(mult(X1,X0),op_k(X0,X1))),mult(X1,X0),op_k(X0,X1)),
inference(paramodulation,[status(thm)],[f34,f65]) ).
fof(f1088,plain,
! [X0,X1] : mult(mult(i(X0),i(X1)),mult(X1,X0)) = asoc(i(mult(i(X1),mult(X1,X0))),i(X1),mult(X1,X0)),
inference(paramodulation,[status(thm)],[f29,f65]) ).
fof(f1093,plain,
! [X0,X1] : mult(mult(i(i(X0)),X1),i(mult(X1,X0))) = asoc(i(mult(X1,i(mult(X1,X0)))),X1,i(mult(X1,X0))),
inference(paramodulation,[status(thm)],[f370,f65]) ).
fof(f1125,plain,
! [X0,X1] : mult(op_k(X0,X1),op_k(X1,X0)) = asoc(i(mult(mult(X0,X1),op_k(X1,X0))),mult(X0,X1),op_k(X1,X0)),
inference(forward_demodulation,[status(thm)],[f299,f1084]) ).
fof(f1126,plain,
! [X0,X1] : mult(op_k(X0,X1),op_k(X1,X0)) = asoc(i(mult(X1,X0)),mult(X0,X1),op_k(X1,X0)),
inference(forward_demodulation,[status(thm)],[f34,f1125]) ).
fof(f1136,plain,
! [X0,X1] : mult(i(mult(X0,X1)),mult(X1,X0)) = asoc(i(mult(i(X1),mult(X1,X0))),i(X1),mult(X1,X0)),
inference(forward_demodulation,[status(thm)],[f28,f1088]) ).
fof(f1137,plain,
! [X0,X1] : op_k(X0,X1) = asoc(i(mult(i(X0),mult(X0,X1))),i(X0),mult(X0,X1)),
inference(forward_demodulation,[status(thm)],[f299,f1136]) ).
fof(f1138,plain,
! [X0,X1] : op_k(X0,X1) = asoc(mult(X0,i(mult(X0,X1))),i(X0),mult(X0,X1)),
inference(forward_demodulation,[status(thm)],[f366,f1137]) ).
fof(f1139,plain,
! [X0,X1] : op_k(X0,X1) = asoc(i(X1),i(X0),mult(X0,X1)),
inference(forward_demodulation,[status(thm)],[f370,f1138]) ).
fof(f1150,plain,
! [X0,X1] : mult(mult(X0,X1),i(mult(X1,X0))) = asoc(i(mult(X1,i(mult(X1,X0)))),X1,i(mult(X1,X0))),
inference(forward_demodulation,[status(thm)],[f279,f1093]) ).
fof(f1151,plain,
! [X0,X1] : i(op_k(X0,X1)) = asoc(i(mult(X0,i(mult(X0,X1)))),X0,i(mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f390,f1150]) ).
fof(f1152,plain,
! [X0,X1] : i(op_k(X0,X1)) = asoc(mult(i(X0),mult(X0,X1)),X0,i(mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f368,f1151]) ).
fof(f1153,plain,
! [X0,X1] : i(op_k(X0,X1)) = asoc(X1,X0,i(mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f29,f1152]) ).
fof(f3186,plain,
! [X0,X1,X2,X3] : asoc(X0,X1,op_k(X2,X3)) = unit,
inference(paramodulation,[status(thm)],[f1139,f45]) ).
fof(f3277,plain,
! [X0,X1] : mult(op_k(X0,X1),op_k(X1,X0)) = unit,
inference(backward_demodulation,[status(thm)],[f3186,f1126]) ).
fof(f3570,plain,
! [X0,X1] : mult(op_k(X0,X1),i(unit)) = i(op_k(X1,X0)),
inference(paramodulation,[status(thm)],[f3277,f370]) ).
fof(f3613,plain,
! [X0,X1] : mult(op_k(X0,X1),unit) = i(op_k(X1,X0)),
inference(forward_demodulation,[status(thm)],[f52,f3570]) ).
fof(f3624,plain,
! [X0,X1] : op_k(X0,X1) = asoc(X0,X1,i(mult(X1,X0))),
inference(backward_demodulation,[status(thm)],[f3626,f1153]) ).
fof(f3626,plain,
! [X0,X1] : op_k(X0,X1) = i(op_k(X1,X0)),
inference(forward_demodulation,[status(thm)],[f25,f3613]) ).
fof(f6158,plain,
! [X0,X1,X2,X3] : op_k(asoc(X0,X1,X2),X3) = unit,
inference(paramodulation,[status(thm)],[f44,f3624]) ).
fof(f6207,plain,
unit != unit,
inference(backward_demodulation,[status(thm)],[f6158,f46]) ).
fof(f6302,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f6207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP731-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n002.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 20 20:38:31 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.45 % Drodi V4.1.1
% 1.19/0.83 % Refutation found
% 1.19/0.83 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.19/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.19/0.89 % Elapsed time: 0.432015 seconds
% 1.19/0.89 % CPU time: 3.164133 seconds
% 1.19/0.89 % Total memory used: 78.978 MB
% 1.19/0.89 % Net memory used: 77.671 MB
%------------------------------------------------------------------------------