%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP729-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 5.12s 1.21s
% Output : CNFRefutation 5.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 37 unt; 0 def)
% Number of atoms : 37 ( 36 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 : 5 ( 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 : 67 ( 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : mult(A,i(A)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : mult(i(A),A) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] : i(mult(A,B)) = mult(i(A),i(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] : mult(i(A),mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] : mult(A,B) = mult(mult(B,A),op_k(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B,C,D,E] : asoc(A,B,asoc(C,D,E)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
asoc(a,b,op_k(c,d)) != unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
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(f45,plain,
! [X0,X1,X2,X3,X4] : asoc(X0,X1,asoc(X2,X3,X4)) = unit,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f46,plain,
asoc(a,b,op_k(c,d)) != unit,
inference(cnf_transformation,[status(thm)],[f23]) ).
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(f370,plain,
! [X0,X1] : mult(X0,i(mult(X0,X1))) = i(X1),
inference(paramodulation,[status(thm)],[f28,f296]) ).
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(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(f3186,plain,
! [X0,X1,X2,X3] : asoc(X0,X1,op_k(X2,X3)) = unit,
inference(paramodulation,[status(thm)],[f1139,f45]) ).
fof(f3273,plain,
unit != unit,
inference(backward_demodulation,[status(thm)],[f3186,f46]) ).
fof(f3312,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP729-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n019.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 20 20:36:20 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 5.12/1.21 % Refutation found
% 5.12/1.21 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.12/1.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.92/1.28 % Elapsed time: 0.811246 seconds
% 5.92/1.28 % CPU time: 6.200987 seconds
% 5.92/1.28 % Total memory used: 142.057 MB
% 5.92/1.28 % Net memory used: 139.931 MB
%------------------------------------------------------------------------------