%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP401-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:33:37 PM UTC 2026
% Result : Unsatisfiable 5.14s 1.17s
% Output : CNFRefutation 5.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 26 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 20 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( A = C
| multiply(A,B) != multiply(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] :
( B = C
| multiply(A,B) != multiply(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : multiply(A,B) = multiply(B,multiply(A,commutator(A,B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : commutator(multiply(A,B),C) = multiply(commutator(A,C),commutator(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
multiply(commutator(a,b),c) != multiply(c,commutator(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [A,C] :
( A = C
| ! [B] : multiply(A,B) != multiply(C,B) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] :
( X0 = X2
| multiply(X0,X1) != multiply(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [B,C] :
( B = C
| ! [A] : multiply(A,B) != multiply(A,C) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] :
( X1 = X2
| multiply(X0,X1) != multiply(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,multiply(X0,commutator(X0,X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0,X1,X2] : commutator(multiply(X0,X1),X2) = multiply(commutator(X0,X2),commutator(X1,X2)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
multiply(commutator(a,b),c) != multiply(c,commutator(a,b)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X2,multiply(X0,multiply(X1,commutator(multiply(X0,X1),X2)))),
inference(paramodulation,[status(thm)],[f7,f12]) ).
fof(f21,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X1,multiply(multiply(X0,commutator(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f12,f7]) ).
fof(f22,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X2,multiply(X0,multiply(X1,commutator(multiply(X0,X1),X2)))),
inference(forward_demodulation,[status(thm)],[f7,f19]) ).
fof(f23,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(multiply(X0,commutator(X0,X1)),X2)),
inference(forward_demodulation,[status(thm)],[f7,f21]) ).
fof(f24,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,multiply(commutator(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f7,f23]) ).
fof(f92,plain,
! [X0] : multiply(X0,multiply(commutator(a,b),c)) != multiply(X0,multiply(c,commutator(a,b))),
inference(resolution,[status(thm)],[f11,f14]) ).
fof(f266,plain,
! [X0,X1] : multiply(X0,multiply(X1,multiply(commutator(a,b),c))) != multiply(X0,multiply(X1,multiply(c,commutator(a,b)))),
inference(resolution,[status(thm)],[f92,f11]) ).
fof(f532,plain,
multiply(a,multiply(b,c)) != multiply(b,multiply(a,multiply(c,commutator(a,b)))),
inference(paramodulation,[status(thm)],[f24,f266]) ).
fof(f553,plain,
! [X0] : multiply(multiply(a,multiply(b,c)),X0) != multiply(multiply(b,multiply(a,multiply(c,commutator(a,b)))),X0),
inference(resolution,[status(thm)],[f532,f9]) ).
fof(f556,plain,
! [X0] : multiply(a,multiply(multiply(b,c),X0)) != multiply(multiply(b,multiply(a,multiply(c,commutator(a,b)))),X0),
inference(forward_demodulation,[status(thm)],[f7,f553]) ).
fof(f557,plain,
! [X0] : multiply(a,multiply(b,multiply(c,X0))) != multiply(multiply(b,multiply(a,multiply(c,commutator(a,b)))),X0),
inference(forward_demodulation,[status(thm)],[f7,f556]) ).
fof(f558,plain,
! [X0] : multiply(a,multiply(b,multiply(c,X0))) != multiply(b,multiply(multiply(a,multiply(c,commutator(a,b))),X0)),
inference(forward_demodulation,[status(thm)],[f7,f557]) ).
fof(f559,plain,
! [X0] : multiply(a,multiply(b,multiply(c,X0))) != multiply(b,multiply(a,multiply(multiply(c,commutator(a,b)),X0))),
inference(forward_demodulation,[status(thm)],[f7,f558]) ).
fof(f560,plain,
! [X0] : multiply(a,multiply(b,multiply(c,X0))) != multiply(b,multiply(a,multiply(c,multiply(commutator(a,b),X0)))),
inference(forward_demodulation,[status(thm)],[f7,f559]) ).
fof(f796,plain,
! [X0] : multiply(a,multiply(b,multiply(c,commutator(X0,b)))) != multiply(b,multiply(a,multiply(c,commutator(multiply(a,X0),b)))),
inference(paramodulation,[status(thm)],[f13,f560]) ).
fof(f1707,plain,
multiply(a,multiply(b,multiply(c,commutator(c,b)))) != multiply(a,multiply(c,b)),
inference(paramodulation,[status(thm)],[f22,f796]) ).
fof(f1733,plain,
multiply(a,multiply(c,b)) != multiply(a,multiply(c,b)),
inference(forward_demodulation,[status(thm)],[f12,f1707]) ).
fof(f1734,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1733]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP401-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n017.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 20:06:26 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 5.14/1.17 % Refutation found
% 5.14/1.17 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.14/1.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.13/1.22 % Elapsed time: 0.862343 seconds
% 6.13/1.22 % CPU time: 6.458979 seconds
% 6.13/1.22 % Total memory used: 145.437 MB
% 6.13/1.22 % Net memory used: 142.889 MB
%------------------------------------------------------------------------------