%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG210+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 11:48:57 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 51 ( 39 unt; 0 def)
% Number of atoms : 81 ( 54 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 62 ( 32 ~; 14 |; 13 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 55 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : times(times(A,B),C) = times(B,times(C,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( element(B)
<=> ? [C] :
( times(B,B) = C
& times(B,C) = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
! [A,B] :
( ( element(B)
& element(A) )
=> element(times(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ! [A,B] :
( ( element(B)
& element(A) )
=> element(times(A,B)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1,X2] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [B] :
( ( ! [C] :
( times(B,B) != C
| times(B,C) != B )
| element(B) )
& ( ? [C] :
( times(B,B) = C
& times(B,C) = B )
| ~ element(B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
( ! [B] :
( ! [C] :
( times(B,B) != C
| times(B,C) != B )
| element(B) )
& ! [B] :
( ? [C] :
( times(B,B) = C
& times(B,C) = B )
| ~ element(B) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
( ! [B] :
( ! [C] :
( times(B,B) != C
| times(B,C) != B )
| element(B) )
& ! [B] :
( ( times(B,B) = sK0_skl(B)
& times(B,sK0_skl(B)) = B )
| ~ element(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B))],[f7]) ).
fof(f9,plain,
! [X0] :
( times(X0,sK0_skl(X0)) = X0
| ~ element(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0] :
( times(X0,X0) = sK0_skl(X0)
| ~ element(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( times(X0,X0) != X1
| times(X0,X1) != X0
| element(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f12,plain,
? [A,B] :
( ~ element(times(A,B))
& element(B)
& element(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
( ~ element(times(sK1_skl,sK2_skl))
& element(sK2_skl)
& element(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(A,sK1_skl),skolemize(B,sK2_skl)],[f12]) ).
fof(f14,plain,
element(sK1_skl),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
element(sK2_skl),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
~ element(times(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
! [X0] :
( times(X0,times(X0,X0)) != X0
| element(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f11]) ).
fof(f18,plain,
times(sK2_skl,sK0_skl(sK2_skl)) = sK2_skl,
inference(resolution,[status(thm)],[f9,f15]) ).
fof(f19,plain,
times(sK1_skl,sK0_skl(sK1_skl)) = sK1_skl,
inference(resolution,[status(thm)],[f9,f14]) ).
fof(f20,plain,
! [X0,X1,X2,X3] : times(times(X0,times(X1,X2)),X3) = times(X1,times(X3,times(X2,X0))),
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f21,plain,
! [X0,X1,X2,X3] : times(times(X0,X1),times(X2,X3)) = times(X0,times(X2,times(X1,X3))),
inference(forward_demodulation,[status(thm)],[f5,f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : times(X0,times(times(X1,X2),X3)) = times(X3,times(X1,times(X0,X2))),
inference(forward_demodulation,[status(thm)],[f5,f21]) ).
fof(f23,plain,
! [X0,X1,X2,X3] : times(X0,times(X1,times(X2,X3))) = times(X2,times(X3,times(X0,X1))),
inference(forward_demodulation,[status(thm)],[f5,f22]) ).
fof(f24,plain,
times(sK2_skl,sK2_skl) = sK0_skl(sK2_skl),
inference(resolution,[status(thm)],[f10,f15]) ).
fof(f25,plain,
times(sK1_skl,sK1_skl) = sK0_skl(sK1_skl),
inference(resolution,[status(thm)],[f10,f14]) ).
fof(f26,plain,
! [X0] : times(sK2_skl,X0) = times(sK0_skl(sK2_skl),times(X0,sK2_skl)),
inference(paramodulation,[status(thm)],[f18,f5]) ).
fof(f28,plain,
! [X0] : times(sK0_skl(sK2_skl),X0) = times(sK2_skl,times(X0,sK2_skl)),
inference(paramodulation,[status(thm)],[f24,f5]) ).
fof(f29,plain,
times(times(sK1_skl,sK2_skl),times(times(sK1_skl,sK2_skl),times(sK1_skl,sK2_skl))) != times(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f17,f16]) ).
fof(f32,plain,
times(sK2_skl,times(times(times(sK1_skl,sK2_skl),times(sK1_skl,sK2_skl)),sK1_skl)) != times(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f5,f29]) ).
fof(f33,plain,
times(sK2_skl,times(times(sK1_skl,sK2_skl),times(sK1_skl,times(sK1_skl,sK2_skl)))) != times(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f5,f32]) ).
fof(f34,plain,
times(sK1_skl,times(times(sK1_skl,sK2_skl),times(sK2_skl,times(sK1_skl,sK2_skl)))) != times(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f23,f33]) ).
fof(f35,plain,
times(sK1_skl,times(sK2_skl,times(times(sK2_skl,times(sK1_skl,sK2_skl)),sK1_skl))) != times(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f5,f34]) ).
fof(f36,plain,
times(sK1_skl,times(sK2_skl,times(times(sK1_skl,sK2_skl),times(sK1_skl,sK2_skl)))) != times(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f5,f35]) ).
fof(f37,plain,
times(sK1_skl,times(sK1_skl,times(sK2_skl,times(sK2_skl,times(sK1_skl,sK2_skl))))) != times(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f23,f36]) ).
fof(f38,plain,
times(sK1_skl,times(sK1_skl,times(sK1_skl,times(sK2_skl,times(sK2_skl,sK2_skl))))) != times(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f23,f37]) ).
fof(f39,plain,
times(sK1_skl,times(sK1_skl,times(sK1_skl,times(sK0_skl(sK2_skl),sK2_skl)))) != times(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f28,f38]) ).
fof(f77,plain,
! [X0,X1] : times(X0,times(sK2_skl,X1)) = times(X1,times(sK2_skl,times(X0,sK0_skl(sK2_skl)))),
inference(paramodulation,[status(thm)],[f26,f23]) ).
fof(f82,plain,
! [X0,X1] : times(X0,times(X1,sK0_skl(sK1_skl))) = times(sK1_skl,times(sK1_skl,times(X0,X1))),
inference(paramodulation,[status(thm)],[f25,f23]) ).
fof(f83,plain,
! [X0,X1] : times(X0,times(X1,sK1_skl)) = times(sK1_skl,times(sK0_skl(sK1_skl),times(X0,X1))),
inference(paramodulation,[status(thm)],[f19,f23]) ).
fof(f125,plain,
times(sK1_skl,times(sK0_skl(sK2_skl),times(sK2_skl,sK0_skl(sK1_skl)))) != times(sK1_skl,sK2_skl),
inference(backward_demodulation,[status(thm)],[f82,f39]) ).
fof(f269,plain,
times(sK0_skl(sK2_skl),sK2_skl) = times(sK2_skl,sK0_skl(sK2_skl)),
inference(paramodulation,[status(thm)],[f24,f28]) ).
fof(f271,plain,
! [X0,X1] : times(X0,times(sK2_skl,times(X1,sK2_skl))) = times(X1,times(sK0_skl(sK2_skl),X0)),
inference(paramodulation,[status(thm)],[f28,f23]) ).
fof(f277,plain,
times(sK0_skl(sK2_skl),sK2_skl) = sK2_skl,
inference(forward_demodulation,[status(thm)],[f18,f269]) ).
fof(f278,plain,
! [X0,X1] : times(X0,times(sK0_skl(sK2_skl),X1)) = times(X1,times(sK0_skl(sK2_skl),X0)),
inference(forward_demodulation,[status(thm)],[f28,f271]) ).
fof(f296,plain,
! [X0] : times(sK2_skl,X0) = times(sK2_skl,times(X0,sK0_skl(sK2_skl))),
inference(paramodulation,[status(thm)],[f277,f5]) ).
fof(f299,plain,
! [X0,X1] : times(X0,times(sK2_skl,X1)) = times(X1,times(sK2_skl,X0)),
inference(backward_demodulation,[status(thm)],[f296,f77]) ).
fof(f300,plain,
times(sK1_skl,times(sK0_skl(sK1_skl),times(sK2_skl,sK0_skl(sK2_skl)))) != times(sK1_skl,sK2_skl),
inference(backward_demodulation,[status(thm)],[f299,f125]) ).
fof(f301,plain,
times(sK2_skl,times(sK0_skl(sK2_skl),sK1_skl)) != times(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f83,f300]) ).
fof(f302,plain,
times(sK1_skl,times(sK0_skl(sK2_skl),sK2_skl)) != times(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f278,f301]) ).
fof(f303,plain,
times(sK1_skl,sK2_skl) != times(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f277,f302]) ).
fof(f304,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG210+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 12:59:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.061466 seconds
% 0.14/0.43 % CPU time: 0.268916 seconds
% 0.14/0.43 % Total memory used: 56.420 MB
% 0.14/0.43 % Net memory used: 56.123 MB
%------------------------------------------------------------------------------