%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE035+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 12:57:49 PM UTC 2026
% Result : Theorem 0.15s 0.56s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 29 unt; 0 def)
% Number of atoms : 63 ( 29 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 40 ( 15 ~; 6 |; 16 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 48 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f32,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f33,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f58,plain,
? [X0,X1,X2,X3] :
( ~ leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f59,plain,
( ~ leq(multiplication(multiplication(sK3_skl,addition(sK1_skl,sK2_skl)),c(sK4_skl)),zero)
& leq(multiplication(multiplication(sK3_skl,sK2_skl),c(sK4_skl)),zero)
& leq(multiplication(multiplication(sK3_skl,sK1_skl),c(sK4_skl)),zero)
& test(sK3_skl)
& test(sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(X0,sK1_skl),skolemize(X1,sK2_skl),skolemize(X2,sK3_skl),skolemize(X3,sK4_skl)],[f58]) ).
fof(f62,plain,
leq(multiplication(multiplication(sK3_skl,sK1_skl),c(sK4_skl)),zero),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f63,plain,
leq(multiplication(multiplication(sK3_skl,sK2_skl),c(sK4_skl)),zero),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f64,plain,
~ leq(multiplication(multiplication(sK3_skl,addition(sK1_skl,sK2_skl)),c(sK4_skl)),zero),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f66,plain,
leq(multiplication(sK3_skl,multiplication(sK1_skl,c(sK4_skl))),zero),
inference(forward_demodulation,[status(thm)],[f25,f62]) ).
fof(f67,plain,
leq(multiplication(sK3_skl,multiplication(sK2_skl,c(sK4_skl))),zero),
inference(forward_demodulation,[status(thm)],[f25,f63]) ).
fof(f68,plain,
~ leq(multiplication(sK3_skl,multiplication(addition(sK1_skl,sK2_skl),c(sK4_skl))),zero),
inference(forward_demodulation,[status(thm)],[f25,f64]) ).
fof(f71,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f199,plain,
addition(multiplication(sK3_skl,multiplication(sK1_skl,c(sK4_skl))),zero) = zero,
inference(resolution,[status(thm)],[f34,f66]) ).
fof(f201,plain,
multiplication(sK3_skl,multiplication(sK1_skl,c(sK4_skl))) = zero,
inference(forward_demodulation,[status(thm)],[f23,f199]) ).
fof(f207,plain,
! [X0] : multiplication(sK3_skl,addition(multiplication(sK1_skl,c(sK4_skl)),X0)) = addition(zero,multiplication(sK3_skl,X0)),
inference(paramodulation,[status(thm)],[f201,f28]) ).
fof(f212,plain,
! [X0] : multiplication(sK3_skl,addition(multiplication(sK1_skl,c(sK4_skl)),X0)) = multiplication(sK3_skl,X0),
inference(forward_demodulation,[status(thm)],[f71,f207]) ).
fof(f215,plain,
addition(multiplication(sK3_skl,multiplication(sK2_skl,c(sK4_skl))),zero) = zero,
inference(resolution,[status(thm)],[f67,f34]) ).
fof(f217,plain,
multiplication(sK3_skl,multiplication(sK2_skl,c(sK4_skl))) = zero,
inference(forward_demodulation,[status(thm)],[f23,f215]) ).
fof(f218,plain,
addition(multiplication(sK3_skl,multiplication(addition(sK1_skl,sK2_skl),c(sK4_skl))),zero) != zero,
inference(resolution,[status(thm)],[f68,f35]) ).
fof(f219,plain,
multiplication(sK3_skl,multiplication(addition(sK1_skl,sK2_skl),c(sK4_skl))) != zero,
inference(forward_demodulation,[status(thm)],[f23,f218]) ).
fof(f286,plain,
! [X0] : multiplication(sK3_skl,multiplication(addition(sK1_skl,X0),c(sK4_skl))) = multiplication(sK3_skl,multiplication(X0,c(sK4_skl))),
inference(paramodulation,[status(thm)],[f29,f212]) ).
fof(f298,plain,
multiplication(sK3_skl,multiplication(sK2_skl,c(sK4_skl))) != zero,
inference(backward_demodulation,[status(thm)],[f286,f219]) ).
fof(f307,plain,
zero != zero,
inference(forward_demodulation,[status(thm)],[f217,f298]) ).
fof(f308,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f307]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE035+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.47 % Computer : n007.cluster.edu
% 0.15/0.47 % Model : x86_64 x86_64
% 0.15/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.47 % Memory : 8046.5625MB
% 0.15/0.47 % OS : Linux 6.8.0-71-generic
% 0.15/0.47 % CPULimit : 300
% 0.15/0.47 % WCLimit : 300
% 0.15/0.47 % DateTime : Sun Sep 20 22:37:35 UTC 2026
% 0.15/0.48 % CPUTime :
% 0.15/0.51 % Drodi V4.1.1
% 0.15/0.56 % Refutation found
% 0.15/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.61 % Elapsed time: 0.121673 seconds
% 0.20/0.61 % CPU time: 0.342218 seconds
% 0.20/0.61 % Total memory used: 48.188 MB
% 0.20/0.61 % Net memory used: 48.030 MB
%------------------------------------------------------------------------------