%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE025+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 : n020.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 12:57:47 PM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 18 unt; 0 def)
% Number of atoms : 83 ( 50 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 74 ( 25 ~; 20 |; 21 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 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 ( 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f26,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f39,plain,
! [X0,X1] :
( ( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
( ! [X0,X1] :
( addition(X0,X1) != one
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| complement(X1,X0) )
& ! [X0,X1] :
( ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero )
| ~ complement(X1,X0) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f43,plain,
! [X0,X1] :
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f46,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0] :
( ( ! [X1] :
( ~ complement(X0,X1)
| c(X0) = X1 )
& ! [X1] :
( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
? [X0,X1,X2] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& test(X2)
& test(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
? [X1,X2] :
( ? [X0] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero )
& test(X2)
& test(X1) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f54,plain,
( multiplication(sK1_skl,sK3_skl) != multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl)
& multiplication(multiplication(sK1_skl,sK3_skl),c(sK2_skl)) = zero
& test(sK2_skl)
& test(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl),skolemize(X0,sK3_skl)],[f53]) ).
fof(f56,plain,
test(sK2_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f57,plain,
multiplication(multiplication(sK1_skl,sK3_skl),c(sK2_skl)) = zero,
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f58,plain,
multiplication(sK1_skl,sK3_skl) != multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f59,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f478,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f21,f19]) ).
fof(f502,plain,
! [X0] :
( ~ test(X0)
| addition(c(X0),X0) = one ),
inference(resolution,[status(thm)],[f43,f59]) ).
fof(f625,plain,
! [X0] : multiplication(multiplication(sK1_skl,sK3_skl),addition(c(sK2_skl),X0)) = addition(zero,multiplication(multiplication(sK1_skl,sK3_skl),X0)),
inference(paramodulation,[status(thm)],[f57,f26]) ).
fof(f672,plain,
! [X0] : multiplication(multiplication(sK1_skl,sK3_skl),addition(c(sK2_skl),X0)) = multiplication(multiplication(sK1_skl,sK3_skl),X0),
inference(forward_demodulation,[status(thm)],[f478,f625]) ).
fof(f1118,plain,
addition(c(sK2_skl),sK2_skl) = one,
inference(resolution,[status(thm)],[f502,f56]) ).
fof(f1123,plain,
multiplication(multiplication(sK1_skl,sK3_skl),one) = multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl),
inference(paramodulation,[status(thm)],[f1118,f672]) ).
fof(f1127,plain,
multiplication(sK1_skl,sK3_skl) = multiplication(multiplication(sK1_skl,sK3_skl),sK2_skl),
inference(forward_demodulation,[status(thm)],[f24,f1123]) ).
fof(f1128,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1127,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE025+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 22:40:17 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.44 % Refutation found
% 0.13/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.46 % Elapsed time: 0.090424 seconds
% 0.13/0.46 % CPU time: 0.473328 seconds
% 0.13/0.46 % Total memory used: 111.685 MB
% 0.13/0.46 % Net memory used: 111.375 MB
%------------------------------------------------------------------------------