%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE027+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 : n018.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 37.27s 5.12s
% Output : CNFRefutation 37.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 36 unt; 0 def)
% Number of atoms : 100 ( 65 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 75 ( 29 ~; 22 |; 18 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 91 ( 81 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
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(f11,axiom,
! [A] : multiplication(zero,A) = zero,
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,X3,X4] :
( ( test(X4)
& test(X3) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X4)
& test(X3) )
=> addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) = addition(multiplication(X3,X0),multiplication(c(X3),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(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
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(f29,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
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(f42,plain,
! [X0,X1] :
( multiplication(X0,X1) = zero
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
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,X3,X4] :
( addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2))
& test(X4)
& test(X3) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
? [X3] :
( ? [X0,X1,X2] : addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)) != addition(multiplication(X3,X0),multiplication(c(X3),X2))
& ? [X4] : test(X4)
& test(X3) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f54,plain,
( addition(multiplication(sK1_skl,addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK4_skl))),multiplication(c(sK1_skl),sK5_skl)) != addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl))
& test(sK2_skl)
& test(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X3,sK1_skl),skolemize(X4,sK2_skl),skolemize(X0,sK3_skl),skolemize(X1,sK4_skl),skolemize(X2,sK5_skl)],[f53]) ).
fof(f55,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f57,plain,
addition(multiplication(sK1_skl,addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK4_skl))),multiplication(c(sK1_skl),sK5_skl)) != addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl)),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f58,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f73,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f97,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X1,X0),X1),
inference(paramodulation,[status(thm)],[f19,f73]) ).
fof(f326,plain,
! [X0] : addition(X0,zero) = addition(zero,X0),
inference(paramodulation,[status(thm)],[f97,f21]) ).
fof(f347,plain,
! [X0] : X0 = addition(zero,X0),
inference(forward_demodulation,[status(thm)],[f21,f326]) ).
fof(f434,plain,
! [X0] :
( ~ test(X0)
| multiplication(X0,c(X0)) = zero ),
inference(resolution,[status(thm)],[f42,f58]) ).
fof(f436,plain,
! [X0] :
( ~ test(X0)
| addition(c(X0),X0) = one ),
inference(resolution,[status(thm)],[f43,f58]) ).
fof(f1000,plain,
multiplication(sK1_skl,c(sK1_skl)) = zero,
inference(resolution,[status(thm)],[f434,f55]) ).
fof(f1018,plain,
! [X0] : multiplication(sK1_skl,addition(c(sK1_skl),X0)) = addition(zero,multiplication(sK1_skl,X0)),
inference(paramodulation,[status(thm)],[f1000,f26]) ).
fof(f1019,plain,
! [X0] : multiplication(sK1_skl,multiplication(c(sK1_skl),X0)) = multiplication(zero,X0),
inference(paramodulation,[status(thm)],[f1000,f23]) ).
fof(f1024,plain,
! [X0] : multiplication(sK1_skl,addition(c(sK1_skl),X0)) = multiplication(sK1_skl,X0),
inference(forward_demodulation,[status(thm)],[f347,f1018]) ).
fof(f1025,plain,
! [X0] : multiplication(sK1_skl,multiplication(c(sK1_skl),X0)) = zero,
inference(forward_demodulation,[status(thm)],[f29,f1019]) ).
fof(f1028,plain,
addition(c(sK1_skl),sK1_skl) = one,
inference(resolution,[status(thm)],[f436,f55]) ).
fof(f4288,plain,
! [X0,X1] : multiplication(sK1_skl,addition(X0,multiplication(c(sK1_skl),X1))) = addition(multiplication(sK1_skl,X0),zero),
inference(paramodulation,[status(thm)],[f1025,f26]) ).
fof(f4300,plain,
addition(multiplication(sK1_skl,multiplication(sK1_skl,sK3_skl)),multiplication(c(sK1_skl),sK5_skl)) != addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl)),
inference(backward_demodulation,[status(thm)],[f4301,f57]) ).
fof(f4301,plain,
! [X0,X1] : multiplication(sK1_skl,addition(X0,multiplication(c(sK1_skl),X1))) = multiplication(sK1_skl,X0),
inference(forward_demodulation,[status(thm)],[f21,f4288]) ).
fof(f15320,plain,
multiplication(sK1_skl,one) = multiplication(sK1_skl,sK1_skl),
inference(paramodulation,[status(thm)],[f1028,f1024]) ).
fof(f15371,plain,
sK1_skl = multiplication(sK1_skl,sK1_skl),
inference(forward_demodulation,[status(thm)],[f24,f15320]) ).
fof(f15430,plain,
! [X0] : multiplication(sK1_skl,multiplication(sK1_skl,X0)) = multiplication(sK1_skl,X0),
inference(paramodulation,[status(thm)],[f15371,f23]) ).
fof(f15445,plain,
addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl)) != addition(multiplication(sK1_skl,sK3_skl),multiplication(c(sK1_skl),sK5_skl)),
inference(backward_demodulation,[status(thm)],[f15430,f4300]) ).
fof(f15451,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f15445]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE027+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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 : Sun Sep 20 22:41:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 37.27/5.12 % Refutation found
% 37.27/5.12 % SZS status Theorem for theBenchmark: Theorem is valid
% 37.27/5.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 37.27/5.18 % Elapsed time: 4.800296 seconds
% 37.27/5.18 % CPU time: 37.751227 seconds
% 37.27/5.18 % Total memory used: 370.850 MB
% 37.27/5.18 % Net memory used: 361.191 MB
%------------------------------------------------------------------------------