%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE010+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:57:44 PM UTC 2026
% Result : Theorem 0.31s 0.43s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 79 ( 57 unt; 0 def)
% Number of atoms : 134 ( 84 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 106 ( 51 ~; 29 |; 19 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 112 ( 107 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
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(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
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(f36,plain,
! [X0] :
( ( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f37,plain,
( ! [X0] :
( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ! [X0] :
( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
( ! [X0] :
( ! [X1] : ~ complement(X1,X0)
| test(X0) )
& ! [X0] :
( complement(sK0_skl(X0),X0)
| ~ test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X1,sK0_skl(X0))],[f37]) ).
fof(f39,plain,
! [X0] :
( complement(sK0_skl(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f48,plain,
! [X0,X1] :
( ( ( ~ complement(X0,X1)
| c(X0) = X1 )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0] :
( ( ! [X1] :
( ~ complement(X0,X1)
| c(X0) = X1 )
& ! [X1] :
( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f58,plain,
? [X0,X1] :
( one != addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))
& test(X0)
& test(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f59,plain,
( one != addition(addition(addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl)))
& test(sK1_skl)
& test(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(X0,sK1_skl),skolemize(X1,sK2_skl)],[f58]) ).
fof(f60,plain,
test(sK2_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
test(sK1_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
one != addition(addition(addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),multiplication(sK1_skl,sK2_skl)),multiplication(c(sK1_skl),sK2_skl)),multiplication(c(sK1_skl),c(sK2_skl))),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f63,plain,
! [X0] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f50]) ).
fof(f64,plain,
one != addition(addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),multiplication(sK1_skl,sK2_skl)),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(c(sK1_skl),c(sK2_skl)))),
inference(forward_demodulation,[status(thm)],[f22,f62]) ).
fof(f65,plain,
one != addition(addition(multiplication(sK2_skl,sK1_skl),multiplication(c(sK2_skl),sK1_skl)),addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(c(sK1_skl),c(sK2_skl))))),
inference(forward_demodulation,[status(thm)],[f22,f64]) ).
fof(f66,plain,
one != addition(multiplication(sK2_skl,sK1_skl),addition(multiplication(c(sK2_skl),sK1_skl),addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(c(sK1_skl),sK2_skl),multiplication(c(sK1_skl),c(sK2_skl)))))),
inference(forward_demodulation,[status(thm)],[f22,f65]) ).
fof(f67,plain,
one != addition(multiplication(sK2_skl,sK1_skl),addition(multiplication(c(sK2_skl),sK1_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl)))))),
inference(forward_demodulation,[status(thm)],[f28,f66]) ).
fof(f74,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f78,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f80,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f84,plain,
one != addition(multiplication(sK2_skl,sK1_skl),addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl))),multiplication(c(sK2_skl),sK1_skl)))),
inference(backward_demodulation,[status(thm)],[f74,f67]) ).
fof(f87,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f22,f78]) ).
fof(f89,plain,
one != addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK2_skl,sK1_skl),addition(multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl))),multiplication(c(sK2_skl),sK1_skl)))),
inference(forward_demodulation,[status(thm)],[f87,f84]) ).
fof(f90,plain,
one != addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(sK2_skl,sK1_skl),addition(multiplication(c(sK2_skl),sK1_skl),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl)))))),
inference(forward_demodulation,[status(thm)],[f21,f89]) ).
fof(f143,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f164,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f21,f143]) ).
fof(f182,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3),
inference(paramodulation,[status(thm)],[f29,f22]) ).
fof(f199,plain,
one != addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl),multiplication(c(sK1_skl),addition(sK2_skl,c(sK2_skl))))),
inference(backward_demodulation,[status(thm)],[f182,f90]) ).
fof(f212,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f80]) ).
fof(f249,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f212,f22]) ).
fof(f269,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f22,f249]) ).
fof(f271,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f22,f269]) ).
fof(f319,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f74,f80]) ).
fof(f370,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f271,f319]) ).
fof(f522,plain,
! [X0] :
( addition(X0,sK0_skl(X0)) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f39,f45]) ).
fof(f524,plain,
! [X0] :
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f63,f45]) ).
fof(f526,plain,
! [X0] :
( addition(X0,c(X0)) = one
| ~ test(X0) ),
inference(forward_demodulation,[status(thm)],[f21,f524]) ).
fof(f718,plain,
addition(sK2_skl,sK0_skl(sK2_skl)) = one,
inference(resolution,[status(thm)],[f522,f60]) ).
fof(f749,plain,
addition(sK2_skl,one) = addition(sK2_skl,sK0_skl(sK2_skl)),
inference(paramodulation,[status(thm)],[f718,f80]) ).
fof(f755,plain,
addition(sK2_skl,one) = one,
inference(forward_demodulation,[status(thm)],[f718,f749]) ).
fof(f1031,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,sK2_skl)),
inference(paramodulation,[status(thm)],[f755,f164]) ).
fof(f1039,plain,
! [X0] : X0 = addition(X0,multiplication(X0,sK2_skl)),
inference(forward_demodulation,[status(thm)],[f26,f1031]) ).
fof(f1110,plain,
! [X0,X1] : addition(X0,addition(X1,multiplication(X0,sK2_skl))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f1039,f87]) ).
fof(f1171,plain,
addition(sK1_skl,c(sK1_skl)) = one,
inference(resolution,[status(thm)],[f526,f61]) ).
fof(f1172,plain,
addition(sK2_skl,c(sK2_skl)) = one,
inference(resolution,[status(thm)],[f526,f60]) ).
fof(f1174,plain,
one != addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl),multiplication(c(sK1_skl),one))),
inference(backward_demodulation,[status(thm)],[f1172,f199]) ).
fof(f1175,plain,
one != addition(multiplication(sK1_skl,sK2_skl),addition(multiplication(c(sK1_skl),one),multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl))),
inference(forward_demodulation,[status(thm)],[f370,f1174]) ).
fof(f1176,plain,
one != addition(multiplication(sK1_skl,sK2_skl),addition(c(sK1_skl),multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl))),
inference(forward_demodulation,[status(thm)],[f26,f1175]) ).
fof(f1177,plain,
one != addition(c(sK1_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(addition(sK2_skl,c(sK2_skl)),sK1_skl))),
inference(forward_demodulation,[status(thm)],[f87,f1176]) ).
fof(f1178,plain,
one != addition(c(sK1_skl),addition(multiplication(sK1_skl,sK2_skl),multiplication(one,sK1_skl))),
inference(forward_demodulation,[status(thm)],[f1172,f1177]) ).
fof(f1179,plain,
one != addition(c(sK1_skl),addition(multiplication(sK1_skl,sK2_skl),sK1_skl)),
inference(forward_demodulation,[status(thm)],[f27,f1178]) ).
fof(f1180,plain,
one != addition(sK1_skl,addition(c(sK1_skl),multiplication(sK1_skl,sK2_skl))),
inference(forward_demodulation,[status(thm)],[f74,f1179]) ).
fof(f1181,plain,
one != addition(c(sK1_skl),sK1_skl),
inference(forward_demodulation,[status(thm)],[f1110,f1180]) ).
fof(f1182,plain,
one != addition(sK1_skl,c(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f21,f1181]) ).
fof(f1183,plain,
one != one,
inference(forward_demodulation,[status(thm)],[f1171,f1182]) ).
fof(f1184,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : KLE010+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sun Sep 20 22:37:37 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.31/0.43 % Refutation found
% 0.31/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.31/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.31/0.44 % Elapsed time: 0.135288 seconds
% 0.31/0.44 % CPU time: 0.963707 seconds
% 0.31/0.44 % Total memory used: 131.183 MB
% 0.31/0.44 % Net memory used: 130.061 MB
%------------------------------------------------------------------------------