%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE040+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:57:50 PM UTC 2026
% Result : Theorem 11.76s 17.05s
% Output : CNFRefutation 11.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 92 ( 50 unt; 2 def)
% Number of atoms : 153 ( 80 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 123 ( 62 ~; 55 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 137 ( 136 !; 1 ?)
% 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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0] : multiplication(star(X0),star(X0)) = star(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] : multiplication(star(X0),star(X0)) = star(X0),
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(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
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(f30,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f38,plain,
! [A,B,C] :
( leq(multiplication(C,star(B)),A)
| ~ leq(addition(multiplication(A,B),C),A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
? [X0] : multiplication(star(X0),star(X0)) != star(X0),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
multiplication(star(sK0_skl),star(sK0_skl)) != star(sK0_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f40]) ).
fof(f42,plain,
multiplication(star(sK0_skl),star(sK0_skl)) != star(sK0_skl),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f56,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f63,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f87,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f63]) ).
fof(f118,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f87,f20]) ).
fof(f134,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f118]) ).
fof(f136,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f134]) ).
fof(f144,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f26]) ).
fof(f149,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f152,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f159,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f26,f144]) ).
fof(f169,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f152]) ).
fof(f221,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f56,f63]) ).
fof(f271,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f136,f221]) ).
fof(f1936,plain,
! [X0,X1] :
( leq(star(X1),X0)
| ~ leq(addition(multiplication(X0,X1),one),X0) ),
inference(paramodulation,[status(thm)],[f25,f39]) ).
fof(f1945,plain,
! [X0,X1] :
( leq(star(X1),X0)
| ~ leq(addition(one,multiplication(X0,X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f19,f1936]) ).
fof(f1946,plain,
! [X0,X1] :
( ~ leq(addition(one,multiplication(X1,X0)),X1)
| addition(star(X0),X1) = X1 ),
inference(resolution,[status(thm)],[f32,f1945]) ).
fof(f1949,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f32,f35]) ).
fof(f1955,plain,
! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f1949]) ).
fof(f1956,plain,
! [X0] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f271,f1955]) ).
fof(f1957,plain,
! [X0] : addition(one,multiplication(star(X0),addition(X0,one))) = star(X0),
inference(forward_demodulation,[status(thm)],[f169,f1956]) ).
fof(f2005,plain,
! [X0] : addition(multiplication(star(X0),addition(X0,one)),star(X0)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(paramodulation,[status(thm)],[f1957,f87]) ).
fof(f2006,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(star(X0),addition(X0,one))),
inference(paramodulation,[status(thm)],[f1957,f63]) ).
fof(f2029,plain,
! [X0] : addition(star(X0),multiplication(star(X0),addition(X0,one))) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f19,f2005]) ).
fof(f2030,plain,
! [X0] : multiplication(star(X0),addition(addition(X0,one),one)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f169,f2029]) ).
fof(f2031,plain,
! [X0] : multiplication(star(X0),addition(one,addition(X0,one))) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f159,f2030]) ).
fof(f2032,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(multiplication(star(X0),addition(X0,one)),one),
inference(forward_demodulation,[status(thm)],[f87,f2031]) ).
fof(f2033,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(one,multiplication(star(X0),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f19,f2032]) ).
fof(f2035,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f1957,f2033]) ).
fof(f2039,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f1957,f2006]) ).
fof(f2047,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f2039,f149]) ).
fof(f2074,plain,
! [X0] : multiplication(star(X0),addition(X0,one)) = star(X0),
inference(paramodulation,[status(thm)],[f159,f2035]) ).
fof(f2894,plain,
! [X0] :
( ~ leq(addition(one,X0),one)
| addition(star(X0),one) = one ),
inference(paramodulation,[status(thm)],[f25,f1946]) ).
fof(f2936,plain,
! [X0] :
( ~ leq(addition(one,X0),one)
| addition(one,star(X0)) = one ),
inference(forward_demodulation,[status(thm)],[f19,f2894]) ).
fof(f2937,plain,
! [X0] :
( ~ leq(addition(one,X0),one)
| star(X0) = one ),
inference(forward_demodulation,[status(thm)],[f2039,f2936]) ).
fof(f3406,plain,
( ~ leq(one,one)
| star(one) = one ),
inference(paramodulation,[status(thm)],[f22,f2937]) ).
fof(f3419,definition,
( sQ5_spl
<=> leq(one,one) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f3421,plain,
( sQ5_spl
| ~ leq(one,one) ),
inference(component_clause,[status(thm)],[f3419]) ).
fof(f3423,definition,
( sQ6_spl
<=> star(one) = one ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f3424,plain,
( ~ sQ6_spl
| star(one) = one ),
inference(component_clause,[status(thm)],[f3423]) ).
fof(f3426,plain,
( ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f3406,f3423,f3419]) ).
fof(f3427,plain,
( sQ5_spl
| addition(one,one) != one ),
inference(resolution,[status(thm)],[f3421,f33]) ).
fof(f3428,plain,
( sQ5_spl
| one != one ),
inference(forward_demodulation,[status(thm)],[f22,f3427]) ).
fof(f3429,plain,
( sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3428]) ).
fof(f3430,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f3429]) ).
fof(f3495,plain,
! [X0,X1] :
( ~ sQ6_spl
| leq(multiplication(X1,one),X0)
| ~ leq(addition(multiplication(X0,one),X1),X0) ),
inference(paramodulation,[status(thm)],[f3424,f39]) ).
fof(f3504,plain,
! [X0,X1] :
( ~ sQ6_spl
| leq(multiplication(X1,one),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f3495]) ).
fof(f3505,plain,
! [X0,X1] :
( ~ sQ6_spl
| leq(X1,X0)
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f3504]) ).
fof(f3524,plain,
! [X0,X1] :
( ~ sQ6_spl
| addition(X1,X0) = X0
| ~ leq(addition(X0,X1),X0) ),
inference(resolution,[status(thm)],[f3505,f32]) ).
fof(f3552,plain,
! [X0,X1] :
( ~ sQ6_spl
| addition(addition(X0,X1),X0) = X0
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f63,f3524]) ).
fof(f3589,plain,
! [X0,X1] :
( ~ sQ6_spl
| addition(X0,addition(X1,X0)) = X0
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f20,f3552]) ).
fof(f3590,plain,
! [X0,X1] :
( ~ sQ6_spl
| addition(X0,X1) = X0
| ~ leq(addition(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f87,f3589]) ).
fof(f4042,plain,
! [X0,X1] :
( ~ sQ6_spl
| addition(X0,multiplication(X0,star(X1))) = X0
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(paramodulation,[status(thm)],[f2047,f3590]) ).
fof(f4152,plain,
! [X0,X1] :
( ~ sQ6_spl
| multiplication(X0,star(X1)) = X0
| ~ leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f2047,f4042]) ).
fof(f4168,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ leq(addition(multiplication(X0,X1),X0),X0)
| multiplication(X0,star(X1)) = X0 ),
inference(resolution,[status(thm)],[f4152,f39]) ).
fof(f4184,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ leq(addition(X0,multiplication(X0,X1)),X0)
| multiplication(X0,star(X1)) = X0 ),
inference(forward_demodulation,[status(thm)],[f19,f4168]) ).
fof(f4914,plain,
! [X0,X1] :
( ~ sQ6_spl
| addition(addition(X0,multiplication(X0,X1)),X0) != X0
| multiplication(X0,star(X1)) = X0 ),
inference(resolution,[status(thm)],[f4184,f33]) ).
fof(f4947,plain,
! [X0,X1] :
( ~ sQ6_spl
| addition(X0,addition(multiplication(X0,X1),X0)) != X0
| multiplication(X0,star(X1)) = X0 ),
inference(forward_demodulation,[status(thm)],[f20,f4914]) ).
fof(f4948,plain,
! [X0,X1] :
( ~ sQ6_spl
| addition(X0,addition(X0,multiplication(X0,X1))) != X0
| multiplication(X0,star(X1)) = X0 ),
inference(forward_demodulation,[status(thm)],[f271,f4947]) ).
fof(f4949,plain,
! [X0,X1] :
( ~ sQ6_spl
| addition(X0,multiplication(X0,X1)) != X0
| multiplication(X0,star(X1)) = X0 ),
inference(forward_demodulation,[status(thm)],[f63,f4948]) ).
fof(f5409,plain,
( ~ sQ6_spl
| addition(star(sK0_skl),multiplication(star(sK0_skl),sK0_skl)) != star(sK0_skl) ),
inference(resolution,[status(thm)],[f4949,f42]) ).
fof(f5423,plain,
( ~ sQ6_spl
| multiplication(star(sK0_skl),addition(sK0_skl,one)) != star(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f169,f5409]) ).
fof(f5424,plain,
( ~ sQ6_spl
| star(sK0_skl) != star(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f2074,f5423]) ).
fof(f5425,plain,
( ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5424]) ).
fof(f5426,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f5425]) ).
fof(f5427,plain,
$false,
inference(sat_refutation,[status(thm)],[f3426,f3430,f5426]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE040+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/15.46 % Computer : n002.cluster.edu
% 0.18/15.46 % Model : x86_64 x86_64
% 0.18/15.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/15.46 % Memory : 8046.5625MB
% 0.18/15.46 % OS : Linux 6.8.0-71-generic
% 0.18/15.46 % CPULimit : 300
% 0.18/15.46 % WCLimit : 300
% 0.18/15.46 % DateTime : Sun Sep 20 22:43:02 UTC 2026
% 0.18/15.46 % CPUTime :
% 0.18/15.48 % Drodi V4.1.1
% 11.76/17.05 % Refutation found
% 11.76/17.05 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.76/17.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.76/17.11 % Elapsed time: 1.623320 seconds
% 11.76/17.11 % CPU time: 12.319297 seconds
% 11.76/17.11 % Total memory used: 146.389 MB
% 11.76/17.11 % Net memory used: 144.105 MB
%------------------------------------------------------------------------------