%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE128+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 : n001.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 12:58:00 PM UTC 2026
% Result : Theorem 0.17s 0.96s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 34 unt; 0 def)
% Number of atoms : 78 ( 77 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 21 ~; 15 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 55 !; 2 ?)
% 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(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X0,X1,X2] :
( addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2))
=> addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [X0] :
( divergence(X0) = zero
=> ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [X0] :
( divergence(X0) = zero
=> ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f40,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f46,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f49,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f56,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f61,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) != addition(forward_diamond(X1,domain(X0)),domain(X2)) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f62,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2)))
| addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) != addition(forward_diamond(X1,domain(X0)),domain(X2)) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( domain(X1) != zero
& addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1)) )
& divergence(X0) = zero ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f64,plain,
( domain(sK1_skl) != zero
& addition(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl))) = forward_diamond(sK0_skl,domain(sK1_skl))
& divergence(sK0_skl) = zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f63]) ).
fof(f65,plain,
divergence(sK0_skl) = zero,
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
addition(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl))) = forward_diamond(sK0_skl,domain(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
domain(sK1_skl) != zero,
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(backward_demodulation,[status(thm)],[f49,f48]) ).
fof(f76,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f33,f31]) ).
fof(f213,plain,
antidomain(one) = zero,
inference(paramodulation,[status(thm)],[f36,f46]) ).
fof(f578,plain,
domain(one) = antidomain(zero),
inference(paramodulation,[status(thm)],[f213,f49]) ).
fof(f1136,plain,
! [X0,X1] :
( addition(domain(X0),addition(zero,forward_diamond(star(sK0_skl),domain(X1)))) = addition(divergence(sK0_skl),forward_diamond(star(sK0_skl),domain(X1)))
| addition(domain(X0),addition(forward_diamond(sK0_skl,domain(X0)),domain(X1))) != addition(forward_diamond(sK0_skl,domain(X0)),domain(X1)) ),
inference(paramodulation,[status(thm)],[f65,f62]) ).
fof(f1151,plain,
! [X0,X1] :
( addition(domain(X0),forward_diamond(star(sK0_skl),domain(X1))) = addition(divergence(sK0_skl),forward_diamond(star(sK0_skl),domain(X1)))
| addition(domain(X0),addition(forward_diamond(sK0_skl,domain(X0)),domain(X1))) != addition(forward_diamond(sK0_skl,domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f76,f1136]) ).
fof(f1152,plain,
! [X0,X1] :
( addition(domain(X0),forward_diamond(star(sK0_skl),domain(X1))) = addition(zero,forward_diamond(star(sK0_skl),domain(X1)))
| addition(domain(X0),addition(forward_diamond(sK0_skl,domain(X0)),domain(X1))) != addition(forward_diamond(sK0_skl,domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f65,f1151]) ).
fof(f1153,plain,
! [X0,X1] :
( addition(domain(X0),forward_diamond(star(sK0_skl),domain(X1))) = forward_diamond(star(sK0_skl),domain(X1))
| addition(domain(X0),addition(forward_diamond(sK0_skl,domain(X0)),domain(X1))) != addition(forward_diamond(sK0_skl,domain(X0)),domain(X1)) ),
inference(forward_demodulation,[status(thm)],[f76,f1152]) ).
fof(f1165,plain,
addition(antidomain(zero),antidomain(one)) = one,
inference(paramodulation,[status(thm)],[f578,f68]) ).
fof(f1184,plain,
addition(antidomain(zero),zero) = one,
inference(forward_demodulation,[status(thm)],[f213,f1165]) ).
fof(f1190,plain,
antidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f33,f1184]) ).
fof(f1671,plain,
domain(zero) = antidomain(one),
inference(paramodulation,[status(thm)],[f1190,f49]) ).
fof(f1677,plain,
domain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f213,f1671]) ).
fof(f2218,plain,
! [X0] :
( addition(domain(X0),forward_diamond(star(sK0_skl),zero)) = forward_diamond(star(sK0_skl),domain(zero))
| addition(domain(X0),addition(forward_diamond(sK0_skl,domain(X0)),domain(zero))) != addition(forward_diamond(sK0_skl,domain(X0)),domain(zero)) ),
inference(paramodulation,[status(thm)],[f1677,f1153]) ).
fof(f2225,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f1677,f56]) ).
fof(f2239,plain,
! [X0] :
( addition(domain(X0),forward_diamond(star(sK0_skl),zero)) = forward_diamond(star(sK0_skl),domain(zero))
| addition(domain(X0),addition(forward_diamond(sK0_skl,domain(X0)),zero)) != addition(forward_diamond(sK0_skl,domain(X0)),domain(zero)) ),
inference(forward_demodulation,[status(thm)],[f1677,f2218]) ).
fof(f2240,plain,
! [X0] :
( addition(domain(X0),forward_diamond(star(sK0_skl),zero)) = forward_diamond(star(sK0_skl),domain(zero))
| addition(domain(X0),forward_diamond(sK0_skl,domain(X0))) != addition(forward_diamond(sK0_skl,domain(X0)),domain(zero)) ),
inference(forward_demodulation,[status(thm)],[f33,f2239]) ).
fof(f2241,plain,
! [X0] :
( addition(domain(X0),forward_diamond(star(sK0_skl),zero)) = forward_diamond(star(sK0_skl),domain(zero))
| addition(domain(X0),forward_diamond(sK0_skl,domain(X0))) != addition(forward_diamond(sK0_skl,domain(X0)),zero) ),
inference(forward_demodulation,[status(thm)],[f1677,f2240]) ).
fof(f2242,plain,
! [X0] :
( addition(domain(X0),forward_diamond(star(sK0_skl),zero)) = forward_diamond(star(sK0_skl),domain(zero))
| addition(domain(X0),forward_diamond(sK0_skl,domain(X0))) != forward_diamond(sK0_skl,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f33,f2241]) ).
fof(f2243,plain,
! [X0] :
( addition(domain(X0),forward_diamond(star(sK0_skl),zero)) = forward_diamond(star(sK0_skl),zero)
| addition(domain(X0),forward_diamond(sK0_skl,domain(X0))) != forward_diamond(sK0_skl,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f1677,f2242]) ).
fof(f2266,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[status(thm)],[f40,f2225]) ).
fof(f2268,plain,
! [X0] :
( addition(domain(X0),forward_diamond(star(sK0_skl),zero)) = zero
| addition(domain(X0),forward_diamond(sK0_skl,domain(X0))) != forward_diamond(sK0_skl,domain(X0)) ),
inference(backward_demodulation,[status(thm)],[f2271,f2243]) ).
fof(f2271,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f1677,f2266]) ).
fof(f2273,plain,
! [X0] :
( addition(domain(X0),zero) = zero
| addition(domain(X0),forward_diamond(sK0_skl,domain(X0))) != forward_diamond(sK0_skl,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f2271,f2268]) ).
fof(f2274,plain,
! [X0] :
( domain(X0) = zero
| addition(domain(X0),forward_diamond(sK0_skl,domain(X0))) != forward_diamond(sK0_skl,domain(X0)) ),
inference(forward_demodulation,[status(thm)],[f33,f2273]) ).
fof(f2725,plain,
addition(domain(sK1_skl),forward_diamond(sK0_skl,domain(sK1_skl))) != forward_diamond(sK0_skl,domain(sK1_skl)),
inference(resolution,[status(thm)],[f2274,f67]) ).
fof(f2730,plain,
forward_diamond(sK0_skl,domain(sK1_skl)) != forward_diamond(sK0_skl,domain(sK1_skl)),
inference(forward_demodulation,[status(thm)],[f66,f2725]) ).
fof(f2731,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2730]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE128+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % Computer : n001.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 20 22:50:44 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.41 % Drodi V4.1.1
% 0.17/0.96 % Refutation found
% 0.17/0.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/1.00 % Elapsed time: 0.601252 seconds
% 0.17/1.00 % CPU time: 4.366482 seconds
% 0.17/1.00 % Total memory used: 112.737 MB
% 0.17/1.00 % Net memory used: 111.634 MB
%------------------------------------------------------------------------------