%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% 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 12:33:04 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 9 unt; 3 def)
% Number of atoms : 123 ( 27 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 121 ( 48 ~; 49 |; 15 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( group_member(X,f)
=> group_member(phi(X),h) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( ( group_member(Y,f)
& group_member(X,f) )
=> multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( group_member(X,h)
=> ? [Y] :
( phi(Y) = X
& group_member(Y,f) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [G,X] :
( left_zero(G,X)
<=> ( ! [Y] :
( group_member(Y,G)
=> multiply(G,X,Y) = X )
& group_member(X,G) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,hypothesis,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f14,plain,
! [X] :
( group_member(phi(X),h)
| ~ group_member(X,f) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f15,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X,Y] :
( multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y))
| ~ group_member(Y,f)
| ~ group_member(X,f) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X1,f)
| ~ group_member(X0,f) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X] :
( ? [Y] :
( phi(Y) = X
& group_member(Y,f) )
| ~ group_member(X,h) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
! [X] :
( ( phi(sK0_skl(X)) = X
& group_member(sK0_skl(X),f) )
| ~ group_member(X,h) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y,sK0_skl(X))],[f18]) ).
fof(f20,plain,
! [X0] :
( group_member(sK0_skl(X0),f)
| ~ group_member(X0,h) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0] :
( phi(sK0_skl(X0)) = X0
| ~ group_member(X0,h) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
! [G,X] :
( left_zero(G,X)
<=> ( ! [Y] :
( multiply(G,X,Y) = X
| ~ group_member(Y,G) )
& group_member(X,G) ) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [G,X] :
( ( ? [Y] :
( multiply(G,X,Y) != X
& group_member(Y,G) )
| ~ group_member(X,G)
| left_zero(G,X) )
& ( ( ! [Y] :
( multiply(G,X,Y) = X
| ~ group_member(Y,G) )
& group_member(X,G) )
| ~ left_zero(G,X) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
( ! [G,X] :
( ? [Y] :
( multiply(G,X,Y) != X
& group_member(Y,G) )
| ~ group_member(X,G)
| left_zero(G,X) )
& ! [G,X] :
( ( ! [Y] :
( multiply(G,X,Y) = X
| ~ group_member(Y,G) )
& group_member(X,G) )
| ~ left_zero(G,X) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [G,X] :
( ( multiply(G,X,sK1_skl(X,G)) != X
& group_member(sK1_skl(X,G),G) )
| ~ group_member(X,G)
| left_zero(G,X) )
& ! [G,X] :
( ( ! [Y] :
( multiply(G,X,Y) = X
| ~ group_member(Y,G) )
& group_member(X,G) )
| ~ left_zero(G,X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(Y,sK1_skl(X,G))],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( group_member(X1,X0)
| ~ left_zero(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0)
| ~ left_zero(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( group_member(sK1_skl(X1,X0),X0)
| ~ group_member(X1,X0)
| left_zero(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
! [X0,X1] :
( multiply(X0,X1,sK1_skl(X1,X0)) != X1
| ~ group_member(X1,X0)
| left_zero(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f30,plain,
left_zero(f,f_left_zero),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
~ left_zero(h,phi(f_left_zero)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f32,plain,
group_member(f_left_zero,f),
inference(resolution,[status(thm)],[f26,f30]) ).
fof(f33,plain,
! [X0] :
( multiply(f,f_left_zero,X0) = f_left_zero
| ~ group_member(X0,f) ),
inference(resolution,[status(thm)],[f27,f30]) ).
fof(f34,plain,
! [X0] :
( multiply(h,phi(f_left_zero),phi(X0)) = phi(multiply(f,f_left_zero,X0))
| ~ group_member(X0,f) ),
inference(resolution,[status(thm)],[f32,f17]) ).
fof(f35,plain,
group_member(phi(f_left_zero),h),
inference(resolution,[status(thm)],[f32,f15]) ).
fof(f45,plain,
( group_member(sK1_skl(phi(f_left_zero),h),h)
| left_zero(h,phi(f_left_zero)) ),
inference(resolution,[status(thm)],[f28,f35]) ).
fof(f47,definition,
( sQ0_spl
<=> left_zero(h,phi(f_left_zero)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( ~ sQ0_spl
| left_zero(h,phi(f_left_zero)) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,definition,
( sQ1_spl
<=> group_member(sK1_skl(phi(f_left_zero),h),h) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ1_spl
| group_member(sK1_skl(phi(f_left_zero),h),h) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f47,f50]) ).
fof(f61,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f48,f31]) ).
fof(f62,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f61]) ).
fof(f63,plain,
( multiply(h,phi(f_left_zero),sK1_skl(phi(f_left_zero),h)) != phi(f_left_zero)
| left_zero(h,phi(f_left_zero)) ),
inference(resolution,[status(thm)],[f29,f35]) ).
fof(f65,definition,
( sQ4_spl
<=> multiply(h,phi(f_left_zero),sK1_skl(phi(f_left_zero),h)) = phi(f_left_zero) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( sQ4_spl
| multiply(h,phi(f_left_zero),sK1_skl(phi(f_left_zero),h)) != phi(f_left_zero) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( ~ sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f47,f65]) ).
fof(f113,plain,
( ~ sQ1_spl
| group_member(sK0_skl(sK1_skl(phi(f_left_zero),h)),f) ),
inference(resolution,[status(thm)],[f51,f20]) ).
fof(f114,plain,
( ~ sQ1_spl
| phi(sK0_skl(sK1_skl(phi(f_left_zero),h))) = sK1_skl(phi(f_left_zero),h) ),
inference(resolution,[status(thm)],[f51,f21]) ).
fof(f134,plain,
( ~ sQ1_spl
| multiply(h,phi(f_left_zero),phi(sK0_skl(sK1_skl(phi(f_left_zero),h)))) = phi(multiply(f,f_left_zero,sK0_skl(sK1_skl(phi(f_left_zero),h)))) ),
inference(resolution,[status(thm)],[f113,f34]) ).
fof(f135,plain,
( ~ sQ1_spl
| multiply(f,f_left_zero,sK0_skl(sK1_skl(phi(f_left_zero),h))) = f_left_zero ),
inference(resolution,[status(thm)],[f113,f33]) ).
fof(f142,plain,
( ~ sQ1_spl
| multiply(h,phi(f_left_zero),sK1_skl(phi(f_left_zero),h)) = phi(multiply(f,f_left_zero,sK0_skl(sK1_skl(phi(f_left_zero),h)))) ),
inference(forward_demodulation,[status(thm)],[f114,f134]) ).
fof(f143,plain,
( ~ sQ1_spl
| multiply(h,phi(f_left_zero),sK1_skl(phi(f_left_zero),h)) = phi(f_left_zero) ),
inference(backward_demodulation,[status(thm)],[f135,f142]) ).
fof(f159,plain,
( ~ sQ1_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f67]) ).
fof(f160,plain,
( ~ sQ1_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f159]) ).
fof(f161,plain,
$false,
inference(sat_refutation,[status(thm)],[f53,f62,f68,f160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:08:17 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.054664 seconds
% 0.13/0.42 % CPU time: 0.201340 seconds
% 0.13/0.42 % Total memory used: 78.545 MB
% 0.13/0.42 % Net memory used: 78.074 MB
%------------------------------------------------------------------------------