%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP747+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 : n006.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 12:35:16 PM UTC 2026
% Result : Theorem 219.25s 28.24s
% Output : CNFRefutation 206.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 11 unt; 7 def)
% Number of atoms : 108 ( 47 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 33 ~; 41 |; 8 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( mult(X0,mult(X1,X2)) = mult(X0,mult(X2,X1))
& mult(mult(X0,X1),X2) = mult(mult(X0,X2),X1) )
| ( mult(mult(X0,X2),X1) = mult(X0,mult(X1,X2))
& mult(mult(X0,X1),X2) = mult(X0,mult(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
mult(mult(a,b),c) = mult(a,mult(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,definition,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
<=> ( mult(mult(X0,X2),X1) = mult(X0,mult(X1,X2))
& mult(mult(X0,X1),X2) = mult(X0,mult(X2,X1)) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( mult(X0,mult(X1,X2)) = mult(X0,mult(X2,X1))
& mult(mult(X0,X1),X2) = mult(mult(X0,X2),X1) )
| sP0_prd(X2,X1,X0) ),
inference(formula_renaming,[status(thm)],[f8,f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( mult(mult(X2,X1),X0) = mult(mult(X2,X0),X1)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( mult(X2,mult(X1,X0)) = mult(X2,mult(X0,X1))
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( mult(mult(X0,X2),X1) != mult(X0,mult(X1,X2))
| mult(mult(X0,X1),X2) != mult(X0,mult(X2,X1))
| sP0_prd(X2,X1,X0) )
& ( ( mult(mult(X0,X2),X1) = mult(X0,mult(X1,X2))
& mult(mult(X0,X1),X2) = mult(X0,mult(X2,X1)) )
| ~ sP0_prd(X2,X1,X0) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f24,plain,
( ! [X0,X1,X2] :
( mult(mult(X0,X2),X1) != mult(X0,mult(X1,X2))
| mult(mult(X0,X1),X2) != mult(X0,mult(X2,X1))
| sP0_prd(X2,X1,X0) )
& ! [X0,X1,X2] :
( ( mult(mult(X0,X2),X1) = mult(X0,mult(X1,X2))
& mult(mult(X0,X1),X2) = mult(X0,mult(X2,X1)) )
| ~ sP0_prd(X2,X1,X0) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( mult(mult(X2,X1),X0) = mult(X2,mult(X0,X1))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f1951,plain,
( sP0_prd(c,b,a)
| mult(mult(a,c),b) != mult(a,mult(b,c)) ),
inference(paramodulation,[status(thm)],[f20,f22]) ).
fof(f2077,definition,
( sQ0_spl
<=> mult(mult(a,c),b) = mult(a,mult(b,c)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f2079,plain,
( sQ0_spl
| mult(mult(a,c),b) != mult(a,mult(b,c)) ),
inference(component_clause,[status(thm)],[f2077]) ).
fof(f2080,definition,
( sQ1_spl
<=> sP0_prd(c,b,a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f2083,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1951,f2077,f2080]) ).
fof(f2207,plain,
! [X0,X1,X2] :
( sP0_prd(X1,X2,X0)
| ld(X0,mult(X0,mult(X1,X2))) = mult(X2,X1) ),
inference(paramodulation,[status(thm)],[f21,f12]) ).
fof(f2304,plain,
! [X0,X1,X2] :
( sP0_prd(X0,X1,X2)
| mult(X0,X1) = mult(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f12,f2207]) ).
fof(f2334,plain,
! [X0,X1] :
( mult(X1,X0) = mult(unit,mult(X0,X1))
| ~ sP0_prd(X0,X1,unit) ),
inference(paramodulation,[status(thm)],[f16,f25]) ).
fof(f2358,plain,
! [X0,X1] :
( mult(X1,X0) = mult(X0,X1)
| ~ sP0_prd(X0,X1,unit) ),
inference(forward_demodulation,[status(thm)],[f16,f2334]) ).
fof(f3557,definition,
( sQ9_spl
<=> mult(c,mult(a,b)) = mult(a,mult(b,c)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f3558,plain,
( ~ sQ9_spl
| mult(c,mult(a,b)) = mult(a,mult(b,c)) ),
inference(component_clause,[status(thm)],[f3557]) ).
fof(f3559,plain,
( sQ9_spl
| mult(c,mult(a,b)) != mult(a,mult(b,c)) ),
inference(component_clause,[status(thm)],[f3557]) ).
fof(f3774,plain,
! [X0,X1] : mult(X0,X1) = mult(X1,X0),
inference(forward_subsumption_resolution,[status(thm)],[f2358,f2304]) ).
fof(f3793,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| mult(X0,mult(X1,X2)) = mult(mult(X2,X1),X0) ),
inference(paramodulation,[status(thm)],[f21,f3774]) ).
fof(f3826,plain,
( sQ0_spl
| mult(mult(c,a),b) != mult(a,mult(b,c)) ),
inference(paramodulation,[status(thm)],[f3774,f2079]) ).
fof(f3837,plain,
mult(c,mult(a,b)) != mult(a,mult(b,c)),
inference(paramodulation,[status(thm)],[f3774,f22]) ).
fof(f3851,plain,
! [X0,X1,X2] :
( mult(X0,mult(X2,X1)) = mult(X2,mult(X0,X1))
| ~ sP0_prd(X0,X1,X2) ),
inference(paramodulation,[status(thm)],[f3774,f25]) ).
fof(f4381,plain,
( sQ9_spl
| mult(c,mult(a,b)) != mult(a,mult(c,b)) ),
inference(paramodulation,[status(thm)],[f3774,f3559]) ).
fof(f4382,definition,
( sQ15_spl
<=> mult(c,mult(a,b)) = mult(a,mult(c,b)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f4384,plain,
( sQ15_spl
| mult(c,mult(a,b)) != mult(a,mult(c,b)) ),
inference(component_clause,[status(thm)],[f4382]) ).
fof(f10999,definition,
( sQ23_spl
<=> mult(mult(c,b),a) = mult(a,mult(b,c)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f11001,plain,
( sQ23_spl
| mult(mult(c,b),a) != mult(a,mult(b,c)) ),
inference(component_clause,[status(thm)],[f10999]) ).
fof(f11002,definition,
( sQ24_spl
<=> sP0_prd(a,b,c) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f11003,plain,
( ~ sQ24_spl
| sP0_prd(a,b,c) ),
inference(component_clause,[status(thm)],[f11002]) ).
fof(f11010,plain,
( sQ0_spl
| sP0_prd(a,b,c)
| mult(mult(c,b),a) != mult(a,mult(b,c)) ),
inference(paramodulation,[status(thm)],[f20,f3826]) ).
fof(f11014,plain,
( sQ0_spl
| sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f11010,f10999,f11002,f2077]) ).
fof(f32632,plain,
( sQ15_spl
| ~ sP0_prd(c,b,a) ),
inference(resolution,[status(thm)],[f3851,f4384]) ).
fof(f32634,plain,
( sQ15_spl
| ~ sP0_prd(a,b,c) ),
inference(resolution,[status(thm)],[f3851,f4384]) ).
fof(f32944,plain,
( sQ9_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4381,f4382,f3557]) ).
fof(f32964,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3558,f3837]) ).
fof(f32965,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f32964]) ).
fof(f32966,plain,
( sQ15_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f32634,f11003]) ).
fof(f32967,plain,
( sQ15_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f32966]) ).
fof(f32968,plain,
( sQ15_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f32632,f2080,f4382]) ).
fof(f43825,plain,
( sQ23_spl
| sP0_prd(c,b,a) ),
inference(resolution,[status(thm)],[f11001,f3793]) ).
fof(f43833,plain,
( sQ23_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f43825,f2080,f10999]) ).
fof(f43838,plain,
$false,
inference(sat_refutation,[status(thm)],[f2083,f11014,f32944,f32965,f32967,f32968,f43833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP747+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:37:12 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.37 % Drodi V4.1.1
% 219.25/28.24 % Refutation found
% 219.25/28.24 % SZS status Theorem for theBenchmark: Theorem is valid
% 219.25/28.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 49.86/28.39 % Elapsed time: 28.009969 seconds
% 49.86/28.39 % CPU time: 220.851854 seconds
% 49.86/28.39 % Total memory used: 890.947 MB
% 49.86/28.39 % Net memory used: 878.080 MB
%------------------------------------------------------------------------------