%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP704+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 : n018.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 12:35:11 PM UTC 2026
% Result : Theorem 0.10s 10.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 59 ( 29 unt; 3 def)
% Number of atoms : 96 ( 63 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 33 ~; 30 |; 4 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 45 ( 37 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,A] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B,A] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B,A] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : op_d = ld(A,mult(op_c,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [B,A] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [X4,X5] :
( mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
& mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X4,X5] :
( mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
& mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [X0,X1] : mult(X0,mult(X1,op_c)) = mult(mult(X0,X1),op_c),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1] : mult(X0,mult(op_c,X1)) = mult(mult(X0,op_c),X1),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0] : op_d = ld(X0,mult(op_c,X0)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0,X1] : op_f = mult(X0,mult(X1,ld(mult(X0,X1),op_c))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
? [X4,X5] :
( mult(X4,mult(op_f,X5)) != mult(mult(X4,op_f),X5)
| mult(X4,mult(X5,op_f)) != mult(mult(X4,X5),op_f)
| mult(op_f,mult(X4,X5)) != mult(mult(op_f,X4),X5) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f30,plain,
( ? [X4,X5] : mult(X4,mult(op_f,X5)) != mult(mult(X4,op_f),X5)
| ? [X4,X5] : mult(X4,mult(X5,op_f)) != mult(mult(X4,X5),op_f)
| ? [X4,X5] : mult(op_f,mult(X4,X5)) != mult(mult(op_f,X4),X5) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
( mult(sK4_skl,mult(op_f,sK5_skl)) != mult(mult(sK4_skl,op_f),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_f)) != mult(mult(sK2_skl,sK3_skl),op_f)
| mult(op_f,mult(sK0_skl,sK1_skl)) != mult(mult(op_f,sK0_skl),sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X4,sK0_skl),skolemize(X5,sK1_skl),skolemize(X4,sK2_skl),skolemize(X5,sK3_skl),skolemize(X4,sK4_skl),skolemize(X5,sK5_skl)],[f30]) ).
fof(f32,plain,
( mult(sK4_skl,mult(op_f,sK5_skl)) != mult(mult(sK4_skl,op_f),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_f)) != mult(mult(sK2_skl,sK3_skl),op_f)
| mult(op_f,mult(sK0_skl,sK1_skl)) != mult(mult(op_f,sK0_skl),sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,definition,
( sQ0_spl
<=> mult(op_f,mult(sK0_skl,sK1_skl)) = mult(mult(op_f,sK0_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( sQ0_spl
| mult(op_f,mult(sK0_skl,sK1_skl)) != mult(mult(op_f,sK0_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,definition,
( sQ1_spl
<=> mult(sK2_skl,mult(sK3_skl,op_f)) = mult(mult(sK2_skl,sK3_skl),op_f) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( sQ1_spl
| mult(sK2_skl,mult(sK3_skl,op_f)) != mult(mult(sK2_skl,sK3_skl),op_f) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ2_spl
<=> mult(sK4_skl,mult(op_f,sK5_skl)) = mult(mult(sK4_skl,op_f),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f41,plain,
( sQ2_spl
| mult(sK4_skl,mult(op_f,sK5_skl)) != mult(mult(sK4_skl,op_f),sK5_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f33,f36,f39]) ).
fof(f43,plain,
! [X0] : X0 = ld(unit,X0),
inference(paramodulation,[status(thm)],[f16,f21]) ).
fof(f150,plain,
op_d = mult(op_c,unit),
inference(paramodulation,[status(thm)],[f43,f26]) ).
fof(f157,plain,
! [X0] : mult(X0,op_d) = mult(op_c,X0),
inference(paramodulation,[status(thm)],[f26,f16]) ).
fof(f159,plain,
op_d = op_c,
inference(forward_demodulation,[status(thm)],[f20,f150]) ).
fof(f164,plain,
! [X0,X1] : mult(X0,mult(X1,op_c)) = mult(op_c,mult(X0,X1)),
inference(backward_demodulation,[status(thm)],[f166,f24]) ).
fof(f166,plain,
! [X0] : mult(X0,op_c) = mult(op_c,X0),
inference(forward_demodulation,[status(thm)],[f159,f157]) ).
fof(f217,plain,
! [X0] : op_f = mult(X0,ld(mult(unit,X0),op_c)),
inference(paramodulation,[status(thm)],[f21,f28]) ).
fof(f236,plain,
! [X0] : op_f = mult(X0,ld(X0,op_c)),
inference(forward_demodulation,[status(thm)],[f21,f217]) ).
fof(f240,plain,
( sQ2_spl
| mult(sK4_skl,mult(op_f,sK5_skl)) != mult(mult(sK4_skl,op_c),sK5_skl) ),
inference(backward_demodulation,[status(thm)],[f241,f41]) ).
fof(f241,plain,
op_f = op_c,
inference(forward_demodulation,[status(thm)],[f16,f236]) ).
fof(f273,plain,
( sQ2_spl
| mult(sK4_skl,mult(op_c,sK5_skl)) != mult(mult(sK4_skl,op_c),sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f241,f240]) ).
fof(f274,plain,
( sQ2_spl
| mult(sK4_skl,mult(sK5_skl,op_c)) != mult(mult(sK4_skl,op_c),sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f166,f273]) ).
fof(f275,plain,
( sQ2_spl
| mult(sK4_skl,mult(sK5_skl,op_c)) != mult(sK4_skl,mult(op_c,sK5_skl)) ),
inference(forward_demodulation,[status(thm)],[f25,f274]) ).
fof(f276,plain,
( sQ2_spl
| mult(sK4_skl,mult(sK5_skl,op_c)) != mult(sK4_skl,mult(sK5_skl,op_c)) ),
inference(forward_demodulation,[status(thm)],[f166,f275]) ).
fof(f277,plain,
( sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f276]) ).
fof(f278,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f277]) ).
fof(f279,plain,
( sQ0_spl
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(mult(op_f,sK0_skl),sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f241,f35]) ).
fof(f280,plain,
( sQ0_spl
| mult(sK0_skl,mult(sK1_skl,op_c)) != mult(mult(op_f,sK0_skl),sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f164,f279]) ).
fof(f281,plain,
( sQ0_spl
| mult(sK0_skl,mult(sK1_skl,op_c)) != mult(mult(op_c,sK0_skl),sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f241,f280]) ).
fof(f282,plain,
( sQ0_spl
| mult(sK0_skl,mult(sK1_skl,op_c)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f23,f281]) ).
fof(f283,plain,
( sQ0_spl
| mult(sK0_skl,mult(sK1_skl,op_c)) != mult(sK0_skl,mult(sK1_skl,op_c)) ),
inference(forward_demodulation,[status(thm)],[f164,f282]) ).
fof(f284,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f283]) ).
fof(f285,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f284]) ).
fof(f290,plain,
( sQ1_spl
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(mult(sK2_skl,sK3_skl),op_f) ),
inference(forward_demodulation,[status(thm)],[f241,f38]) ).
fof(f291,plain,
( sQ1_spl
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(mult(sK2_skl,sK3_skl),op_c) ),
inference(forward_demodulation,[status(thm)],[f241,f290]) ).
fof(f292,plain,
( sQ1_spl
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(op_c,mult(sK2_skl,sK3_skl)) ),
inference(forward_demodulation,[status(thm)],[f166,f291]) ).
fof(f293,plain,
( sQ1_spl
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(sK2_skl,mult(sK3_skl,op_c)) ),
inference(forward_demodulation,[status(thm)],[f164,f292]) ).
fof(f294,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f293]) ).
fof(f295,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f294]) ).
fof(f296,plain,
$false,
inference(sat_refutation,[status(thm)],[f42,f278,f285,f295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP704+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.36 % Computer : n018.cluster.edu
% 0.10/10.36 % Model : x86_64 x86_64
% 0.10/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.36 % Memory : 8046.5625MB
% 0.10/10.36 % OS : Linux 6.8.0-71-generic
% 0.10/10.36 % CPULimit : 300
% 0.10/10.36 % WCLimit : 300
% 0.10/10.36 % DateTime : Sun Sep 20 20:36:38 UTC 2026
% 0.10/10.37 % CPUTime :
% 0.10/10.38 % Drodi V4.1.1
% 0.10/10.39 % Refutation found
% 0.10/10.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/10.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/10.42 % Elapsed time: 0.045308 seconds
% 0.13/10.42 % CPU time: 0.158493 seconds
% 0.13/10.42 % Total memory used: 51.654 MB
% 0.13/10.42 % Net memory used: 51.362 MB
%------------------------------------------------------------------------------