%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP703+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 : n011.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 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 46 ( 21 unt; 3 def)
% Number of atoms : 78 ( 50 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 60 ( 28 ~; 25 |; 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 38 ( 30 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [B,A] : mult(rd(A,B),B) = A,
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(f12,axiom,
! [B,A] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [X2,X3] :
( mult(X2,mult(op_e,X3)) = mult(mult(X2,op_e),X3)
& mult(X2,mult(X3,op_e)) = mult(mult(X2,X3),op_e)
& mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X2,X3] :
( mult(X2,mult(op_e,X3)) = mult(mult(X2,op_e),X3)
& mult(X2,mult(X3,op_e)) = mult(mult(X2,X3),op_e)
& mult(op_e,mult(X2,X3)) = mult(mult(op_e,X2),X3) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f18,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
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(f27,plain,
! [X0,X1] : op_e = mult(mult(rd(op_c,mult(X0,X1)),X1),X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
? [X2,X3] :
( mult(X2,mult(op_e,X3)) != mult(mult(X2,op_e),X3)
| mult(X2,mult(X3,op_e)) != mult(mult(X2,X3),op_e)
| mult(op_e,mult(X2,X3)) != mult(mult(op_e,X2),X3) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f30,plain,
( ? [X2,X3] : mult(X2,mult(op_e,X3)) != mult(mult(X2,op_e),X3)
| ? [X2,X3] : mult(X2,mult(X3,op_e)) != mult(mult(X2,X3),op_e)
| ? [X2,X3] : mult(op_e,mult(X2,X3)) != mult(mult(op_e,X2),X3) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
( mult(sK4_skl,mult(op_e,sK5_skl)) != mult(mult(sK4_skl,op_e),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_e)) != mult(mult(sK2_skl,sK3_skl),op_e)
| mult(op_e,mult(sK0_skl,sK1_skl)) != mult(mult(op_e,sK0_skl),sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X2,sK0_skl),skolemize(X3,sK1_skl),skolemize(X2,sK2_skl),skolemize(X3,sK3_skl),skolemize(X2,sK4_skl),skolemize(X3,sK5_skl)],[f30]) ).
fof(f32,plain,
( mult(sK4_skl,mult(op_e,sK5_skl)) != mult(mult(sK4_skl,op_e),sK5_skl)
| mult(sK2_skl,mult(sK3_skl,op_e)) != mult(mult(sK2_skl,sK3_skl),op_e)
| mult(op_e,mult(sK0_skl,sK1_skl)) != mult(mult(op_e,sK0_skl),sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,definition,
( sQ0_spl
<=> mult(op_e,mult(sK0_skl,sK1_skl)) = mult(mult(op_e,sK0_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( sQ0_spl
| mult(op_e,mult(sK0_skl,sK1_skl)) != mult(mult(op_e,sK0_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,definition,
( sQ1_spl
<=> mult(sK2_skl,mult(sK3_skl,op_e)) = mult(mult(sK2_skl,sK3_skl),op_e) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( sQ1_spl
| mult(sK2_skl,mult(sK3_skl,op_e)) != mult(mult(sK2_skl,sK3_skl),op_e) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ2_spl
<=> mult(sK4_skl,mult(op_e,sK5_skl)) = mult(mult(sK4_skl,op_e),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f41,plain,
( sQ2_spl
| mult(sK4_skl,mult(op_e,sK5_skl)) != mult(mult(sK4_skl,op_e),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(f291,plain,
! [X0] : op_e = mult(rd(op_c,mult(unit,X0)),X0),
inference(paramodulation,[status(thm)],[f20,f27]) ).
fof(f318,plain,
! [X0] : op_e = mult(rd(op_c,X0),X0),
inference(forward_demodulation,[status(thm)],[f21,f291]) ).
fof(f319,plain,
op_e = op_c,
inference(forward_demodulation,[status(thm)],[f18,f318]) ).
fof(f389,plain,
( sQ2_spl
| mult(sK4_skl,mult(op_c,sK5_skl)) != mult(mult(sK4_skl,op_e),sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f319,f41]) ).
fof(f390,plain,
( sQ2_spl
| mult(sK4_skl,mult(op_c,sK5_skl)) != mult(mult(sK4_skl,op_c),sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f319,f389]) ).
fof(f391,plain,
( sQ2_spl
| mult(sK4_skl,mult(op_c,sK5_skl)) != mult(sK4_skl,mult(op_c,sK5_skl)) ),
inference(forward_demodulation,[status(thm)],[f25,f390]) ).
fof(f392,plain,
( sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f391]) ).
fof(f393,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f394,plain,
( sQ0_spl
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(mult(op_e,sK0_skl),sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f319,f35]) ).
fof(f395,plain,
( sQ0_spl
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(mult(op_c,sK0_skl),sK1_skl) ),
inference(forward_demodulation,[status(thm)],[f319,f394]) ).
fof(f396,plain,
( sQ0_spl
| mult(op_c,mult(sK0_skl,sK1_skl)) != mult(op_c,mult(sK0_skl,sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f23,f395]) ).
fof(f397,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f396]) ).
fof(f398,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f397]) ).
fof(f401,plain,
( sQ1_spl
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(mult(sK2_skl,sK3_skl),op_e) ),
inference(forward_demodulation,[status(thm)],[f319,f38]) ).
fof(f402,plain,
( sQ1_spl
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(mult(sK2_skl,sK3_skl),op_c) ),
inference(forward_demodulation,[status(thm)],[f319,f401]) ).
fof(f403,plain,
( sQ1_spl
| mult(sK2_skl,mult(sK3_skl,op_c)) != mult(sK2_skl,mult(sK3_skl,op_c)) ),
inference(forward_demodulation,[status(thm)],[f24,f402]) ).
fof(f404,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f403]) ).
fof(f405,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f404]) ).
fof(f406,plain,
$false,
inference(sat_refutation,[status(thm)],[f42,f393,f398,f405]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP703+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:34:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.060300 seconds
% 0.11/0.44 % CPU time: 0.189638 seconds
% 0.11/0.44 % Total memory used: 67.625 MB
% 0.11/0.44 % Net memory used: 67.217 MB
%------------------------------------------------------------------------------