%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP710+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 12:35:12 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 49 unt; 2 def)
% Number of atoms : 83 ( 65 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 44 ( 27 ~; 13 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 116 ( 108 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [C,B,A] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : mult(A,i(A)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(i(A),A) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
( ! [X3,X4] :
? [X5] : mult(X5,X4) = X3
& ! [X0,X1] :
? [X2] : mult(X0,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ( ! [X3,X4] :
? [X5] : mult(X5,X4) = X3
& ! [X0,X1] :
? [X2] : mult(X0,X2) = X1 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X1,X2))) = mult(mult(mult(X0,X1),X1),X2),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0] : mult(X0,i(X0)) = unit,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0] : mult(i(X0),X0) = unit,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
( ? [X3,X4] :
! [X5] : mult(X5,X4) != X3
| ? [X0,X1] :
! [X2] : mult(X0,X2) != X1 ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f14,plain,
( ! [X5] : mult(X5,sK3_skl) != sK2_skl
| ! [X2] : mult(sK0_skl,X2) != sK1_skl ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X3,sK2_skl),skolemize(X4,sK3_skl)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( mult(X1,sK3_skl) != sK2_skl
| mult(sK0_skl,X0) != sK1_skl ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,definition,
! [X0] :
( sQ0_spl
<=> mult(sK0_skl,X0) != sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f17,plain,
! [X0] :
( ~ sQ0_spl
| mult(sK0_skl,X0) != sK1_skl ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,definition,
! [X1] :
( sQ1_spl
<=> mult(X1,sK3_skl) != sK2_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f20,plain,
! [X0] :
( ~ sQ1_spl
| mult(X0,sK3_skl) != sK2_skl ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f15,f16,f19]) ).
fof(f30,plain,
! [X0,X1] : mult(X0,mult(X1,mult(X1,unit))) = mult(mult(X0,X1),X1),
inference(paramodulation,[status(thm)],[f8,f10]) ).
fof(f33,plain,
! [X0,X1,X2,X3] : mult(mult(mult(X0,X1),X1),mult(X2,mult(X2,X3))) = mult(mult(mult(X0,mult(X1,mult(X1,X2))),X2),X3),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f34,plain,
! [X0,X1] : mult(unit,mult(X0,mult(X0,X1))) = mult(mult(X0,X0),X1),
inference(paramodulation,[status(thm)],[f9,f10]) ).
fof(f39,plain,
! [X0,X1] : mult(X0,mult(X1,X1)) = mult(mult(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f8,f30]) ).
fof(f42,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X1,mult(X1,mult(X2,mult(X2,X3))))) = mult(mult(mult(X0,mult(X1,mult(X1,X2))),X2),X3),
inference(forward_demodulation,[status(thm)],[f10,f33]) ).
fof(f43,plain,
! [X0,X1] : mult(X0,mult(X0,X1)) = mult(mult(X0,X0),X1),
inference(forward_demodulation,[status(thm)],[f9,f34]) ).
fof(f52,plain,
! [X0,X1] : mult(i(X0),mult(X0,mult(X0,X1))) = mult(mult(unit,X0),X1),
inference(paramodulation,[status(thm)],[f12,f10]) ).
fof(f53,plain,
! [X0,X1] : mult(i(X0),mult(X0,mult(X0,X1))) = mult(X0,X1),
inference(forward_demodulation,[status(thm)],[f9,f52]) ).
fof(f54,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X1,X2))) = mult(mult(X0,mult(X1,X1)),X2),
inference(backward_demodulation,[status(thm)],[f39,f10]) ).
fof(f56,plain,
! [X0] : mult(i(X0),mult(X0,X0)) = mult(unit,X0),
inference(paramodulation,[status(thm)],[f12,f39]) ).
fof(f59,plain,
! [X0] : mult(X0,mult(i(X0),i(X0))) = mult(unit,i(X0)),
inference(paramodulation,[status(thm)],[f11,f39]) ).
fof(f62,plain,
! [X0] : mult(i(X0),mult(X0,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f9,f56]) ).
fof(f63,plain,
! [X0] : mult(X0,mult(i(X0),i(X0))) = i(X0),
inference(forward_demodulation,[status(thm)],[f9,f59]) ).
fof(f88,plain,
! [X0,X1] : mult(i(mult(X0,X0)),mult(X0,mult(X0,X1))) = mult(unit,X1),
inference(paramodulation,[status(thm)],[f12,f54]) ).
fof(f106,plain,
! [X0,X1] : mult(i(mult(X0,X0)),mult(X0,mult(X0,X1))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f88]) ).
fof(f193,plain,
! [X0] : mult(i(i(X0)),mult(i(X0),X0)) = mult(i(X0),mult(X0,X0)),
inference(paramodulation,[status(thm)],[f62,f53]) ).
fof(f212,plain,
! [X0] : mult(i(i(X0)),unit) = mult(i(X0),mult(X0,X0)),
inference(forward_demodulation,[status(thm)],[f12,f193]) ).
fof(f213,plain,
! [X0] : i(i(X0)) = mult(i(X0),mult(X0,X0)),
inference(forward_demodulation,[status(thm)],[f8,f212]) ).
fof(f214,plain,
! [X0] : i(i(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f62,f213]) ).
fof(f365,plain,
! [X0] : mult(i(mult(X0,X0)),mult(X0,i(X0))) = mult(i(X0),i(X0)),
inference(paramodulation,[status(thm)],[f63,f106]) ).
fof(f371,plain,
! [X0,X1] : mult(i(i(mult(X0,X0))),mult(i(mult(X0,X0)),X1)) = mult(i(mult(X0,X0)),mult(X0,mult(X0,X1))),
inference(paramodulation,[status(thm)],[f106,f53]) ).
fof(f398,plain,
! [X0] : mult(i(mult(X0,X0)),unit) = mult(i(X0),i(X0)),
inference(forward_demodulation,[status(thm)],[f11,f365]) ).
fof(f399,plain,
! [X0] : i(mult(X0,X0)) = mult(i(X0),i(X0)),
inference(forward_demodulation,[status(thm)],[f8,f398]) ).
fof(f404,plain,
! [X0,X1] : mult(mult(X0,X0),mult(i(mult(X0,X0)),X1)) = mult(i(mult(X0,X0)),mult(X0,mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f214,f371]) ).
fof(f405,plain,
! [X0,X1] : mult(X0,mult(X0,mult(i(mult(X0,X0)),X1))) = mult(i(mult(X0,X0)),mult(X0,mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f43,f404]) ).
fof(f406,plain,
! [X0,X1] : mult(X0,mult(X0,mult(i(mult(X0,X0)),X1))) = X1,
inference(forward_demodulation,[status(thm)],[f106,f405]) ).
fof(f662,plain,
( ~ sQ0_spl
| $false ),
inference(resolution,[status(thm)],[f406,f17]) ).
fof(f683,plain,
! [X0,X1] : mult(i(X0),mult(i(X0),mult(i(i(mult(X0,X0))),X1))) = X1,
inference(paramodulation,[status(thm)],[f399,f406]) ).
fof(f699,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f662]) ).
fof(f735,plain,
! [X0,X1] : mult(i(X0),mult(i(X0),mult(mult(X0,X0),X1))) = X1,
inference(forward_demodulation,[status(thm)],[f214,f683]) ).
fof(f736,plain,
! [X0,X1] : mult(i(X0),mult(i(X0),mult(X0,mult(X0,X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f43,f735]) ).
fof(f737,plain,
! [X0,X1] : mult(i(X0),mult(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f53,f736]) ).
fof(f763,plain,
! [X0,X1] :
( ~ sQ1_spl
| mult(X0,mult(X1,mult(X1,sK3_skl))) != sK2_skl ),
inference(paramodulation,[status(thm)],[f54,f20]) ).
fof(f865,plain,
! [X0,X1,X2] : mult(X0,mult(i(X1),mult(i(X1),mult(X1,mult(X1,X2))))) = mult(mult(mult(X0,mult(i(X1),unit)),X1),X2),
inference(paramodulation,[status(thm)],[f12,f42]) ).
fof(f950,plain,
! [X0,X1,X2] : mult(X0,mult(i(X1),mult(X1,X2))) = mult(mult(mult(X0,mult(i(X1),unit)),X1),X2),
inference(forward_demodulation,[status(thm)],[f737,f865]) ).
fof(f951,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(mult(mult(X0,mult(i(X2),unit)),X2),X1),
inference(forward_demodulation,[status(thm)],[f737,f950]) ).
fof(f952,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(mult(mult(X0,i(X2)),X2),X1),
inference(forward_demodulation,[status(thm)],[f8,f951]) ).
fof(f1101,plain,
! [X0] :
( ~ sQ1_spl
| mult(X0,mult(i(sK3_skl),unit)) != sK2_skl ),
inference(paramodulation,[status(thm)],[f12,f763]) ).
fof(f1113,plain,
! [X0] :
( ~ sQ1_spl
| mult(X0,i(sK3_skl)) != sK2_skl ),
inference(forward_demodulation,[status(thm)],[f8,f1101]) ).
fof(f1126,plain,
! [X0] :
( ~ sQ1_spl
| mult(X0,mult(i(sK3_skl),i(sK3_skl))) != sK2_skl ),
inference(paramodulation,[status(thm)],[f39,f1113]) ).
fof(f1130,plain,
! [X0] :
( ~ sQ1_spl
| mult(X0,i(mult(sK3_skl,sK3_skl))) != sK2_skl ),
inference(forward_demodulation,[status(thm)],[f399,f1126]) ).
fof(f1508,plain,
! [X0,X1] : mult(X0,unit) = mult(mult(X0,i(X1)),X1),
inference(paramodulation,[status(thm)],[f8,f952]) ).
fof(f1590,plain,
! [X0,X1] : X0 = mult(mult(X0,i(X1)),X1),
inference(forward_demodulation,[status(thm)],[f8,f1508]) ).
fof(f1684,plain,
( ~ sQ1_spl
| $false ),
inference(resolution,[status(thm)],[f1590,f1130]) ).
fof(f1734,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1684]) ).
fof(f1735,plain,
$false,
inference(sat_refutation,[status(thm)],[f22,f699,f1734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP710+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:34:25 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.12/0.45 % Refutation found
% 0.12/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.47 % Elapsed time: 0.105285 seconds
% 0.12/0.47 % CPU time: 0.516906 seconds
% 0.12/0.47 % Total memory used: 82.405 MB
% 0.12/0.47 % Net memory used: 81.995 MB
%------------------------------------------------------------------------------