%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP774+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 12:35:18 PM UTC 2026
% Result : Theorem 12.96s 2.18s
% Output : CNFRefutation 12.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 79 ( 56 unt; 2 def)
% Number of atoms : 116 ( 75 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 62 ( 25 ~; 21 |; 11 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 115 ( 111 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [C,B,A] : product(product(A,B),C) = product(A,product(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : product(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X0,X1] :
( d(X0,X1)
<=> ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
! [X2,X3,X4,X5] :
( ( d(X4,X5)
& d(X2,X3) )
=> d(product(X2,X4),product(X3,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [X2,X3,X4,X5] :
( ( d(X4,X5)
& d(X2,X3) )
=> d(product(X2,X4),product(X3,X5)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2] : product(product(X0,X1),X2) = product(X0,product(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0] : product(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1] :
( ( product(X1,product(X0,X1)) != X1
| product(X0,product(X1,X0)) != X0
| d(X0,X1) )
& ( ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 )
| ~ d(X0,X1) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
( ! [X0,X1] :
( product(X1,product(X0,X1)) != X1
| product(X0,product(X1,X0)) != X0
| d(X0,X1) )
& ! [X0,X1] :
( ( product(X1,product(X0,X1)) = X1
& product(X0,product(X1,X0)) = X0 )
| ~ d(X0,X1) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( product(X0,product(X1,X0)) = X0
| ~ d(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( product(X1,product(X0,X1)) = X1
| ~ d(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( product(X1,product(X0,X1)) != X1
| product(X0,product(X1,X0)) != X0
| d(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f13,plain,
? [X2,X3,X4,X5] :
( ~ d(product(X2,X4),product(X3,X5))
& d(X4,X5)
& d(X2,X3) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
( ~ d(product(sK0_skl,sK2_skl),product(sK1_skl,sK3_skl))
& d(sK2_skl,sK3_skl)
& d(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X2,sK0_skl),skolemize(X3,sK1_skl),skolemize(X4,sK2_skl),skolemize(X5,sK3_skl)],[f13]) ).
fof(f15,plain,
d(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
d(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
~ d(product(sK0_skl,sK2_skl),product(sK1_skl,sK3_skl)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,plain,
product(sK2_skl,product(sK3_skl,sK2_skl)) = sK2_skl,
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f19,plain,
product(sK0_skl,product(sK1_skl,sK0_skl)) = sK0_skl,
inference(resolution,[status(thm)],[f10,f15]) ).
fof(f20,plain,
! [X0,X1] : product(X0,X1) = product(X0,product(X1,product(X0,X1))),
inference(paramodulation,[status(thm)],[f7,f6]) ).
fof(f22,plain,
! [X0,X1] : product(X0,X1) = product(X0,product(X0,X1)),
inference(paramodulation,[status(thm)],[f7,f6]) ).
fof(f26,plain,
product(sK3_skl,product(sK2_skl,sK3_skl)) = sK3_skl,
inference(resolution,[status(thm)],[f11,f16]) ).
fof(f27,plain,
product(sK1_skl,product(sK0_skl,sK1_skl)) = sK1_skl,
inference(resolution,[status(thm)],[f11,f15]) ).
fof(f28,plain,
! [X0,X1,X2] : product(product(X0,X1),X2) = product(X0,product(X1,product(product(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f6,f22]) ).
fof(f34,plain,
! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(product(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f6,f28]) ).
fof(f35,plain,
! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(X0,product(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f6,f34]) ).
fof(f43,plain,
! [X0] : product(sK2_skl,X0) = product(sK2_skl,product(product(sK3_skl,sK2_skl),X0)),
inference(paramodulation,[status(thm)],[f18,f6]) ).
fof(f45,plain,
! [X0] : product(sK2_skl,X0) = product(sK2_skl,product(sK3_skl,product(sK2_skl,X0))),
inference(forward_demodulation,[status(thm)],[f6,f43]) ).
fof(f47,plain,
! [X0] : product(sK0_skl,X0) = product(sK0_skl,product(product(sK1_skl,sK0_skl),X0)),
inference(paramodulation,[status(thm)],[f19,f6]) ).
fof(f49,plain,
! [X0] : product(sK0_skl,X0) = product(sK0_skl,product(sK1_skl,product(sK0_skl,X0))),
inference(forward_demodulation,[status(thm)],[f6,f47]) ).
fof(f52,plain,
( product(product(sK1_skl,sK3_skl),product(product(sK0_skl,sK2_skl),product(sK1_skl,sK3_skl))) != product(sK1_skl,sK3_skl)
| product(product(sK0_skl,sK2_skl),product(product(sK1_skl,sK3_skl),product(sK0_skl,sK2_skl))) != product(sK0_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f17,f12]) ).
fof(f53,definition,
( sQ0_spl
<=> product(product(sK0_skl,sK2_skl),product(product(sK1_skl,sK3_skl),product(sK0_skl,sK2_skl))) = product(sK0_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ0_spl
| product(product(sK0_skl,sK2_skl),product(product(sK1_skl,sK3_skl),product(sK0_skl,sK2_skl))) != product(sK0_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ1_spl
<=> product(product(sK1_skl,sK3_skl),product(product(sK0_skl,sK2_skl),product(sK1_skl,sK3_skl))) = product(sK1_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( sQ1_spl
| product(product(sK1_skl,sK3_skl),product(product(sK0_skl,sK2_skl),product(sK1_skl,sK3_skl))) != product(sK1_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f53,f56]) ).
fof(f60,plain,
( sQ0_spl
| product(sK0_skl,product(sK2_skl,product(product(sK1_skl,sK3_skl),product(sK0_skl,sK2_skl)))) != product(sK0_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f6,f55]) ).
fof(f61,plain,
( sQ0_spl
| product(sK0_skl,product(sK2_skl,product(sK1_skl,product(sK3_skl,product(sK0_skl,sK2_skl))))) != product(sK0_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f6,f60]) ).
fof(f62,plain,
! [X0,X1,X2] : product(product(X0,X1),X2) = product(X0,product(X1,product(X2,product(product(X0,X1),X2)))),
inference(paramodulation,[status(thm)],[f6,f20]) ).
fof(f78,plain,
! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(X2,product(product(X0,X1),X2)))),
inference(forward_demodulation,[status(thm)],[f6,f62]) ).
fof(f79,plain,
! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(X2,product(X0,product(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f6,f78]) ).
fof(f110,plain,
! [X0] : product(sK3_skl,X0) = product(sK3_skl,product(product(sK2_skl,sK3_skl),X0)),
inference(paramodulation,[status(thm)],[f26,f6]) ).
fof(f115,plain,
! [X0] : product(sK3_skl,X0) = product(sK3_skl,product(sK2_skl,product(sK3_skl,X0))),
inference(forward_demodulation,[status(thm)],[f6,f110]) ).
fof(f119,plain,
! [X0] : product(sK1_skl,X0) = product(sK1_skl,product(product(sK0_skl,sK1_skl),X0)),
inference(paramodulation,[status(thm)],[f27,f6]) ).
fof(f124,plain,
! [X0] : product(sK1_skl,X0) = product(sK1_skl,product(sK0_skl,product(sK1_skl,X0))),
inference(forward_demodulation,[status(thm)],[f6,f119]) ).
fof(f173,plain,
! [X0,X1,X2,X3] : product(product(X0,X1),product(X2,X3)) = product(X0,product(X1,product(X2,product(product(X0,X1),product(X2,X3))))),
inference(paramodulation,[status(thm)],[f6,f35]) ).
fof(f214,plain,
! [X0,X1,X2,X3] : product(X0,product(X1,product(X2,X3))) = product(X0,product(X1,product(X2,product(product(X0,X1),product(X2,X3))))),
inference(forward_demodulation,[status(thm)],[f6,f173]) ).
fof(f215,plain,
! [X0,X1,X2,X3] : product(X0,product(X1,product(X2,X3))) = product(X0,product(X1,product(X2,product(X0,product(X1,product(X2,X3)))))),
inference(forward_demodulation,[status(thm)],[f6,f214]) ).
fof(f375,plain,
! [X0] : product(sK0_skl,product(X0,product(sK1_skl,product(sK0_skl,X0)))) = product(sK0_skl,product(sK1_skl,product(sK0_skl,X0))),
inference(paramodulation,[status(thm)],[f79,f49]) ).
fof(f378,plain,
! [X0] : product(sK1_skl,product(X0,product(sK0_skl,product(sK1_skl,X0)))) = product(sK1_skl,product(sK0_skl,product(sK1_skl,X0))),
inference(paramodulation,[status(thm)],[f79,f124]) ).
fof(f531,plain,
! [X0] : product(sK0_skl,product(X0,product(sK1_skl,product(sK0_skl,X0)))) = product(sK0_skl,X0),
inference(forward_demodulation,[status(thm)],[f49,f375]) ).
fof(f533,plain,
! [X0] : product(sK1_skl,product(X0,product(sK0_skl,product(sK1_skl,X0)))) = product(sK1_skl,X0),
inference(forward_demodulation,[status(thm)],[f124,f378]) ).
fof(f564,plain,
! [X0,X1,X2,X3,X4] : product(product(X0,X1),product(X2,product(X3,X4))) = product(X0,product(X1,product(X2,product(X3,product(product(X0,X1),product(X2,product(X3,X4))))))),
inference(paramodulation,[status(thm)],[f6,f215]) ).
fof(f599,plain,
! [X0,X1] : product(X0,product(sK3_skl,product(sK2_skl,product(sK3_skl,X1)))) = product(X0,product(sK3_skl,product(sK2_skl,product(X0,product(sK3_skl,X1))))),
inference(paramodulation,[status(thm)],[f115,f215]) ).
fof(f600,plain,
! [X0] : product(X0,product(sK3_skl,product(sK2_skl,sK3_skl))) = product(X0,product(sK3_skl,product(sK2_skl,product(X0,sK3_skl)))),
inference(paramodulation,[status(thm)],[f26,f215]) ).
fof(f603,plain,
! [X0,X1] : product(X0,product(sK2_skl,product(sK3_skl,product(sK2_skl,X1)))) = product(X0,product(sK2_skl,product(sK3_skl,product(X0,product(sK2_skl,X1))))),
inference(paramodulation,[status(thm)],[f45,f215]) ).
fof(f604,plain,
! [X0] : product(X0,product(sK2_skl,product(sK3_skl,sK2_skl))) = product(X0,product(sK2_skl,product(sK3_skl,product(X0,sK2_skl)))),
inference(paramodulation,[status(thm)],[f18,f215]) ).
fof(f658,plain,
! [X0,X1,X2,X3,X4] : product(X0,product(X1,product(X2,product(X3,X4)))) = product(X0,product(X1,product(X2,product(X3,product(product(X0,X1),product(X2,product(X3,X4))))))),
inference(forward_demodulation,[status(thm)],[f6,f564]) ).
fof(f659,plain,
! [X0,X1,X2,X3,X4] : product(X0,product(X1,product(X2,product(X3,X4)))) = product(X0,product(X1,product(X2,product(X3,product(X0,product(X1,product(X2,product(X3,X4)))))))),
inference(forward_demodulation,[status(thm)],[f6,f658]) ).
fof(f722,plain,
! [X0,X1] : product(X0,product(sK3_skl,X1)) = product(X0,product(sK3_skl,product(sK2_skl,product(X0,product(sK3_skl,X1))))),
inference(forward_demodulation,[status(thm)],[f115,f599]) ).
fof(f723,plain,
! [X0] : product(X0,sK3_skl) = product(X0,product(sK3_skl,product(sK2_skl,product(X0,sK3_skl)))),
inference(forward_demodulation,[status(thm)],[f26,f600]) ).
fof(f726,plain,
! [X0,X1] : product(X0,product(sK2_skl,X1)) = product(X0,product(sK2_skl,product(sK3_skl,product(X0,product(sK2_skl,X1))))),
inference(forward_demodulation,[status(thm)],[f45,f603]) ).
fof(f727,plain,
! [X0] : product(X0,sK2_skl) = product(X0,product(sK2_skl,product(sK3_skl,product(X0,sK2_skl)))),
inference(forward_demodulation,[status(thm)],[f18,f604]) ).
fof(f1871,plain,
! [X0,X1] : product(X0,product(sK1_skl,product(X1,product(sK0_skl,product(sK1_skl,X1))))) = product(X0,product(sK1_skl,product(X1,product(sK0_skl,product(X0,product(sK1_skl,X1)))))),
inference(paramodulation,[status(thm)],[f533,f659]) ).
fof(f1875,plain,
! [X0,X1] : product(X0,product(sK0_skl,product(X1,product(sK1_skl,product(sK0_skl,X1))))) = product(X0,product(sK0_skl,product(X1,product(sK1_skl,product(X0,product(sK0_skl,X1)))))),
inference(paramodulation,[status(thm)],[f531,f659]) ).
fof(f2106,plain,
! [X0,X1] : product(X0,product(sK1_skl,X1)) = product(X0,product(sK1_skl,product(X1,product(sK0_skl,product(X0,product(sK1_skl,X1)))))),
inference(forward_demodulation,[status(thm)],[f533,f1871]) ).
fof(f2112,plain,
! [X0,X1] : product(X0,product(sK0_skl,X1)) = product(X0,product(sK0_skl,product(X1,product(sK1_skl,product(X0,product(sK0_skl,X1)))))),
inference(forward_demodulation,[status(thm)],[f531,f1875]) ).
fof(f15562,plain,
product(sK1_skl,product(sK3_skl,product(sK0_skl,product(sK2_skl,product(sK1_skl,sK3_skl))))) = product(sK1_skl,product(sK3_skl,product(sK2_skl,product(sK1_skl,sK3_skl)))),
inference(paramodulation,[status(thm)],[f2106,f722]) ).
fof(f16192,plain,
product(sK1_skl,product(sK3_skl,product(sK0_skl,product(sK2_skl,product(sK1_skl,sK3_skl))))) = product(sK1_skl,sK3_skl),
inference(forward_demodulation,[status(thm)],[f723,f15562]) ).
fof(f19115,plain,
product(sK0_skl,product(sK2_skl,product(sK1_skl,product(sK3_skl,product(sK0_skl,sK2_skl))))) = product(sK0_skl,product(sK2_skl,product(sK3_skl,product(sK0_skl,sK2_skl)))),
inference(paramodulation,[status(thm)],[f2112,f726]) ).
fof(f19820,plain,
product(sK0_skl,product(sK2_skl,product(sK1_skl,product(sK3_skl,product(sK0_skl,sK2_skl))))) = product(sK0_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f727,f19115]) ).
fof(f19821,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19820,f61]) ).
fof(f19822,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f19821]) ).
fof(f20045,plain,
( sQ1_spl
| product(sK1_skl,product(sK3_skl,product(product(sK0_skl,sK2_skl),product(sK1_skl,sK3_skl)))) != product(sK1_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f6,f58]) ).
fof(f20046,plain,
( sQ1_spl
| product(sK1_skl,product(sK3_skl,product(sK0_skl,product(sK2_skl,product(sK1_skl,sK3_skl))))) != product(sK1_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f6,f20045]) ).
fof(f20047,plain,
( sQ1_spl
| product(sK1_skl,sK3_skl) != product(sK1_skl,sK3_skl) ),
inference(forward_demodulation,[status(thm)],[f16192,f20046]) ).
fof(f20048,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f20047]) ).
fof(f20049,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f20048]) ).
fof(f20050,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f19822,f20049]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP774+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 % Computer : n007.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 20 20:37:20 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 12.96/2.18 % Refutation found
% 12.96/2.18 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.96/2.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.00/2.25 % Elapsed time: 1.768975 seconds
% 1.00/2.25 % CPU time: 13.590883 seconds
% 1.00/2.25 % Total memory used: 225.865 MB
% 1.00/2.25 % Net memory used: 221.122 MB
%------------------------------------------------------------------------------