TSTP Solution File: ALG210+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG210+2 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:11:01 EDT 2024
% Result : Theorem 3.21s 0.77s
% Output : CNFRefutation 3.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 72 ( 59 unt; 0 def)
% Number of atoms : 109 ( 79 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 57 ( 20 ~; 14 |; 20 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 65 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : times(times(A,B),C) = times(B,times(C,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( element(B)
<=> ? [C] :
( times(B,C) = B
& times(B,B) = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
! [A,B,C] :
( ( element(A)
& element(B)
& C = times(A,B) )
=> element(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ! [A,B,C] :
( ( element(A)
& element(B)
& C = times(A,B) )
=> element(C) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1,X2] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f6,plain,
! [B] :
( ( ~ element(B)
| ? [C] :
( times(B,C) = B
& times(B,B) = C ) )
& ( element(B)
| ! [C] :
( times(B,C) != B
| times(B,B) != C ) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f7,plain,
( ! [B] :
( ~ element(B)
| ? [C] :
( times(B,C) = B
& times(B,B) = C ) )
& ! [B] :
( element(B)
| ! [C] :
( times(B,C) != B
| times(B,B) != C ) ) ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f8,plain,
( ! [B] :
( ~ element(B)
| ( times(B,sk0_0(B)) = B
& times(B,B) = sk0_0(B) ) )
& ! [B] :
( element(B)
| ! [C] :
( times(B,C) != B
| times(B,B) != C ) ) ),
inference(skolemization,[status(esa)],[f7]) ).
fof(f9,plain,
! [X0] :
( ~ element(X0)
| times(X0,sk0_0(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f10,plain,
! [X0] :
( ~ element(X0)
| times(X0,X0) = sk0_0(X0) ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( element(X0)
| times(X0,X1) != X0
| times(X0,X0) != X1 ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f12,plain,
? [A,B,C] :
( element(A)
& element(B)
& C = times(A,B)
& ~ element(C) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f13,plain,
? [C] :
( ? [A,B] :
( element(A)
& element(B)
& C = times(A,B) )
& ~ element(C) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f14,plain,
( element(sk0_2)
& element(sk0_3)
& sk0_1 = times(sk0_2,sk0_3)
& ~ element(sk0_1) ),
inference(skolemization,[status(esa)],[f13]) ).
fof(f15,plain,
element(sk0_2),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
element(sk0_3),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f17,plain,
sk0_1 = times(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f18,plain,
~ element(sk0_1),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f19,plain,
! [X0] :
( element(X0)
| times(X0,times(X0,X0)) != X0 ),
inference(destructive_equality_resolution,[status(esa)],[f11]) ).
fof(f20,plain,
times(sk0_1,times(sk0_1,sk0_1)) != sk0_1,
inference(resolution,[status(thm)],[f19,f18]) ).
fof(f21,plain,
! [X0,X1,X2,X3] : times(times(X0,times(X1,X2)),X3) = times(X1,times(X3,times(X2,X0))),
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : times(times(X0,X1),times(X2,X3)) = times(X0,times(X2,times(X1,X3))),
inference(forward_demodulation,[status(thm)],[f5,f21]) ).
fof(f23,plain,
! [X0,X1,X2,X3] : times(X0,times(times(X1,X2),X3)) = times(X3,times(X1,times(X0,X2))),
inference(forward_demodulation,[status(thm)],[f5,f22]) ).
fof(f24,plain,
! [X0,X1,X2,X3] : times(X0,times(X1,times(X2,X3))) = times(X2,times(X3,times(X0,X1))),
inference(forward_demodulation,[status(thm)],[f5,f23]) ).
fof(f25,plain,
! [X0] : times(sk0_1,X0) = times(sk0_3,times(X0,sk0_2)),
inference(paramodulation,[status(thm)],[f17,f5]) ).
fof(f26,plain,
! [X0,X1] : times(sk0_1,times(X0,X1)) = times(sk0_3,times(X1,times(sk0_2,X0))),
inference(paramodulation,[status(thm)],[f5,f25]) ).
fof(f27,plain,
! [X0,X1] : times(times(sk0_1,X0),X1) = times(times(X0,sk0_2),times(X1,sk0_3)),
inference(paramodulation,[status(thm)],[f25,f5]) ).
fof(f28,plain,
! [X0,X1] : times(X0,times(X1,sk0_1)) = times(times(X0,sk0_2),times(X1,sk0_3)),
inference(forward_demodulation,[status(thm)],[f5,f27]) ).
fof(f29,plain,
! [X0,X1] : times(X0,times(X1,sk0_1)) = times(sk0_2,times(times(X1,sk0_3),X0)),
inference(forward_demodulation,[status(thm)],[f5,f28]) ).
fof(f30,plain,
! [X0,X1] : times(X0,times(X1,sk0_1)) = times(sk0_2,times(sk0_3,times(X0,X1))),
inference(forward_demodulation,[status(thm)],[f5,f29]) ).
fof(f36,plain,
! [X0,X1] : times(X0,times(sk0_1,X1)) = times(X1,times(sk0_2,times(X0,sk0_3))),
inference(paramodulation,[status(thm)],[f25,f24]) ).
fof(f119,plain,
! [X0,X1] : times(sk0_1,times(X0,X1)) = times(sk0_2,times(X0,times(sk0_3,X1))),
inference(forward_demodulation,[status(thm)],[f24,f26]) ).
fof(f154,plain,
! [X0] : times(sk0_3,times(X0,sk0_1)) = times(sk0_1,times(sk0_3,X0)),
inference(paramodulation,[status(thm)],[f119,f30]) ).
fof(f157,plain,
! [X0] : times(X0,times(sk0_2,sk0_1)) = times(sk0_2,times(sk0_1,X0)),
inference(paramodulation,[status(thm)],[f25,f30]) ).
fof(f1247,plain,
times(sk0_3,sk0_0(sk0_3)) = sk0_3,
inference(resolution,[status(thm)],[f9,f16]) ).
fof(f1248,plain,
times(sk0_2,sk0_0(sk0_2)) = sk0_2,
inference(resolution,[status(thm)],[f9,f15]) ).
fof(f1250,plain,
times(sk0_3,sk0_3) = sk0_0(sk0_3),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f1251,plain,
times(sk0_2,sk0_2) = sk0_0(sk0_2),
inference(resolution,[status(thm)],[f10,f15]) ).
fof(f1265,plain,
! [X0] : times(sk0_3,X0) = times(sk0_0(sk0_3),times(X0,sk0_3)),
inference(paramodulation,[status(thm)],[f1247,f5]) ).
fof(f1282,plain,
times(sk0_3,times(sk0_3,sk0_1)) = times(sk0_2,times(sk0_3,sk0_0(sk0_3))),
inference(paramodulation,[status(thm)],[f1250,f30]) ).
fof(f1283,plain,
times(sk0_1,times(sk0_3,sk0_3)) = times(sk0_2,times(sk0_3,sk0_0(sk0_3))),
inference(forward_demodulation,[status(thm)],[f154,f1282]) ).
fof(f1284,plain,
times(sk0_1,sk0_0(sk0_3)) = times(sk0_2,times(sk0_3,sk0_0(sk0_3))),
inference(forward_demodulation,[status(thm)],[f1250,f1283]) ).
fof(f1285,plain,
times(sk0_1,sk0_0(sk0_3)) = times(sk0_2,sk0_3),
inference(forward_demodulation,[status(thm)],[f1247,f1284]) ).
fof(f1286,plain,
times(sk0_1,sk0_0(sk0_3)) = sk0_1,
inference(forward_demodulation,[status(thm)],[f17,f1285]) ).
fof(f1289,plain,
! [X0] : times(sk0_0(sk0_3),X0) = times(sk0_3,times(X0,sk0_3)),
inference(paramodulation,[status(thm)],[f1250,f5]) ).
fof(f1298,plain,
! [X0] : times(sk0_0(sk0_2),X0) = times(sk0_2,times(X0,sk0_2)),
inference(paramodulation,[status(thm)],[f1251,f5]) ).
fof(f1308,plain,
! [X0] : times(sk0_1,X0) = times(sk0_0(sk0_3),times(X0,sk0_1)),
inference(paramodulation,[status(thm)],[f1286,f5]) ).
fof(f1530,plain,
times(sk0_3,sk0_2) = times(sk0_0(sk0_3),sk0_1),
inference(paramodulation,[status(thm)],[f17,f1265]) ).
fof(f3116,plain,
times(sk0_0(sk0_3),sk0_3) = times(sk0_3,sk0_0(sk0_3)),
inference(paramodulation,[status(thm)],[f1250,f1289]) ).
fof(f3117,plain,
times(sk0_0(sk0_3),sk0_3) = sk0_3,
inference(forward_demodulation,[status(thm)],[f1247,f3116]) ).
fof(f3119,plain,
times(sk0_0(sk0_3),sk0_2) = times(sk0_3,sk0_1),
inference(paramodulation,[status(thm)],[f17,f1289]) ).
fof(f3189,plain,
! [X0] : times(sk0_0(sk0_3),times(sk0_1,X0)) = times(X0,times(sk0_2,sk0_3)),
inference(paramodulation,[status(thm)],[f3117,f36]) ).
fof(f3190,plain,
! [X0] : times(sk0_0(sk0_3),times(sk0_1,X0)) = times(X0,sk0_1),
inference(forward_demodulation,[status(thm)],[f17,f3189]) ).
fof(f3224,plain,
times(sk0_0(sk0_3),times(sk0_2,sk0_1)) = times(sk0_2,times(sk0_3,times(sk0_3,sk0_1))),
inference(paramodulation,[status(thm)],[f3119,f30]) ).
fof(f3225,plain,
times(sk0_2,times(sk0_1,sk0_0(sk0_3))) = times(sk0_2,times(sk0_3,times(sk0_3,sk0_1))),
inference(forward_demodulation,[status(thm)],[f157,f3224]) ).
fof(f3226,plain,
times(sk0_2,sk0_1) = times(sk0_2,times(sk0_3,times(sk0_3,sk0_1))),
inference(forward_demodulation,[status(thm)],[f1286,f3225]) ).
fof(f3227,plain,
times(sk0_2,sk0_1) = times(sk0_3,times(sk0_1,sk0_1)),
inference(forward_demodulation,[status(thm)],[f30,f3226]) ).
fof(f3228,plain,
times(sk0_2,sk0_1) = times(sk0_1,times(sk0_3,sk0_1)),
inference(forward_demodulation,[status(thm)],[f154,f3227]) ).
fof(f3236,plain,
times(sk0_0(sk0_2),sk0_2) = times(sk0_2,sk0_0(sk0_2)),
inference(paramodulation,[status(thm)],[f1251,f1298]) ).
fof(f3237,plain,
times(sk0_0(sk0_2),sk0_2) = sk0_2,
inference(forward_demodulation,[status(thm)],[f1248,f3236]) ).
fof(f3305,plain,
times(sk0_1,sk0_0(sk0_2)) = times(sk0_3,sk0_2),
inference(paramodulation,[status(thm)],[f3237,f25]) ).
fof(f3344,plain,
times(sk0_1,sk0_2) = times(sk0_2,times(sk0_1,sk0_0(sk0_3))),
inference(paramodulation,[status(thm)],[f157,f1308]) ).
fof(f3345,plain,
times(sk0_1,sk0_2) = times(sk0_2,sk0_1),
inference(forward_demodulation,[status(thm)],[f1286,f3344]) ).
fof(f3346,plain,
times(sk0_1,sk0_0(sk0_3)) = times(sk0_0(sk0_3),times(sk0_3,sk0_2)),
inference(paramodulation,[status(thm)],[f1530,f1308]) ).
fof(f3347,plain,
sk0_1 = times(sk0_0(sk0_3),times(sk0_3,sk0_2)),
inference(forward_demodulation,[status(thm)],[f1286,f3346]) ).
fof(f3621,plain,
times(sk0_0(sk0_3),times(sk0_3,sk0_2)) = times(sk0_0(sk0_2),sk0_1),
inference(paramodulation,[status(thm)],[f3305,f3190]) ).
fof(f3622,plain,
sk0_1 = times(sk0_0(sk0_2),sk0_1),
inference(forward_demodulation,[status(thm)],[f3347,f3621]) ).
fof(f3891,plain,
times(sk0_1,sk0_2) = times(sk0_1,times(sk0_3,sk0_1)),
inference(forward_demodulation,[status(thm)],[f3345,f3228]) ).
fof(f3896,plain,
times(sk0_1,times(sk0_1,sk0_1)) = times(sk0_2,times(sk0_1,sk0_2)),
inference(paramodulation,[status(thm)],[f3891,f119]) ).
fof(f3897,plain,
times(sk0_1,times(sk0_1,sk0_1)) = times(sk0_0(sk0_2),sk0_1),
inference(forward_demodulation,[status(thm)],[f1298,f3896]) ).
fof(f3898,plain,
times(sk0_1,times(sk0_1,sk0_1)) = sk0_1,
inference(forward_demodulation,[status(thm)],[f3622,f3897]) ).
fof(f3899,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3898,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ALG210+2 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 23:31:41 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 3.21/0.77 % Refutation found
% 3.21/0.77 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.21/0.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.21/0.80 % Elapsed time: 0.441432 seconds
% 3.21/0.80 % CPU time: 3.295274 seconds
% 3.21/0.80 % Total memory used: 68.422 MB
% 3.21/0.80 % Net memory used: 68.167 MB
%------------------------------------------------------------------------------