TSTP Solution File: GRP748+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP748+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.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 20:21:32 EDT 2024
% Result : Theorem 15.23s 2.33s
% Output : CNFRefutation 15.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 28 unt; 0 def)
% Number of atoms : 62 ( 61 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 12 ~; 16 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-2 aty)
% Number of variables : 94 ( 82 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [C,B,A] : mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,A] : mult(mult(A,B),i(B)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : mult(A,i(A)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : mult(i(A),A) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [B,A] :
( mult(A,B) = mult(B,A)
| mult(i(A),mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
( ! [X0,X1,X2] : mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)
| ! [X3,X4,X5] : mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)
| ! [X6,X7,X8] : mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)
| ! [X9,X10,X11] : mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ( ! [X0,X1,X2] : mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)
| ! [X3,X4,X5] : mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)
| ! [X6,X7,X8] : mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)
| ! [X9,X10,X11] : mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f15,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f17,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f19,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f20,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),X2),X1) = mult(X0,mult(mult(X1,X2),X1)),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f21,plain,
! [X0,X1] : mult(mult(X0,X1),i(X1)) = X0,
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f22,plain,
! [X0] : mult(X0,i(X0)) = unit,
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f23,plain,
! [X0] : mult(i(X0),X0) = unit,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f24,plain,
! [X0,X1] :
( mult(X0,X1) = mult(X1,X0)
| mult(i(X0),mult(X0,X1)) = X1 ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f25,plain,
( ? [X0,X1,X2] : mult(X2,mult(X0,mult(X2,X1))) != mult(mult(mult(X2,X0),X2),X1)
& ? [X3,X4,X5] : mult(X3,mult(X5,mult(X4,X5))) != mult(mult(mult(X3,X5),X4),X5)
& ? [X6,X7,X8] : mult(mult(X8,X6),mult(X7,X8)) != mult(mult(X8,mult(X6,X7)),X8)
& ? [X9,X10,X11] : mult(mult(X11,X9),mult(X10,X11)) != mult(X11,mult(mult(X9,X10),X11)) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f26,plain,
( mult(sk0_2,mult(sk0_0,mult(sk0_2,sk0_1))) != mult(mult(mult(sk0_2,sk0_0),sk0_2),sk0_1)
& mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(mult(mult(sk0_3,sk0_5),sk0_4),sk0_5)
& mult(mult(sk0_8,sk0_6),mult(sk0_7,sk0_8)) != mult(mult(sk0_8,mult(sk0_6,sk0_7)),sk0_8)
& mult(mult(sk0_11,sk0_9),mult(sk0_10,sk0_11)) != mult(sk0_11,mult(mult(sk0_9,sk0_10),sk0_11)) ),
inference(skolemization,[status(esa)],[f25]) ).
fof(f28,plain,
mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(mult(mult(sk0_3,sk0_5),sk0_4),sk0_5),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f31,plain,
mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(sk0_3,mult(mult(sk0_5,sk0_4),sk0_5)),
inference(backward_demodulation,[status(thm)],[f20,f28]) ).
fof(f1043,plain,
! [X0,X1] : mult(mult(unit,X0),X1) = mult(i(X1),mult(mult(X1,X0),X1)),
inference(paramodulation,[status(thm)],[f23,f20]) ).
fof(f1044,plain,
! [X0,X1] : mult(X0,X1) = mult(i(X1),mult(mult(X1,X0),X1)),
inference(forward_demodulation,[status(thm)],[f19,f1043]) ).
fof(f1058,plain,
! [X0,X1] : mult(X0,i(i(X1))) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f21,f21]) ).
fof(f1059,plain,
! [X0] : mult(unit,i(i(X0))) = X0,
inference(paramodulation,[status(thm)],[f22,f21]) ).
fof(f1060,plain,
! [X0] : i(i(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f19,f1059]) ).
fof(f1136,plain,
! [X0,X1] : mult(mult(X0,i(X1)),X1) = X0,
inference(paramodulation,[status(thm)],[f1060,f21]) ).
fof(f1210,plain,
! [X0,X1] : rd(X0,X1) = mult(X0,i(X1)),
inference(paramodulation,[status(thm)],[f1136,f17]) ).
fof(f1385,plain,
! [X0,X1] : rd(X0,i(X1)) = mult(X0,X1),
inference(forward_demodulation,[status(thm)],[f1210,f1058]) ).
fof(f1870,plain,
! [X0,X1] :
( rd(mult(X0,X1),X0) = X1
| mult(i(X0),mult(X0,X1)) = X1 ),
inference(paramodulation,[status(thm)],[f24,f17]) ).
fof(f1907,plain,
! [X0,X1] :
( ld(i(X0),X1) = mult(X0,X1)
| mult(X0,X1) = mult(X1,X0) ),
inference(paramodulation,[status(thm)],[f24,f15]) ).
fof(f4566,plain,
! [X0,X1] :
( mult(mult(i(X0),X1),X0) = X1
| mult(i(i(X0)),mult(i(X0),X1)) = X1 ),
inference(paramodulation,[status(thm)],[f1385,f1870]) ).
fof(f4567,plain,
! [X0,X1] :
( mult(mult(i(X0),X1),X0) = X1
| mult(X0,mult(i(X0),X1)) = X1 ),
inference(forward_demodulation,[status(thm)],[f1060,f4566]) ).
fof(f13057,plain,
! [X0,X1] :
( mult(X0,mult(i(X0),X1)) = X1
| mult(X0,mult(i(X0),X1)) = X1
| ld(i(X0),mult(i(X0),X1)) = mult(X0,mult(i(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1907,f4567]) ).
fof(f13058,plain,
! [X0,X1] :
( mult(X0,mult(i(X0),X1)) = X1
| mult(X0,mult(i(X0),X1)) = X1
| X1 = mult(X0,mult(i(X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f15,f13057]) ).
fof(f13059,plain,
! [X0,X1] : mult(X0,mult(i(X0),X1)) = X1,
inference(duplicate_literals_removal,[status(esa)],[f13058]) ).
fof(f13406,plain,
! [X0,X1] : mult(X0,mult(X1,X0)) = mult(mult(X0,X1),X0),
inference(paramodulation,[status(thm)],[f1044,f13059]) ).
fof(f15069,plain,
mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))),
inference(forward_demodulation,[status(thm)],[f13406,f31]) ).
fof(f15070,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f15069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP748+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 30 00:29:55 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 15.23/2.33 % Refutation found
% 15.23/2.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 15.23/2.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.86/2.41 % Elapsed time: 2.046759 seconds
% 15.86/2.41 % CPU time: 15.865140 seconds
% 15.86/2.41 % Total memory used: 344.500 MB
% 15.86/2.41 % Net memory used: 342.772 MB
%------------------------------------------------------------------------------