TSTP Solution File: GRP704+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP704+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 20:21:28 EDT 2024
% Result : Theorem 4.37s 0.92s
% Output : CNFRefutation 4.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 67 ( 40 unt; 0 def)
% Number of atoms : 101 ( 71 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 30 ~; 27 |; 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 : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 72 ( 64 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [C,B,A] : mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,A] : mult(op_c,mult(A,B)) = mult(mult(op_c,A),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B,A] : mult(A,mult(B,op_c)) = mult(mult(A,B),op_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B,A] : mult(A,mult(op_c,B)) = mult(mult(A,op_c),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : op_d = ld(A,mult(op_c,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [B,A] : op_e = mult(mult(rd(op_c,mult(A,B)),B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [B,A] : op_f = mult(A,mult(B,ld(mult(A,B),op_c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,conjecture,
! [X4,X5] :
( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
& mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ ! [X4,X5] :
( mult(op_f,mult(X4,X5)) = mult(mult(op_f,X4),X5)
& mult(X4,mult(X5,op_f)) = mult(mult(X4,X5),op_f)
& mult(X4,mult(op_f,X5)) = mult(mult(X4,op_f),X5) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f17,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f18,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X1,X2))) = mult(mult(mult(X0,X1),X1),X2),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f23,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f24,plain,
! [X0,X1] : mult(X0,mult(X1,op_c)) = mult(mult(X0,X1),op_c),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f25,plain,
! [X0,X1] : mult(X0,mult(op_c,X1)) = mult(mult(X0,op_c),X1),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f26,plain,
! [X0] : op_d = ld(X0,mult(op_c,X0)),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f27,plain,
! [X0,X1] : op_e = mult(mult(rd(op_c,mult(X0,X1)),X1),X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f28,plain,
! [X0,X1] : op_f = mult(X0,mult(X1,ld(mult(X0,X1),op_c))),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f29,plain,
? [X4,X5] :
( mult(op_f,mult(X4,X5)) != mult(mult(op_f,X4),X5)
| mult(X4,mult(X5,op_f)) != mult(mult(X4,X5),op_f)
| mult(X4,mult(op_f,X5)) != mult(mult(X4,op_f),X5) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f30,plain,
( ? [X4,X5] : mult(op_f,mult(X4,X5)) != mult(mult(op_f,X4),X5)
| ? [X4,X5] : mult(X4,mult(X5,op_f)) != mult(mult(X4,X5),op_f)
| ? [X4,X5] : mult(X4,mult(op_f,X5)) != mult(mult(X4,op_f),X5) ),
inference(miniscoping,[status(esa)],[f29]) ).
fof(f31,plain,
( mult(op_f,mult(sk0_0,sk0_1)) != mult(mult(op_f,sk0_0),sk0_1)
| mult(sk0_2,mult(sk0_3,op_f)) != mult(mult(sk0_2,sk0_3),op_f)
| mult(sk0_4,mult(op_f,sk0_5)) != mult(mult(sk0_4,op_f),sk0_5) ),
inference(skolemization,[status(esa)],[f30]) ).
fof(f32,plain,
( mult(op_f,mult(sk0_0,sk0_1)) != mult(mult(op_f,sk0_0),sk0_1)
| mult(sk0_2,mult(sk0_3,op_f)) != mult(mult(sk0_2,sk0_3),op_f)
| mult(sk0_4,mult(op_f,sk0_5)) != mult(mult(sk0_4,op_f),sk0_5) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
( spl0_0
<=> mult(op_f,mult(sk0_0,sk0_1)) = mult(mult(op_f,sk0_0),sk0_1) ),
introduced(split_symbol_definition) ).
fof(f35,plain,
( mult(op_f,mult(sk0_0,sk0_1)) != mult(mult(op_f,sk0_0),sk0_1)
| spl0_0 ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( spl0_1
<=> mult(sk0_2,mult(sk0_3,op_f)) = mult(mult(sk0_2,sk0_3),op_f) ),
introduced(split_symbol_definition) ).
fof(f38,plain,
( mult(sk0_2,mult(sk0_3,op_f)) != mult(mult(sk0_2,sk0_3),op_f)
| spl0_1 ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( spl0_2
<=> mult(sk0_4,mult(op_f,sk0_5)) = mult(mult(sk0_4,op_f),sk0_5) ),
introduced(split_symbol_definition) ).
fof(f41,plain,
( mult(sk0_4,mult(op_f,sk0_5)) != mult(mult(sk0_4,op_f),sk0_5)
| spl0_2 ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f32,f33,f36,f39]) ).
fof(f3279,plain,
! [X0,X1] : mult(X0,mult(X1,mult(X1,unit))) = mult(mult(X0,X1),X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f3280,plain,
! [X0,X1] : mult(X0,mult(X1,X1)) = mult(mult(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f20,f3279]) ).
fof(f3820,plain,
! [X0] : ld(X0,X0) = unit,
inference(paramodulation,[status(thm)],[f20,f17]) ).
fof(f4971,plain,
! [X0,X1] : ld(mult(X0,X1),mult(X0,mult(X1,X1))) = X1,
inference(paramodulation,[status(thm)],[f3280,f17]) ).
fof(f5822,plain,
op_d = op_c,
inference(paramodulation,[status(thm)],[f26,f4971]) ).
fof(f5902,plain,
! [X0] : op_c = ld(X0,mult(op_c,X0)),
inference(backward_demodulation,[status(thm)],[f5822,f26]) ).
fof(f5908,plain,
! [X0] : mult(X0,op_c) = mult(op_c,X0),
inference(paramodulation,[status(thm)],[f5902,f16]) ).
fof(f6090,plain,
! [X0] : op_e = mult(rd(op_c,mult(X0,X0)),mult(X0,X0)),
inference(paramodulation,[status(thm)],[f3280,f27]) ).
fof(f6091,plain,
op_e = op_c,
inference(forward_demodulation,[status(thm)],[f18,f6090]) ).
fof(f6577,plain,
! [X0,X1] : op_c = mult(mult(rd(op_c,mult(X0,X1)),X1),X0),
inference(backward_demodulation,[status(thm)],[f6091,f27]) ).
fof(f6683,plain,
! [X0,X1] : op_f = mult(mult(rd(op_c,mult(X0,X1)),X1),mult(X0,ld(op_c,op_c))),
inference(paramodulation,[status(thm)],[f6577,f28]) ).
fof(f6684,plain,
! [X0,X1] : op_f = mult(mult(rd(op_c,mult(X0,X1)),X1),mult(X0,unit)),
inference(forward_demodulation,[status(thm)],[f3820,f6683]) ).
fof(f6685,plain,
! [X0,X1] : op_f = mult(mult(rd(op_c,mult(X0,X1)),X1),X0),
inference(forward_demodulation,[status(thm)],[f20,f6684]) ).
fof(f6686,plain,
op_f = op_c,
inference(forward_demodulation,[status(thm)],[f6577,f6685]) ).
fof(f6717,plain,
( mult(sk0_4,mult(op_f,sk0_5)) != mult(mult(sk0_4,op_c),sk0_5)
| spl0_2 ),
inference(backward_demodulation,[status(thm)],[f6686,f41]) ).
fof(f6718,plain,
( mult(sk0_4,mult(op_c,sk0_5)) != mult(mult(sk0_4,op_c),sk0_5)
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f6686,f6717]) ).
fof(f6719,plain,
( mult(sk0_4,mult(op_c,sk0_5)) != mult(sk0_4,mult(op_c,sk0_5))
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f25,f6718]) ).
fof(f6720,plain,
( $false
| spl0_2 ),
inference(trivial_equality_resolution,[status(esa)],[f6719]) ).
fof(f6721,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f6720]) ).
fof(f6722,plain,
( mult(op_c,mult(sk0_0,sk0_1)) != mult(mult(op_f,sk0_0),sk0_1)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f6686,f35]) ).
fof(f6723,plain,
( mult(op_c,mult(sk0_0,sk0_1)) != mult(mult(op_c,sk0_0),sk0_1)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f6686,f6722]) ).
fof(f6724,plain,
( mult(op_c,mult(sk0_0,sk0_1)) != mult(op_c,mult(sk0_0,sk0_1))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f23,f6723]) ).
fof(f6725,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f6724]) ).
fof(f6726,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f6725]) ).
fof(f6729,plain,
( mult(sk0_2,mult(sk0_3,op_c)) != mult(mult(sk0_2,sk0_3),op_f)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f6686,f38]) ).
fof(f6730,plain,
( mult(sk0_2,mult(op_c,sk0_3)) != mult(mult(sk0_2,sk0_3),op_f)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f5908,f6729]) ).
fof(f6731,plain,
( mult(sk0_2,mult(op_c,sk0_3)) != mult(mult(sk0_2,sk0_3),op_c)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f6686,f6730]) ).
fof(f6732,plain,
( mult(sk0_2,mult(op_c,sk0_3)) != mult(sk0_2,mult(sk0_3,op_c))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f24,f6731]) ).
fof(f6733,plain,
( mult(sk0_2,mult(op_c,sk0_3)) != mult(sk0_2,mult(op_c,sk0_3))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f5908,f6732]) ).
fof(f6734,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f6733]) ).
fof(f6735,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f6734]) ).
fof(f6736,plain,
$false,
inference(sat_refutation,[status(thm)],[f42,f6721,f6726,f6735]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP704+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n031.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 : Tue Apr 30 01:07:58 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 4.37/0.92 % Refutation found
% 4.37/0.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.37/0.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.51/0.95 % Elapsed time: 0.597390 seconds
% 4.51/0.95 % CPU time: 4.628667 seconds
% 4.51/0.95 % Total memory used: 195.584 MB
% 4.51/0.95 % Net memory used: 194.202 MB
%------------------------------------------------------------------------------