TSTP Solution File: BOO007-1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : BOO007-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.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 20:12:52 EDT 2024
% Result : Unsatisfiable 41.00s 5.56s
% Output : CNFRefutation 41.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 40
% Syntax : Number of formulae : 185 ( 62 unt; 0 def)
% Number of atoms : 382 ( 24 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 369 ( 172 ~; 179 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 19 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 252 ( 252 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : product(multiplicative_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : product(X,multiplicative_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| sum(V1,V2,V4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3)
| ~ sum(X,V3,V4)
| product(V1,V2,V4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3)
| ~ product(V1,V2,V4)
| sum(X,V3,V4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| U = V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| U = V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
product(y,z,y_times_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
product(x,y_times_z,x_times__y_times_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
product(x,y,x_times_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
product(x_times_y,z,x_times_y__times_z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
x_times__y_times_z != x_times_y__times_z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f29,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f32,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f33,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f34,plain,
! [X0] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f35,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f36,plain,
! [V1,V2,V4] :
( ! [X,V3] :
( ! [Y,Z] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3) )
| ~ product(X,V3,V4) )
| sum(V1,V2,V4) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ product(X0,X5,X6)
| sum(X2,X4,X6) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [X,V3,V4] :
( ! [V1,V2] :
( ! [Y,Z] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3) )
| ~ sum(V1,V2,V4) )
| product(X,V3,V4) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ sum(X2,X4,X6)
| product(X0,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [V1,V2,V4] :
( ! [X,V3] :
( ! [Y,Z] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3) )
| ~ product(V3,X,V4) )
| sum(V1,V2,V4) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X5)
| ~ product(X5,X1,X6)
| sum(X2,X4,X6) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f44,plain,
! [V1,V2,V4] :
( ! [X,V3] :
( ! [Y,Z] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3) )
| ~ sum(X,V3,V4) )
| product(V1,V2,V4) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ product(X1,X3,X5)
| ~ sum(X0,X5,X6)
| product(X2,X4,X6) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
! [X,V3,V4] :
( ! [V1,V2] :
( ! [Y,Z] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3) )
| ~ product(V1,V2,V4) )
| sum(X,V3,V4) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ product(X1,X3,X5)
| ~ product(X2,X4,X6)
| sum(X0,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f52,plain,
! [X0] : sum(inverse(X0),X0,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f55,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f56,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f58,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f60,plain,
product(y,z,y_times_z),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f61,plain,
product(x,y_times_z,x_times__y_times_z),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f62,plain,
product(x,y,x_times_y),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f63,plain,
product(x_times_y,z,x_times_y__times_z),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f64,plain,
x_times__y_times_z != x_times_y__times_z,
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f69,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f30,f28]) ).
fof(f70,plain,
product(z,y,y_times_z),
inference(resolution,[status(thm)],[f31,f60]) ).
fof(f74,plain,
product(y,x,x_times_y),
inference(resolution,[status(thm)],[f31,f62]) ).
fof(f75,plain,
product(y_times_z,x,x_times__y_times_z),
inference(resolution,[status(thm)],[f31,f61]) ).
fof(f78,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f31,f29]) ).
fof(f88,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f57,f33]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| X2 = add(X1,X0) ),
inference(resolution,[status(thm)],[f57,f69]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| X2 = add(X0,X1) ),
inference(resolution,[status(thm)],[f57,f28]) ).
fof(f138,plain,
! [X0,X1,X2,X3] :
( ~ product(x_times_y,X0,X1)
| ~ sum(X0,z,X2)
| ~ product(x_times_y,X2,X3)
| sum(X1,x_times_y__times_z,X3) ),
inference(resolution,[status(thm)],[f37,f63]) ).
fof(f139,plain,
! [X0,X1] :
( ~ product(x,X0,X1)
| ~ sum(X0,y,y)
| sum(X1,x_times_y,x_times_y) ),
inference(resolution,[status(thm)],[f37,f62]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| ~ sum(X1,inverse(X0),inverse(X0))
| sum(X2,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f37,f55]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| ~ sum(X1,multiplicative_identity,multiplicative_identity)
| sum(X2,X0,X0) ),
inference(resolution,[status(thm)],[f37,f35]) ).
fof(f178,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X3,X4)
| ~ sum(X2,multiply(X0,X3),X5)
| product(X0,X4,X5) ),
inference(resolution,[status(thm)],[f39,f29]) ).
fof(f187,plain,
! [X0,X1] :
( ~ product(X0,z,X1)
| ~ sum(X0,y,y)
| sum(X1,y_times_z,y_times_z) ),
inference(resolution,[status(thm)],[f41,f60]) ).
fof(f191,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| ~ sum(X0,multiplicative_identity,multiplicative_identity)
| sum(X2,X1,X1) ),
inference(resolution,[status(thm)],[f41,f34]) ).
fof(f197,plain,
! [X0,X1] :
( ~ product(X0,y_times_z,X1)
| ~ sum(X0,x,x)
| sum(X1,x_times__y_times_z,x_times__y_times_z) ),
inference(resolution,[status(thm)],[f41,f61]) ).
fof(f289,plain,
! [X0,X1] :
( ~ product(x_times_y,X0,X1)
| ~ sum(X0,z,multiplicative_identity)
| sum(X1,x_times_y__times_z,x_times_y) ),
inference(resolution,[status(thm)],[f138,f35]) ).
fof(f326,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f89,f28]) ).
fof(f354,plain,
! [X0] :
( ~ product(y_times_z,x,X0)
| X0 = x_times__y_times_z ),
inference(resolution,[status(thm)],[f59,f75]) ).
fof(f365,plain,
! [X0,X1] :
( ~ product(X0,multiplicative_identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f59,f35]) ).
fof(f366,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| X2 = multiply(X1,X0) ),
inference(resolution,[status(thm)],[f59,f78]) ).
fof(f387,plain,
multiply(y_times_z,x) = x_times__y_times_z,
inference(resolution,[status(thm)],[f354,f29]) ).
fof(f414,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| ~ product(X1,additive_identity,additive_identity)
| product(X2,X0,X0) ),
inference(resolution,[status(thm)],[f45,f33]) ).
fof(f463,plain,
! [X0] :
( ~ sum(X0,x_times_y,x_times_y)
| ~ sum(X0,z,z)
| sum(X0,x_times_y__times_z,x_times_y__times_z) ),
inference(resolution,[status(thm)],[f47,f63]) ).
fof(f608,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[f366,f29]) ).
fof(f1073,plain,
( spl0_31
<=> sum(x,multiplicative_identity,multiplicative_identity) ),
introduced(split_symbol_definition) ).
fof(f1075,plain,
( ~ sum(x,multiplicative_identity,multiplicative_identity)
| spl0_31 ),
inference(component_clause,[status(thm)],[f1073]) ).
fof(f1081,plain,
( spl0_33
<=> sum(y,multiplicative_identity,multiplicative_identity) ),
introduced(split_symbol_definition) ).
fof(f1083,plain,
( ~ sum(y,multiplicative_identity,multiplicative_identity)
| spl0_33 ),
inference(component_clause,[status(thm)],[f1081]) ).
fof(f1084,plain,
( spl0_34
<=> sum(y_times_z,z,z) ),
introduced(split_symbol_definition) ).
fof(f1085,plain,
( sum(y_times_z,z,z)
| ~ spl0_34 ),
inference(component_clause,[status(thm)],[f1084]) ).
fof(f1087,plain,
( ~ sum(y,multiplicative_identity,multiplicative_identity)
| sum(y_times_z,z,z) ),
inference(resolution,[status(thm)],[f145,f70]) ).
fof(f1088,plain,
( ~ spl0_33
| spl0_34 ),
inference(split_clause,[status(thm)],[f1087,f1081,f1084]) ).
fof(f1089,plain,
( spl0_35
<=> sum(x_times_y,multiplicative_identity,multiplicative_identity) ),
introduced(split_symbol_definition) ).
fof(f1091,plain,
( ~ sum(x_times_y,multiplicative_identity,multiplicative_identity)
| spl0_35 ),
inference(component_clause,[status(thm)],[f1089]) ).
fof(f1097,plain,
( spl0_37
<=> sum(x_times_y,y,y) ),
introduced(split_symbol_definition) ).
fof(f1100,plain,
( ~ sum(x,multiplicative_identity,multiplicative_identity)
| sum(x_times_y,y,y) ),
inference(resolution,[status(thm)],[f145,f74]) ).
fof(f1101,plain,
( ~ spl0_31
| spl0_37 ),
inference(split_clause,[status(thm)],[f1100,f1073,f1097]) ).
fof(f1102,plain,
( spl0_38
<=> sum(z,multiplicative_identity,multiplicative_identity) ),
introduced(split_symbol_definition) ).
fof(f1104,plain,
( ~ sum(z,multiplicative_identity,multiplicative_identity)
| spl0_38 ),
inference(component_clause,[status(thm)],[f1102]) ).
fof(f1105,plain,
( spl0_39
<=> sum(y_times_z,y,y) ),
introduced(split_symbol_definition) ).
fof(f1108,plain,
( ~ sum(z,multiplicative_identity,multiplicative_identity)
| sum(y_times_z,y,y) ),
inference(resolution,[status(thm)],[f145,f60]) ).
fof(f1109,plain,
( ~ spl0_38
| spl0_39 ),
inference(split_clause,[status(thm)],[f1108,f1102,f1105]) ).
fof(f1116,plain,
( spl0_41
<=> sum(x_times_y,x,x) ),
introduced(split_symbol_definition) ).
fof(f1117,plain,
( sum(x_times_y,x,x)
| ~ spl0_41 ),
inference(component_clause,[status(thm)],[f1116]) ).
fof(f1119,plain,
( ~ sum(y,multiplicative_identity,multiplicative_identity)
| sum(x_times_y,x,x) ),
inference(resolution,[status(thm)],[f145,f62]) ).
fof(f1120,plain,
( ~ spl0_33
| spl0_41 ),
inference(split_clause,[status(thm)],[f1119,f1081,f1116]) ).
fof(f1139,plain,
! [X0,X1] :
( ~ sum(X0,multiplicative_identity,multiplicative_identity)
| sum(multiply(X1,X0),X1,X1) ),
inference(resolution,[status(thm)],[f145,f29]) ).
fof(f1153,plain,
( spl0_47
<=> sum(x_times__y_times_z,x_times_y,x_times_y) ),
introduced(split_symbol_definition) ).
fof(f1154,plain,
( sum(x_times__y_times_z,x_times_y,x_times_y)
| ~ spl0_47 ),
inference(component_clause,[status(thm)],[f1153]) ).
fof(f1156,plain,
( ~ sum(y_times_z,y,y)
| sum(x_times__y_times_z,x_times_y,x_times_y) ),
inference(resolution,[status(thm)],[f139,f61]) ).
fof(f1157,plain,
( ~ spl0_39
| spl0_47 ),
inference(split_clause,[status(thm)],[f1156,f1105,f1153]) ).
fof(f1455,plain,
! [X0,X1] :
( ~ product(X0,additive_identity,X1)
| sum(X1,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f143,f32]) ).
fof(f1689,plain,
( spl0_52
<=> sum(x_times__y_times_z,z,z) ),
introduced(split_symbol_definition) ).
fof(f1691,plain,
( ~ sum(x_times__y_times_z,z,z)
| spl0_52 ),
inference(component_clause,[status(thm)],[f1689]) ).
fof(f1692,plain,
( spl0_53
<=> sum(x_times__y_times_z,x_times_y__times_z,x_times_y__times_z) ),
introduced(split_symbol_definition) ).
fof(f1693,plain,
( sum(x_times__y_times_z,x_times_y__times_z,x_times_y__times_z)
| ~ spl0_53 ),
inference(component_clause,[status(thm)],[f1692]) ).
fof(f1695,plain,
( ~ sum(x_times__y_times_z,z,z)
| sum(x_times__y_times_z,x_times_y__times_z,x_times_y__times_z)
| ~ spl0_47 ),
inference(resolution,[status(thm)],[f463,f1154]) ).
fof(f1696,plain,
( ~ spl0_52
| spl0_53
| ~ spl0_47 ),
inference(split_clause,[status(thm)],[f1695,f1689,f1692,f1153]) ).
fof(f1706,plain,
! [X0] : sum(multiply(additive_identity,X0),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f1455,f78]) ).
fof(f1708,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(resolution,[status(thm)],[f1706,f88]) ).
fof(f1755,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f1708,f78]) ).
fof(f1786,plain,
( spl0_56
<=> sum(additive_identity,x,x) ),
introduced(split_symbol_definition) ).
fof(f1788,plain,
( ~ sum(additive_identity,x,x)
| spl0_56 ),
inference(component_clause,[status(thm)],[f1786]) ).
fof(f1927,plain,
! [X0] :
( ~ sum(X0,z,multiplicative_identity)
| sum(multiply(X0,x_times_y),x_times_y__times_z,x_times_y) ),
inference(resolution,[status(thm)],[f289,f78]) ).
fof(f1945,plain,
sum(multiply(inverse(z),x_times_y),x_times_y__times_z,x_times_y),
inference(resolution,[status(thm)],[f1927,f52]) ).
fof(f1946,plain,
sum(multiply(x_times_y,inverse(z)),x_times_y__times_z,x_times_y),
inference(forward_demodulation,[status(thm)],[f608,f1945]) ).
fof(f1962,plain,
sum(x_times_y__times_z,multiply(x_times_y,inverse(z)),x_times_y),
inference(resolution,[status(thm)],[f1946,f30]) ).
fof(f2228,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| product(X2,X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f414,f1755]) ).
fof(f2233,plain,
product(x_times_y,x_times_y__times_z,x_times_y__times_z),
inference(resolution,[status(thm)],[f2228,f1962]) ).
fof(f2245,plain,
! [X0,X1] : product(add(X0,X1),X1,X1),
inference(resolution,[status(thm)],[f2228,f69]) ).
fof(f2433,plain,
( spl0_77
<=> sum(x_times_y__times_z,x_times__y_times_z,x_times__y_times_z) ),
introduced(split_symbol_definition) ).
fof(f2434,plain,
( sum(x_times_y__times_z,x_times__y_times_z,x_times__y_times_z)
| ~ spl0_77 ),
inference(component_clause,[status(thm)],[f2433]) ).
fof(f2591,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(resolution,[status(thm)],[f2245,f365]) ).
fof(f2623,plain,
! [X0,X1] : product(X0,add(X1,X0),X0),
inference(resolution,[status(thm)],[f2245,f31]) ).
fof(f2637,plain,
! [X0] : sum(multiplicative_identity,X0,multiplicative_identity),
inference(paramodulation,[status(thm)],[f2591,f69]) ).
fof(f2638,plain,
! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
inference(paramodulation,[status(thm)],[f2591,f28]) ).
fof(f2719,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| sum(X2,X1,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f2638]) ).
fof(f2723,plain,
( $false
| spl0_33 ),
inference(backward_subsumption_resolution,[status(thm)],[f1083,f2638]) ).
fof(f2724,plain,
spl0_33,
inference(contradiction_clause,[status(thm)],[f2723]) ).
fof(f2725,plain,
( $false
| spl0_31 ),
inference(backward_subsumption_resolution,[status(thm)],[f1075,f2638]) ).
fof(f2726,plain,
spl0_31,
inference(contradiction_clause,[status(thm)],[f2725]) ).
fof(f2727,plain,
( $false
| spl0_38 ),
inference(backward_subsumption_resolution,[status(thm)],[f1104,f2638]) ).
fof(f2728,plain,
spl0_38,
inference(contradiction_clause,[status(thm)],[f2727]) ).
fof(f2729,plain,
! [X0,X1] : sum(multiply(X0,X1),X0,X0),
inference(backward_subsumption_resolution,[status(thm)],[f1139,f2638]) ).
fof(f2885,plain,
product(x_times_y__times_z,x_times_y,x_times_y__times_z),
inference(resolution,[status(thm)],[f2233,f31]) ).
fof(f2942,plain,
( $false
| spl0_35 ),
inference(forward_subsumption_resolution,[status(thm)],[f1091,f2638]) ).
fof(f2943,plain,
spl0_35,
inference(contradiction_clause,[status(thm)],[f2942]) ).
fof(f2995,plain,
( spl0_86
<=> sum(y_times_z,additive_identity,y_times_z) ),
introduced(split_symbol_definition) ).
fof(f2997,plain,
( ~ sum(y_times_z,additive_identity,y_times_z)
| spl0_86 ),
inference(component_clause,[status(thm)],[f2995]) ).
fof(f3011,plain,
( $false
| spl0_86 ),
inference(forward_subsumption_resolution,[status(thm)],[f2997,f33]) ).
fof(f3012,plain,
spl0_86,
inference(contradiction_clause,[status(thm)],[f3011]) ).
fof(f3269,plain,
! [X0,X1] : X0 = add(multiply(X0,X1),X0),
inference(resolution,[status(thm)],[f2729,f90]) ).
fof(f3270,plain,
! [X0,X1] : X0 = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f326,f3269]) ).
fof(f3273,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),X0),
inference(resolution,[status(thm)],[f2729,f30]) ).
fof(f3973,plain,
y_times_z = add(y_times_z,x_times__y_times_z),
inference(paramodulation,[status(thm)],[f387,f3270]) ).
fof(f4047,plain,
( spl0_96
<=> sum(x_times_y__times_z,y_times_z,y_times_z) ),
introduced(split_symbol_definition) ).
fof(f4048,plain,
( sum(x_times_y__times_z,y_times_z,y_times_z)
| ~ spl0_96 ),
inference(component_clause,[status(thm)],[f4047]) ).
fof(f4050,plain,
( ~ sum(x_times_y,y,y)
| sum(x_times_y__times_z,y_times_z,y_times_z) ),
inference(resolution,[status(thm)],[f187,f63]) ).
fof(f4051,plain,
( ~ spl0_37
| spl0_96 ),
inference(split_clause,[status(thm)],[f4050,f1097,f4047]) ).
fof(f4324,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X0)
| ~ sum(X1,X2,X3)
| product(X0,X3,X0) ),
inference(resolution,[status(thm)],[f3273,f178]) ).
fof(f5068,plain,
product(x_times__y_times_z,y_times_z,x_times__y_times_z),
inference(paramodulation,[status(thm)],[f3973,f2623]) ).
fof(f5898,plain,
( $false
| spl0_56 ),
inference(forward_subsumption_resolution,[status(thm)],[f1788,f32]) ).
fof(f5899,plain,
spl0_56,
inference(contradiction_clause,[status(thm)],[f5898]) ).
fof(f6702,plain,
( sum(x_times_y__times_z,x_times__y_times_z,x_times_y__times_z)
| ~ spl0_53 ),
inference(resolution,[status(thm)],[f1693,f30]) ).
fof(f6741,plain,
( product(y_times_z,x_times_y__times_z,x_times_y__times_z)
| ~ spl0_96 ),
inference(resolution,[status(thm)],[f4048,f2228]) ).
fof(f7910,plain,
! [X0] :
( ~ sum(x_times_y__times_z,x_times__y_times_z,X0)
| X0 = x_times_y__times_z
| ~ spl0_53 ),
inference(resolution,[status(thm)],[f6702,f57]) ).
fof(f7947,plain,
( product(x_times_y__times_z,y_times_z,x_times_y__times_z)
| ~ spl0_96 ),
inference(resolution,[status(thm)],[f6741,f31]) ).
fof(f11763,plain,
( spl0_127
<=> sum(x_times_y__times_z,x,x) ),
introduced(split_symbol_definition) ).
fof(f11765,plain,
( ~ sum(x_times_y__times_z,x,x)
| spl0_127 ),
inference(component_clause,[status(thm)],[f11763]) ).
fof(f11766,plain,
( ~ sum(x_times_y__times_z,x,x)
| sum(x_times_y__times_z,x_times__y_times_z,x_times__y_times_z)
| ~ spl0_96 ),
inference(resolution,[status(thm)],[f197,f7947]) ).
fof(f11767,plain,
( ~ spl0_127
| spl0_77
| ~ spl0_96 ),
inference(split_clause,[status(thm)],[f11766,f11763,f2433,f4047]) ).
fof(f17022,plain,
( spl0_133
<=> sum(multiplicative_identity,additive_identity,multiplicative_identity) ),
introduced(split_symbol_definition) ).
fof(f17024,plain,
( ~ sum(multiplicative_identity,additive_identity,multiplicative_identity)
| spl0_133 ),
inference(component_clause,[status(thm)],[f17022]) ).
fof(f17902,plain,
( spl0_137
<=> sum(x,additive_identity,x) ),
introduced(split_symbol_definition) ).
fof(f17904,plain,
( ~ sum(x,additive_identity,x)
| spl0_137 ),
inference(component_clause,[status(thm)],[f17902]) ).
fof(f18025,plain,
( $false
| spl0_133 ),
inference(forward_subsumption_resolution,[status(thm)],[f17024,f2637]) ).
fof(f18026,plain,
spl0_133,
inference(contradiction_clause,[status(thm)],[f18025]) ).
fof(f18027,plain,
( $false
| spl0_137 ),
inference(forward_subsumption_resolution,[status(thm)],[f17904,f33]) ).
fof(f18028,plain,
spl0_137,
inference(contradiction_clause,[status(thm)],[f18027]) ).
fof(f23569,plain,
( x_times__y_times_z = x_times_y__times_z
| ~ spl0_77
| ~ spl0_53 ),
inference(resolution,[status(thm)],[f2434,f7910]) ).
fof(f23570,plain,
( $false
| ~ spl0_77
| ~ spl0_53 ),
inference(forward_subsumption_resolution,[status(thm)],[f23569,f64]) ).
fof(f23571,plain,
( ~ spl0_77
| ~ spl0_53 ),
inference(contradiction_clause,[status(thm)],[f23570]) ).
fof(f34446,plain,
! [X0,X1] :
( ~ sum(x_times_y,X0,X1)
| product(x_times_y__times_z,X1,x_times_y__times_z) ),
inference(resolution,[status(thm)],[f4324,f2885]) ).
fof(f34453,plain,
! [X0,X1] :
( ~ sum(y_times_z,X0,X1)
| product(x_times__y_times_z,X1,x_times__y_times_z) ),
inference(resolution,[status(thm)],[f4324,f5068]) ).
fof(f34541,plain,
( product(x_times_y__times_z,x,x_times_y__times_z)
| ~ spl0_41 ),
inference(resolution,[status(thm)],[f34446,f1117]) ).
fof(f34588,plain,
( sum(x_times_y__times_z,x,x)
| ~ spl0_41 ),
inference(resolution,[status(thm)],[f34541,f2719]) ).
fof(f34589,plain,
( $false
| spl0_127
| ~ spl0_41 ),
inference(forward_subsumption_resolution,[status(thm)],[f34588,f11765]) ).
fof(f34590,plain,
( spl0_127
| ~ spl0_41 ),
inference(contradiction_clause,[status(thm)],[f34589]) ).
fof(f41830,plain,
( product(x_times__y_times_z,z,x_times__y_times_z)
| ~ spl0_34 ),
inference(resolution,[status(thm)],[f34453,f1085]) ).
fof(f41885,plain,
( sum(x_times__y_times_z,z,z)
| ~ spl0_34 ),
inference(resolution,[status(thm)],[f41830,f2719]) ).
fof(f41886,plain,
( $false
| spl0_52
| ~ spl0_34 ),
inference(forward_subsumption_resolution,[status(thm)],[f41885,f1691]) ).
fof(f41887,plain,
( spl0_52
| ~ spl0_34 ),
inference(contradiction_clause,[status(thm)],[f41886]) ).
fof(f41888,plain,
$false,
inference(sat_refutation,[status(thm)],[f1088,f1101,f1109,f1120,f1157,f1696,f2724,f2726,f2728,f2943,f3012,f4051,f5899,f11767,f18026,f18028,f23571,f34590,f41887]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : BOO007-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n028.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 22:55:14 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 41.00/5.56 % Refutation found
% 41.00/5.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 41.00/5.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 41.99/5.64 % Elapsed time: 5.273231 seconds
% 41.99/5.64 % CPU time: 41.707436 seconds
% 41.99/5.64 % Total memory used: 357.488 MB
% 41.99/5.64 % Net memory used: 331.645 MB
%------------------------------------------------------------------------------