TSTP Solution File: COL074-3 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : COL074-3 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 20:13:46 EDT 2024
% Result : Unsatisfiable 0.14s 0.37s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 23 unt; 0 def)
% Number of atoms : 62 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 16 ~; 18 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X,Y] : apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : apply(eq,pair(X,X)) = projection1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( X = Y
| apply(eq,pair(X,Y)) = projection2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
projection1 != projection2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
apply(k,projection2) = k_projection2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f19,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f20,plain,
! [X0] : apply(eq,pair(X0,X0)) = projection1,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f21,plain,
! [X0,X1] :
( X0 = X1
| apply(eq,pair(X0,X1)) = projection2 ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f23,plain,
projection1 != projection2,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f25,plain,
apply(k,projection2) = k_projection2,
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f26,plain,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f28,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(k,X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f14,f19]) ).
fof(f29,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(X0,apply(k,X1))),X2),X1) = apply(apply(apply(apply(abstraction,X0),k),X1),apply(X2,X1)),
inference(paramodulation,[status(thm)],[f19,f19]) ).
fof(f39,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(abstraction,apply(k,X0))),X1),X2) = apply(X0,apply(apply(k,X2),apply(X1,X2))),
inference(paramodulation,[status(thm)],[f19,f28]) ).
fof(f40,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(abstraction,apply(k,X0))),X1),X2) = apply(X0,X2),
inference(forward_demodulation,[status(thm)],[f14,f39]) ).
fof(f84,plain,
! [X0,X1] : apply(apply(apply(apply(abstraction,abstraction),k),X0),apply(X1,X0)) = apply(X0,X0),
inference(paramodulation,[status(thm)],[f29,f40]) ).
fof(f101,plain,
! [X0,X1] : apply(apply(apply(apply(abstraction,abstraction),k),X0),X1) = apply(X0,X0),
inference(paramodulation,[status(thm)],[f14,f84]) ).
fof(f131,plain,
! [X0,X1] : apply(apply(apply(apply(abstraction,abstraction),k),apply(k,X0)),X1) = X0,
inference(paramodulation,[status(thm)],[f14,f101]) ).
fof(f333,plain,
! [X0] : apply(k_projection2,X0) = projection2,
inference(paramodulation,[status(thm)],[f25,f14]) ).
fof(f458,plain,
s = apply(eq,pair(apply(k,s),k_projection2)),
inference(forward_demodulation,[status(thm)],[f25,f26]) ).
fof(f459,plain,
( spl0_2
<=> s = projection2 ),
introduced(split_symbol_definition) ).
fof(f460,plain,
( s = projection2
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f461,plain,
( s != projection2
| spl0_2 ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,plain,
( spl0_3
<=> apply(k,s) = k_projection2 ),
introduced(split_symbol_definition) ).
fof(f463,plain,
( apply(k,s) = k_projection2
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( s = projection2
| apply(k,s) = k_projection2 ),
inference(paramodulation,[status(thm)],[f21,f458]) ).
fof(f466,plain,
( spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f465,f459,f462]) ).
fof(f488,plain,
( s = apply(eq,pair(apply(k,projection2),k_projection2))
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f460,f458]) ).
fof(f489,plain,
( projection2 = apply(eq,pair(apply(k,projection2),k_projection2))
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f460,f488]) ).
fof(f490,plain,
( projection2 = apply(eq,pair(k_projection2,k_projection2))
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f25,f489]) ).
fof(f491,plain,
( projection2 = projection1
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f20,f490]) ).
fof(f492,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f23]) ).
fof(f493,plain,
~ spl0_2,
inference(contradiction_clause,[status(thm)],[f492]) ).
fof(f495,plain,
! [X0] :
( apply(apply(apply(apply(abstraction,abstraction),k),k_projection2),X0) = s
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f463,f131]) ).
fof(f496,plain,
( apply(k_projection2,k_projection2) = s
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f101,f495]) ).
fof(f497,plain,
( projection2 = s
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f333,f496]) ).
fof(f498,plain,
( $false
| spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f461]) ).
fof(f499,plain,
( spl0_2
| ~ spl0_3 ),
inference(contradiction_clause,[status(thm)],[f498]) ).
fof(f500,plain,
$false,
inference(sat_refutation,[status(thm)],[f466,f493,f499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : COL074-3 : TPTP v8.1.2. Released v1.2.0.
% 0.12/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 22:31:31 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.14/0.37 % Refutation found
% 0.14/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.38 % Elapsed time: 0.027736 seconds
% 0.14/0.38 % CPU time: 0.088542 seconds
% 0.14/0.38 % Total memory used: 16.819 MB
% 0.14/0.38 % Net memory used: 16.745 MB
%------------------------------------------------------------------------------