%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL076-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:08:41 PM UTC 2026
% Result : Unsatisfiable 9.09s 1.55s
% Output : CNFRefutation 9.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 22 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : apply(projection2,pair(X,Y)) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] : apply(pair(X,Y),Z) = pair(apply(X,Z),apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] : apply(apply(f,X),Y) = apply(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [Y] : Y != apply(eq,pair(apply(k,Y),apply(k,projection2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1] : apply(projection2,pair(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] : apply(pair(X0,X1),X2) = pair(apply(X0,X2),apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [X0,X1] : apply(apply(f,X0),X1) = apply(X0,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f18,plain,
! [X0] : X0 != apply(eq,pair(apply(k,X0),apply(k,projection2))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
! [X0,X1,X2] : apply(pair(apply(k,X0),X1),X2) = pair(X0,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f10,f14]) ).
fof(f23,plain,
! [X0,X1,X2] : apply(pair(X0,projection2),pair(X1,X2)) = pair(apply(X0,pair(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f12,f14]) ).
fof(f138,plain,
! [X0,X1] :
( X0 != apply(X1,n(apply(k,X0),X1))
| apply(k,X0) = X1 ),
inference(paramodulation,[status(thm)],[f10,f16]) ).
fof(f142,plain,
! [X0,X1] :
( apply(X0,n(X0,apply(f,X1))) != apply(X1,X1)
| X0 = apply(f,X1) ),
inference(paramodulation,[status(thm)],[f17,f16]) ).
fof(f147,plain,
! [X0,X1,X2] :
( X0 != pair(X1,apply(X2,n(apply(k,X0),pair(apply(k,X1),X2))))
| apply(k,X0) = pair(apply(k,X1),X2) ),
inference(paramodulation,[status(thm)],[f22,f138]) ).
fof(f185,plain,
! [X0,X1,X2] :
( apply(X0,n(X0,apply(f,X1))) != apply(apply(f,X1),X2)
| X0 = apply(f,X1) ),
inference(paramodulation,[status(thm)],[f17,f142]) ).
fof(f188,plain,
! [X0,X1] : apply(k,apply(apply(f,X0),X1)) = apply(f,X0),
inference(resolution,[status(thm)],[f185,f10]) ).
fof(f222,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(k,X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f10,f15]) ).
fof(f634,plain,
! [X0,X1,X2] :
( X0 != pair(X1,X2)
| apply(k,X0) = pair(apply(k,X1),apply(k,X2)) ),
inference(paramodulation,[status(thm)],[f10,f147]) ).
fof(f644,plain,
! [X0] : X0 != apply(eq,apply(k,pair(X0,projection2))),
inference(backward_demodulation,[status(thm)],[f645,f18]) ).
fof(f645,plain,
! [X0,X1] : apply(k,pair(X0,X1)) = pair(apply(k,X0),apply(k,X1)),
inference(destructive_equality_resolution,[status(thm)],[f634]) ).
fof(f785,plain,
! [X0,X1] : apply(X0,pair(X1,projection2)) != apply(eq,apply(k,apply(pair(X0,projection2),pair(X1,projection2)))),
inference(paramodulation,[status(thm)],[f23,f644]) ).
fof(f1042,plain,
! [X0,X1] : apply(X0,pair(X0,projection2)) != apply(eq,apply(k,apply(apply(f,pair(X0,projection2)),X1))),
inference(paramodulation,[status(thm)],[f17,f785]) ).
fof(f1048,plain,
! [X0] : apply(X0,pair(X0,projection2)) != apply(eq,apply(f,pair(X0,projection2))),
inference(forward_demodulation,[status(thm)],[f188,f1042]) ).
fof(f3016,plain,
$false,
inference(resolution,[status(thm)],[f222,f1048]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL076-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 14:08:53 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.31 % Drodi V4.1.1
% 9.09/1.55 % Refutation found
% 9.09/1.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.09/1.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.09/1.60 % Elapsed time: 1.287947 seconds
% 9.09/1.60 % CPU time: 9.842063 seconds
% 9.09/1.60 % Total memory used: 251.179 MB
% 9.09/1.60 % Net memory used: 246.176 MB
%------------------------------------------------------------------------------