%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 18 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 2 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X,Y] : apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : apply(eq,pair(X,X)) = projection1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( apply(eq,pair(X,Y)) = projection2
| X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
projection1 != projection2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
apply(k,projection2) = k_projection2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,plain,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0] : apply(eq,pair(X0,X0)) = projection1,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
! [X0,X1] :
( apply(eq,pair(X0,X1)) = projection2
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
projection1 != projection2,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
apply(k,projection2) = k_projection2,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f26,plain,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f147,plain,
! [X0] : apply(k_projection2,X0) = projection2,
inference(paramodulation,[status(thm)],[f25,f14]) ).
fof(f619,plain,
s = apply(eq,pair(apply(k,s),k_projection2)),
inference(forward_demodulation,[status(thm)],[f25,f26]) ).
fof(f620,plain,
( apply(k,s) = k_projection2
| s = projection2 ),
inference(paramodulation,[status(thm)],[f21,f619]) ).
fof(f1097,plain,
! [X0] :
( s = projection2
| apply(k_projection2,X0) = s ),
inference(paramodulation,[status(thm)],[f620,f14]) ).
fof(f1107,plain,
( s = projection2
| projection2 = s ),
inference(forward_demodulation,[status(thm)],[f147,f1097]) ).
fof(f1108,plain,
projection2 = s,
inference(duplicate_literals_removal,[status(thm)],[f1107]) ).
fof(f1110,plain,
s = apply(eq,pair(apply(k,projection2),k_projection2)),
inference(backward_demodulation,[status(thm)],[f1108,f619]) ).
fof(f1111,plain,
projection2 = apply(eq,pair(apply(k,projection2),k_projection2)),
inference(forward_demodulation,[status(thm)],[f1108,f1110]) ).
fof(f1112,plain,
projection2 = apply(eq,pair(k_projection2,k_projection2)),
inference(forward_demodulation,[status(thm)],[f25,f1111]) ).
fof(f1113,plain,
projection2 = projection1,
inference(forward_demodulation,[status(thm)],[f20,f1112]) ).
fof(f1114,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1113,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 14:08:25 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.059436 seconds
% 0.12/0.42 % CPU time: 0.221567 seconds
% 0.12/0.42 % Total memory used: 105.297 MB
% 0.12/0.42 % Net memory used: 104.780 MB
%------------------------------------------------------------------------------