%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 03:13:26 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 23 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 5 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 29 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
pA != pE,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,X2] : proj2C(c2(X,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [Y] : append(nil,Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [Y,Z,Xs] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
linP(pA) = cons(a,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
linP(pE) = nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [P,Q] : linC(c2(P,Q)) = append(linP(P),linP(Q)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,conjecture,
? [U,V] :
~ ( linC(U) = linC(V)
=> U = V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ? [U,V] :
~ ( linC(U) = linC(V)
=> U = V ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f43,plain,
pA != pE,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f46,plain,
! [X0,X1] : proj2C(c2(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f47,plain,
! [X0] : append(nil,X0) = X0,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f48,plain,
! [X0,X1,X2] : append(cons(X0,X1),X2) = cons(X0,append(X1,X2)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f51,plain,
linP(pA) = cons(a,nil),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f53,plain,
linP(pE) = nil,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f54,plain,
! [X0,X1] : linC(c2(X0,X1)) = append(linP(X0),linP(X1)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f55,plain,
! [U,V] :
( U = V
| linC(U) != linC(V) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f56,plain,
! [X0,X1] :
( X0 = X1
| linC(X0) != linC(X1) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f72,plain,
! [X0] : linC(c2(X0,pE)) = append(linP(X0),nil),
inference(paramodulation,[status(thm)],[f53,f54]) ).
fof(f73,plain,
! [X0] : linC(c2(pE,X0)) = append(nil,linP(X0)),
inference(paramodulation,[status(thm)],[f53,f54]) ).
fof(f74,plain,
! [X0] : linC(c2(pE,X0)) = linP(X0),
inference(forward_demodulation,[status(thm)],[f47,f73]) ).
fof(f79,plain,
! [X0] : append(linP(pA),X0) = cons(a,append(nil,X0)),
inference(paramodulation,[status(thm)],[f51,f48]) ).
fof(f81,plain,
! [X0] : append(linP(pA),X0) = cons(a,X0),
inference(forward_demodulation,[status(thm)],[f47,f79]) ).
fof(f87,plain,
! [X0,X1] :
( X0 = c2(X1,pE)
| linC(X0) != append(linP(X1),nil) ),
inference(paramodulation,[status(thm)],[f72,f56]) ).
fof(f143,plain,
! [X0] :
( X0 = c2(pA,pE)
| linC(X0) != cons(a,nil) ),
inference(paramodulation,[status(thm)],[f81,f87]) ).
fof(f147,plain,
! [X0] :
( X0 = c2(pA,pE)
| linC(X0) != linP(pA) ),
inference(forward_demodulation,[status(thm)],[f51,f143]) ).
fof(f165,plain,
c2(pE,pA) = c2(pA,pE),
inference(resolution,[status(thm)],[f147,f74]) ).
fof(f171,plain,
proj2C(c2(pA,pE)) = pA,
inference(paramodulation,[status(thm)],[f165,f46]) ).
fof(f182,plain,
pE = pA,
inference(forward_demodulation,[status(thm)],[f46,f171]) ).
fof(f183,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f182,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 10:32:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.045466 seconds
% 0.11/0.43 % CPU time: 0.138725 seconds
% 0.11/0.43 % Total memory used: 56.736 MB
% 0.11/0.43 % Net memory used: 56.521 MB
%------------------------------------------------------------------------------