%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL384+2 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 : Fri Sep 25 02:01:52 PM UTC 2026
% Result : Theorem 79.73s 31.12s
% Output : Proof 79.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 30 unt; 0 def)
% Number of atoms : 42 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 6 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 148 ( 20 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f0_nnf,plain,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,Y)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f1,axiom,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O] : is_a_theorem(implies(implies(implies(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F)),F),implies(implies(implies(implies(implies(implies(implies(G,H),implies(implies(H,I),implies(G,I))),implies(implies(implies(n(J),J),J),K)),K),implies(implies(L,implies(n(L),M)),N)),N),O)),O)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f2) ).
fof(f1_nnf,plain,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O] : is_a_theorem(implies(implies(implies(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F)),F),implies(implies(implies(implies(implies(implies(implies(G,H),implies(implies(H,I),implies(G,I))),implies(implies(implies(n(J),J),J),K)),K),implies(implies(L,implies(n(L),M)),N)),N),O)),O)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O] : is_a_theorem(implies(implies(implies(implies(implies(A,implies(B,A)),implies(implies(C,implies(D,implies(E,D))),F)),F),implies(implies(implies(implies(implies(implies(implies(G,H),implies(implies(H,I),implies(G,I))),implies(implies(implies(n(J),J),J),K)),K),implies(implies(L,implies(n(L),M)),N)),N),O)),O)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(implies(implies(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5)),X5),implies(implies(implies(implies(implies(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8))),implies(implies(implies(n(X9),X9),X9),X10)),X10),implies(implies(X11,implies(n(X11),X12)),X13)),X13),X14)),X14)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(implies(implies(implies(implies(implies(X0,implies(X1,X0)),implies(implies(X2,implies(X3,implies(X4,X3))),X5)),X5),implies(implies(implies(implies(implies(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8))),implies(implies(implies(n(X9),X9),X9),X10)),X10),implies(implies(X11,implies(n(X11),X12)),X13)),X13),X14)),X14)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
is_a_theorem(implies(V0,implies(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h1,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h0]) ).
cnf(h4,plain,
is_a_theorem(implies(V0,implies(implies(implies(implies(implies(implies(V1,V2),implies(implies(V2,V3),implies(V1,V3))),implies(implies(implies(n(V4),V4),V4),V5)),V5),implies(implies(V6,implies(n(V6),V7)),V8)),V8))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1]) ).
cnf(h7,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(V0,V1),implies(implies(V1,V2),implies(V0,V2))),implies(implies(implies(n(V3),V3),V3),V4)),V4),implies(implies(V5,implies(n(V5),V6)),V7)),V7)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4,h4]) ).
cnf(h20,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(implies(V1,V2),implies(V0,V2))),implies(implies(implies(n(V3),V3),V3),V4)),V4)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,h0]) ).
cnf(h2,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V0)),implies(implies(V2,implies(V3,implies(V4,V3))),V5)),V5)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h0]) ).
cnf(h49,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V0)),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h20]) ).
cnf(h94,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h20,h49]) ).
cnf(h109,plain,
is_a_theorem(implies(implies(implies(implies(n(V0),V0),V0),V1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h94,h20]) ).
cnf(h51,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(V1,V2),implies(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h20,h0]) ).
cnf(h127,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(V2,V1)),V3),implies(implies(V2,V0),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h51,h51]) ).
cnf(h964,plain,
is_a_theorem(implies(implies(V0,implies(n(V1),V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h127,h109]) ).
cnf(h16440,plain,
is_a_theorem(implies(implies(n(V0),V1),implies(implies(V1,V0),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h127,h964]) ).
cnf(h932,plain,
is_a_theorem(implies(implies(V0,implies(V1,V2)),implies(implies(V3,V1),implies(V0,implies(V3,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h127,h127]) ).
cnf(t250,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(n(X3),X2),implies(X1,X3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h932,h16440]) ).
cnf(t298,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(n(X3),X2),implies(X1,X3)))) = true,
inference(orient,[status(thm)],[t250]) ).
fof(f2,conjecture,
is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(n(z),y),implies(x,z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f3) ).
fof(f2_neg,negated_conjecture,
~ is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(n(z),y),implies(x,z)))),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
~ is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(n(z),y),implies(x,z)))),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
~ is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(n(z),y),implies(x,z)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(n(z),y),implies(x,z)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(x,implies(y,z)),implies(implies(n(z),y),implies(x,z)))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t298]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL384+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/20.44 % Computer : n017.cluster.edu
% 0.15/20.44 % Model : x86_64 x86_64
% 0.15/20.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/20.44 % Memory : 8046.5625MB
% 0.15/20.44 % OS : Linux 6.8.0-71-generic
% 0.15/20.44 % CPULimit : 300
% 0.15/20.44 % WCLimit : 300
% 0.15/20.44 % DateTime : Wed Sep 23 23:02:37 UTC 2026
% 0.15/20.45 % CPUTime :
% 0.15/20.45 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 79.73/31.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 79.73/31.12 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------