%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL372+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 02:01:49 PM UTC 2026
% Result : Theorem 158.40s 21.23s
% Output : Proof 158.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 62 ( 58 unt; 0 def)
% Number of atoms : 70 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 6 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 136 ( 28 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ),
file('/export/starexec/sandbox2/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,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
fof(f1_nnf,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
fof(f3,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
fof(f3_nnf,plain,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
is_a_theorem(implies(X0,implies(not(X0),X1))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h6,plain,
is_a_theorem(implies(implies(implies(not(V0),V1),V2),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi3]) ).
fof(f2,axiom,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
fof(f2_nnf,plain,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : is_a_theorem(implies(implies(not(X),X),X)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
is_a_theorem(implies(implies(not(X0),X0),X0)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h10,plain,
is_a_theorem(implies(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,hi2]) ).
cnf(h12,plain,
is_a_theorem(implies(not(implies(V0,V0)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h10]) ).
cnf(h14,plain,
is_a_theorem(implies(implies(V0,V1),implies(not(implies(V2,V2)),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h12]) ).
cnf(h31,plain,
is_a_theorem(implies(V0,implies(not(implies(V1,V1)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h14]) ).
cnf(h34,plain,
is_a_theorem(implies(implies(implies(not(implies(V0,V0)),V1),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h31]) ).
cnf(h38,plain,
is_a_theorem(implies(V0,implies(V1,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h34,hi2]) ).
cnf(h43,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h38]) ).
cnf(h46,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(implies(V3,V3),V1),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h43]) ).
cnf(h88,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h46,hi2]) ).
cnf(h7,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(not(V0),V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi2]) ).
cnf(h243,plain,
is_a_theorem(implies(implies(implies(implies(not(V0),V0),V1),V2),implies(implies(V0,V1),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h7]) ).
cnf(h695,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),V2),V3),implies(implies(implies(implies(not(V0),V0),V1),V2),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h243]) ).
cnf(h731,plain,
is_a_theorem(implies(implies(implies(implies(not(V0),V0),V0),V1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h695,h88]) ).
cnf(h232,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,hi1,hi1]) ).
cnf(h2988,plain,
is_a_theorem(implies(implies(V0,implies(not(V1),V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h232,h731]) ).
cnf(h3123,plain,
is_a_theorem(implies(implies(not(V0),V1),implies(implies(V1,V0),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h232,h2988]) ).
cnf(h20,plain,
is_a_theorem(implies(V0,implies(implies(not(not(V0)),not(V0)),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,h7]) ).
cnf(h241,plain,
is_a_theorem(implies(implies(implies(implies(not(not(V0)),not(V0)),V1),V2),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h20]) ).
cnf(h11,plain,
is_a_theorem(implies(V0,implies(implies(V1,V2),implies(not(V0),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,hi1]) ).
cnf(h242,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(not(V2),V1)),V3),implies(V2,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h11]) ).
cnf(h588,plain,
is_a_theorem(implies(V0,implies(V1,implies(not(V0),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h242,h241]) ).
cnf(h613,plain,
is_a_theorem(implies(implies(implies(V0,implies(not(V1),V2)),V3),implies(V1,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h588]) ).
cnf(h3116,plain,
is_a_theorem(implies(V0,implies(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h613,h2988]) ).
cnf(h3166,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h3116]) ).
cnf(h3484,plain,
is_a_theorem(implies(V0,implies(implies(V0,V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3166,h3123]) ).
cnf(h3651,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),V1),V2),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h3484]) ).
cnf(h4804,plain,
is_a_theorem(implies(not(V0),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3651,h6]) ).
cnf(h4912,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3123,h4804]) ).
cnf(h4795,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(V2,V0),implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3651,h232]) ).
cnf(h35898,plain,
is_a_theorem(implies(implies(V0,implies(implies(V1,V2),V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4795,h4912]) ).
cnf(h72915,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(V2,V0),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h232,h35898]) ).
cnf(t5,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(implies(implies(X2,X4),X1),X3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h72915]) ).
cnf(t265,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(implies(implies(X2,X4),X1),X3))) = true,
inference(orient,[status(thm)],[t5]) ).
fof(f4,conjecture,
is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_28) ).
fof(f4_neg,negated_conjecture,
~ is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
~ is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
~ is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t265]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL372+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 23:06:11 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 158.40/21.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 158.40/21.23 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------