%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL085-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 02:00:54 PM UTC 2026
% Result : Unsatisfiable 36.62s 5.47s
% Output : Proof 36.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 3
% Syntax : Number of formulae : 75 ( 71 unt; 0 def)
% Number of atoms : 83 ( 62 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 238 ( 98 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,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]) ).
cnf(f1,axiom,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_JLukasiewicz) ).
fof(f1_nnf,plain,
! [X,Y,Z,U] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z,U] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X2,X0),implies(X3,X0)))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(X2,X0),implies(X3,X0)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(V2,V1)),implies(V1,V3)),implies(V4,implies(V1,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h1,plain,
is_a_theorem(implies(V0,implies(implies(V1,V2),implies(V2,implies(V1,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h0]) ).
cnf(h3,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),implies(V1,implies(V0,V1))),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1]) ).
cnf(h10,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,implies(V2,V1)),V2),implies(V3,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,hi1]) ).
cnf(h11,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,implies(V1,V0)),V1),implies(V2,V1)),V3),implies(V4,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h10]) ).
cnf(h92,plain,
is_a_theorem(implies(V0,implies(implies(V1,V2),implies(V3,implies(V1,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h11]) ).
cnf(h96,plain,
is_a_theorem(implies(implies(V0,V1),implies(V2,implies(V0,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h92,h92]) ).
cnf(h101,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V2)),V1),implies(V3,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h96]) ).
cnf(h128,plain,
is_a_theorem(implies(implies(implies(V0,V1),implies(V2,implies(V1,V3))),implies(V4,implies(V2,implies(V1,V3))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h101]) ).
cnf(h149,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h128,h96]) ).
cnf(h151,plain,
is_a_theorem(implies(V0,implies(V1,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h149,h149]) ).
cnf(h154,plain,
is_a_theorem(implies(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h151,h151]) ).
cnf(h156,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),implies(V2,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h154]) ).
cnf(h166,plain,
is_a_theorem(implies(implies(implies(V0,V1),implies(V1,V2)),implies(V3,implies(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h156]) ).
cnf(h176,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V2)),implies(V3,V1)),implies(V4,implies(V3,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h166]) ).
cnf(h177,plain,
is_a_theorem(implies(V0,implies(implies(implies(implies(V1,V2),V3),V2),implies(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h176,hi1]) ).
cnf(h178,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),V2),V1),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h177,h177]) ).
cnf(h181,plain,
is_a_theorem(implies(implies(implies(V0,V1),implies(implies(V0,V1),V2)),implies(V3,implies(implies(V0,V1),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h178]) ).
cnf(h204,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,implies(V2,V3)),V2),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h181,h101]) ).
cnf(h153,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V1)),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h149]) ).
cnf(h199,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,implies(V2,V2)),V3),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h181,h153]) ).
cnf(h155,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h151]) ).
cnf(h160,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h155]) ).
cnf(h165,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V0)),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h160]) ).
cnf(h195,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,implies(V2,V1)),V3),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h181,h165]) ).
cnf(h198,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,V1),V2),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h181,h155]) ).
cnf(h197,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,V2),V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h181,h156]) ).
cnf(h209,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h197,h197]) ).
cnf(h212,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h209,h198]) ).
cnf(h218,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V0)),V2),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h212,h195]) ).
cnf(h221,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V1)),V2),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h218,h199]) ).
cnf(h224,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V2)),V1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h221,h204]) ).
cnf(h227,plain,
is_a_theorem(implies(implies(V0,implies(V1,implies(V0,V2))),implies(V3,implies(V1,implies(V0,V2))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h224]) ).
cnf(h211,plain,
is_a_theorem(implies(implies(V0,implies(V0,V1)),implies(V2,implies(V0,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h209]) ).
cnf(h228,plain,
is_a_theorem(implies(V0,implies(implies(V1,implies(V1,V2)),implies(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h211,h211]) ).
cnf(h230,plain,
is_a_theorem(implies(implies(V0,implies(V0,V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h228,h228]) ).
cnf(h296,plain,
is_a_theorem(implies(implies(V0,implies(V1,implies(V0,V2))),implies(V1,implies(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h230,h227]) ).
cnf(h300,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(implies(V1,V2),V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h296,hi1]) ).
cnf(h457,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,V1),implies(V2,V1)),V3),implies(implies(V1,V4),V0)),implies(implies(V0,V1),implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h300,hi1]) ).
cnf(h509,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h457,h176]) ).
cnf(h515,plain,
is_a_theorem(implies(V0,implies(implies(V0,V1),implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h509,hi1]) ).
cnf(h523,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,V1),V2),implies(V3,V2)),V0),implies(V4,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h515]) ).
cnf(h547,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,V1),V2),implies(V3,V2)),V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h230,h523]) ).
cnf(h347,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),V2),implies(implies(V3,implies(V1,V4)),V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h300,h101]) ).
cnf(h555,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,implies(implies(V1,V2),V3)),implies(V1,V2)),V4),V2),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h347,h547]) ).
cnf(h161,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,V2),V1),implies(V3,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h155,hi1]) ).
cnf(h173,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,V1),V0),implies(V2,V0)),V3),implies(V4,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h161]) ).
cnf(h235,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,V1),V0),implies(V2,V0)),V3),V3)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h230,h173]) ).
cnf(h310,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),V2),implies(implies(V1,V3),V1)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h235,h300]) ).
cnf(h891,plain,
is_a_theorem(implies(implies(implies(V0,implies(implies(implies(V1,V2),V1),V3)),implies(implies(V1,V2),V1)),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h310,h555]) ).
cnf(h519,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,V1),implies(V2,V1)),V3),V0),implies(implies(V0,V1),implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h300,h515]) ).
cnf(h893,plain,
is_a_theorem(implies(implies(V0,V1),implies(implies(implies(V0,V2),V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h519,h891]) ).
cnf(h516,plain,
is_a_theorem(implies(implies(implies(V0,implies(implies(V0,V1),implies(V2,V1))),V3),implies(V4,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h515,h515]) ).
cnf(h542,plain,
is_a_theorem(implies(implies(implies(V0,implies(implies(V0,V1),implies(V2,V1))),V3),V3)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h230,h516]) ).
cnf(h904,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),implies(implies(V0,V2),implies(V3,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h542,h893]) ).
cnf(h342,plain,
is_a_theorem(implies(implies(implies(implies(V0,implies(V1,V2)),V3),implies(V1,implies(V1,V2))),implies(V0,implies(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h300,h211]) ).
cnf(t7,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h342,h904]) ).
cnf(t272,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ic_5) ).
fof(f2_nnf,plain,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(implies(a,implies(implies(a,b),b))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(a,implies(implies(a,b),b))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t272]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL085-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 21:54:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 36.62/5.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.62/5.47 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------