%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL077-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 02:00:52 PM UTC 2026
% Result : Unsatisfiable 7.08s 1.50s
% Output : Proof 7.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 38 unt; 0 def)
% Number of atoms : 62 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-4 aty)
% Number of variables : 90 ( 18 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
fof(f4_nnf,plain,
! [X1,X2,X3] :
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X1,X2,X3] :
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(X0,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f3,axiom,
is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_49) ).
fof(f3_nnf,plain,
! [X,Y] : is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h8,plain,
is_a_theorem(implies(implies(not(not(V0)),not(not(V1))),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi3,hi3]) ).
cnf(f1,axiom,
is_a_theorem(implies(X,implies(Y,X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_18) ).
fof(f1_nnf,plain,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(X0,implies(X1,X0))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(implies(X0,implies(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h9,plain,
is_a_theorem(implies(not(V0),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi1,hi3]) ).
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(implies(X,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]) ).
cnf(f2,axiom,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_35) ).
fof(f2_nnf,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h115,plain,
is_a_theorem(implies(implies(not(V0),V0),implies(not(V0),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,h9]) ).
cnf(h165,plain,
is_a_theorem(implies(implies(not(not(V0)),not(V0)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h115,h8]) ).
cnf(h0,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi1,hi1]) ).
cnf(h161,plain,
is_a_theorem(implies(V0,implies(not(implies(V1,V0)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0,h115]) ).
cnf(h259,plain,
is_a_theorem(implies(implies(V0,not(implies(V1,V0))),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,h161]) ).
cnf(h528,plain,
is_a_theorem(implies(not(implies(V0,V1)),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi1,h259]) ).
cnf(h546,plain,
is_a_theorem(implies(not(implies(V0,not(not(V1)))),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h528,h165]) ).
cnf(h168,plain,
is_a_theorem(implies(implies(not(V0),V0),implies(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h115,hi3]) ).
cnf(h702,plain,
is_a_theorem(implies(V0,implies(V1,not(not(V1))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h168,h546]) ).
cnf(h723,plain,
is_a_theorem(implies(V0,not(not(V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h702,h702]) ).
cnf(t3,plain,
is_a_theorem(implies(not(not(X1)),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h723]) ).
cnf(t464,plain,
is_a_theorem(implies(not(not(X1)),X1)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f5,negated_conjecture,
~ is_a_theorem(implies(not(not(a)),a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_39) ).
fof(f5_nnf,plain,
~ is_a_theorem(implies(not(not(a)),a)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ is_a_theorem(implies(not(not(a)),a)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ is_a_theorem(implies(not(not(a)),a)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(not(not(a)),a)) != true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t464]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL077-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Wed Sep 23 21:48:37 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.08/1.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.08/1.50 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------