%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL072-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 02:00:51 PM UTC 2026
% Result : Unsatisfiable 6.40s 1.22s
% Output : Proof 6.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 32 unt; 0 def)
% Number of atoms : 44 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 66 ( 9 sgn 24 !; 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(f3,axiom,
is_a_theorem(implies(implies(X,implies(not(Y),Z)),implies(X,implies(implies(U,Z),implies(implies(Y,U),Z))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_60) ).
fof(f3_nnf,plain,
! [X,Y,Z,U] : is_a_theorem(implies(implies(X,implies(not(Y),Z)),implies(X,implies(implies(U,Z),implies(implies(Y,U),Z))))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z,U] : is_a_theorem(implies(implies(X,implies(not(Y),Z)),implies(X,implies(implies(U,Z),implies(implies(Y,U),Z))))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
is_a_theorem(implies(implies(X0,implies(not(X1),X2)),implies(X0,implies(implies(X3,X2),implies(implies(X1,X3),X2))))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
is_a_theorem(implies(implies(X0,implies(not(X1),X2)),implies(X0,implies(implies(X3,X2),implies(implies(X1,X3),X2))))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f2,axiom,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_37) ).
fof(f2_nnf,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X0),X2))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h4,plain,
is_a_theorem(implies(implies(implies(implies(V0,not(a)),b),implies(not(a),b)),implies(implies(a,implies(not(a),b)),implies(implies(implies(V0,not(a)),a),implies(not(a),b))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi2]) ).
cnf(f1,axiom,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_19) ).
fof(f1_nnf,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(implies(implies(implies(X0,X1),X2),implies(X1,X2))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h5,plain,
is_a_theorem(implies(implies(a,implies(not(a),b)),implies(implies(implies(V0,not(a)),a),implies(not(a),b)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4,hi1]) ).
cnf(h6,plain,
is_a_theorem(implies(not(a),implies(implies(implies(V0,not(a)),a),implies(not(a),b)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,h5]) ).
cnf(h1,plain,
is_a_theorem(implies(implies(not(a),b),implies(a,implies(not(a),b)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h0,plain,
is_a_theorem(implies(implies(implies(not(a),b),implies(a,implies(not(a),b))),implies(implies(implies(implies(implies(V0,not(a)),a),implies(not(a),b)),implies(a,implies(not(a),b))),implies(implies(not(a),implies(implies(implies(V0,not(a)),a),implies(not(a),b))),implies(a,implies(not(a),b)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi2]) ).
cnf(h2,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,not(a)),a),implies(not(a),b)),implies(a,implies(not(a),b))),implies(implies(not(a),implies(implies(implies(V0,not(a)),a),implies(not(a),b))),implies(a,implies(not(a),b))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h1]) ).
cnf(h3,plain,
is_a_theorem(implies(implies(not(a),implies(implies(implies(V0,not(a)),a),implies(not(a),b))),implies(a,implies(not(a),b)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,hi1]) ).
cnf(t1,plain,
is_a_theorem(implies(a,implies(not(a),b))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3,h6]) ).
cnf(t10,plain,
is_a_theorem(implies(a,implies(not(a),b))) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(f4,negated_conjecture,
~ is_a_theorem(implies(a,implies(not(a),b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_3) ).
fof(f4_nnf,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(a,implies(not(a),b))) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t10]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL072-1 : 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 : n007.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 21:47:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.40/1.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.40/1.22 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------