%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL080-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 19.14s 3.02s
% Output : Proof 19.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 40 unt; 0 def)
% Number of atoms : 52 ( 23 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 : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 46 ( 7 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
is_a_theorem(implies(X,implies(Y,X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_2) ).
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(h15,plain,
is_a_theorem(implies(a,implies(e,a))) = true,
inference(hyper_resolution,[status(thm)],[hi1]) ).
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,Y),implies(implies(Y,Z),implies(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_4) ).
fof(f3_nnf,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f2,axiom,
is_a_theorem(implies(implies(implies(X,Y),X),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ic_3) ).
fof(f2_nnf,plain,
! [X,Y] : is_a_theorem(implies(implies(implies(X,Y),X),X)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : is_a_theorem(implies(implies(implies(X,Y),X),X)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
is_a_theorem(implies(implies(implies(X0,X1),X0),X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
is_a_theorem(implies(implies(implies(X0,X1),X0),X0)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h20,plain,
is_a_theorem(implies(implies(a,implies(e,a)),implies(implies(implies(a,b),a),implies(e,a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi2]) ).
cnf(h21,plain,
is_a_theorem(implies(implies(implies(a,b),a),implies(e,a))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h20,h15]) ).
cnf(h30,plain,
is_a_theorem(implies(implies(implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(implies(a,b),a),implies(e,a))),implies(implies(implies(implies(implies(a,b),a),implies(e,a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a))))),implies(implies(implies(implies(a,b),a),implies(e,a)),implies(implies(implies(implies(implies(a,b),a),implies(e,a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a))))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi1]) ).
cnf(h31,plain,
is_a_theorem(implies(implies(implies(implies(a,b),a),implies(e,a)),implies(implies(implies(implies(implies(a,b),a),implies(e,a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h30,hi3]) ).
cnf(h32,plain,
is_a_theorem(implies(implies(implies(implies(implies(a,b),a),implies(e,a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h31,h21]) ).
cnf(h27,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a))),implies(implies(c,a),implies(e,a))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))),implies(implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi3]) ).
cnf(h28,plain,
is_a_theorem(implies(implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h27,hi2]) ).
cnf(h25,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(a,b),a),implies(e,a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi3]) ).
cnf(h26,plain,
is_a_theorem(implies(implies(implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))),implies(implies(implies(implies(implies(implies(a,b),a),implies(e,a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h25]) ).
cnf(h29,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(a,b),a),implies(e,a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))),implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h26,h28]) ).
cnf(h33,plain,
is_a_theorem(implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h29,h32]) ).
cnf(h22,plain,
is_a_theorem(implies(implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi3]) ).
cnf(h23,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))),V0),implies(implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h22]) ).
cnf(h24,plain,
is_a_theorem(implies(implies(implies(implies(c,a),implies(implies(a,b),a)),implies(implies(c,a),implies(e,a))),implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,h23]) ).
cnf(t5,plain,
is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h24,h33]) ).
cnf(t10,plain,
is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f4,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ic_JLukasiewicz) ).
fof(f4_nnf,plain,
~ is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(implies(a,b),c),implies(implies(c,a),implies(e,a)))) != 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 : LCL080-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 21:54:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 19.14/3.02 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.14/3.02 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------