%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 02:00:53 PM UTC 2026
% Result : Unsatisfiable 0.06s 5.87s
% Output : Proof 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 31 unt; 0 def)
% Number of atoms : 43 ( 18 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 : 6 ( 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 : 75 ( 24 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f1,axiom,
is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))),
file('/export/starexec/sandbox/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(f2,axiom,
is_a_theorem(implies(X,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ic_1) ).
fof(f2_nnf,plain,
! [X] : is_a_theorem(implies(X,X)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : is_a_theorem(implies(X,X)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
is_a_theorem(implies(X0,X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
is_a_theorem(implies(X0,X0)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h0,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),implies(V2,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi2]) ).
cnf(h2,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,h0]) ).
cnf(h12,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,h2]) ).
cnf(h18,plain,
is_a_theorem(implies(V0,implies(implies(implies(implies(V1,V2),V3),V2),implies(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h12,hi1]) ).
cnf(h19,plain,
is_a_theorem(implies(implies(implies(implies(V0,V1),V2),V1),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h18,h18]) ).
cnf(h38,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,h19]) ).
cnf(h58,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,V2),V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h38,h0]) ).
cnf(h1,plain,
is_a_theorem(implies(V0,implies(V1,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h0]) ).
cnf(h3,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1]) ).
cnf(h56,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,V1),V2),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h38,h3]) ).
cnf(h59,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h56,h56]) ).
cnf(t7,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h59,h58]) ).
cnf(t110,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f3,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ic_3) ).
fof(f3_nnf,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(implies(a,b),a),a)) != true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t110]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.04/5.31 % Computer : n012.cluster.edu
% 0.04/5.31 % Model : x86_64 x86_64
% 0.04/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.31 % Memory : 8046.5625MB
% 0.04/5.31 % OS : Linux 6.8.0-71-generic
% 0.04/5.31 % CPULimit : 300
% 0.04/5.31 % WCLimit : 300
% 0.04/5.31 % DateTime : Wed Sep 23 21:51:26 UTC 2026
% 0.04/5.31 % CPUTime :
% 0.04/5.31 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/5.87 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/5.87 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------