%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL034-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 02:00:43 PM UTC 2026
% Result : Unsatisfiable 7.59s 1.42s
% Output : Proof 7.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of formulae : 46 ( 42 unt; 0 def)
% Number of atoms : 54 ( 33 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 : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 121 ( 53 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(implies(implies(X,Y),implies(Z,falsehood)),U),V),implies(implies(V,X),implies(Z,X)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c0_CAMeredith) ).
fof(f1_nnf,plain,
! [X,Y,Z,U,V] : is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),U),V),implies(implies(V,X),implies(Z,X)))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z,U,V] : is_a_theorem(implies(implies(implies(implies(implies(X,Y),implies(Z,falsehood)),U),V),implies(implies(V,X),implies(Z,X)))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(implies(implies(implies(implies(X0,X1),implies(X2,falsehood)),X3),X4),implies(implies(X4,X0),implies(X2,X0)))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(implies(implies(implies(implies(implies(X0,X1),implies(X2,falsehood)),X3),X4),implies(implies(X4,X0),implies(X2,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(h2,plain,
is_a_theorem(implies(implies(implies(V0,implies(falsehood,V1)),V2),implies(V3,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h0]) ).
cnf(h8,plain,
is_a_theorem(implies(V0,implies(V1,implies(falsehood,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h2]) ).
cnf(h12,plain,
is_a_theorem(implies(V0,implies(falsehood,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h8,h8]) ).
cnf(h15,plain,
is_a_theorem(implies(implies(implies(falsehood,V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h12]) ).
cnf(h16,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h15]) ).
cnf(h17,plain,
is_a_theorem(implies(V0,implies(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h16,h16]) ).
cnf(h21,plain,
is_a_theorem(implies(implies(implies(V0,implies(implies(implies(V1,V2),implies(V3,falsehood)),V4)),V1),implies(V3,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h17]) ).
cnf(h34,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(implies(implies(V1,V3),implies(V0,falsehood)),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h21]) ).
cnf(h43,plain,
is_a_theorem(implies(implies(implies(V0,V1),implies(implies(falsehood,V2),falsehood)),implies(V3,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h34,h15]) ).
cnf(h50,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V2)),V1),implies(V3,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h43]) ).
cnf(h54,plain,
is_a_theorem(implies(implies(implies(V0,V1),V2),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h50]) ).
cnf(h59,plain,
is_a_theorem(implies(implies(implies(implies(V0,falsehood),V1),V2),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h54]) ).
cnf(h96,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),implies(V2,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h59]) ).
cnf(h89,plain,
is_a_theorem(implies(implies(V0,falsehood),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h59,h59]) ).
cnf(h105,plain,
is_a_theorem(implies(V0,implies(implies(V0,falsehood),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h59,h89]) ).
cnf(h121,plain,
is_a_theorem(implies(V0,implies(implies(implies(implies(V0,falsehood),V1),falsehood),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h59,h105]) ).
cnf(h42,plain,
is_a_theorem(implies(implies(implies(V0,V1),implies(V2,falsehood)),implies(V3,implies(V2,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h34,h17]) ).
cnf(h106,plain,
is_a_theorem(implies(V0,implies(V1,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h42,h89]) ).
cnf(h110,plain,
is_a_theorem(implies(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h106,h106]) ).
cnf(h116,plain,
is_a_theorem(implies(implies(implies(V0,V1),implies(V2,falsehood)),implies(V2,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h34,h110]) ).
cnf(h355,plain,
is_a_theorem(implies(implies(implies(implies(implies(V0,V1),falsehood),V2),falsehood),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h116,h121]) ).
cnf(h457,plain,
is_a_theorem(implies(implies(V0,implies(V0,V1)),implies(V2,implies(V0,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h355]) ).
cnf(h473,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,V2),V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h457,h96]) ).
cnf(h115,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),implies(V2,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h106]) ).
cnf(h471,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,V1),V2),V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h457,h115]) ).
cnf(h484,plain,
is_a_theorem(implies(implies(implies(V0,V0),V1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h471,h471]) ).
cnf(t14,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h484,h473]) ).
cnf(t364,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c0_3) ).
fof(f2_nnf,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(implies(a,b),a),a)) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t364]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL034-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 21:40:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.59/1.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.59/1.42 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------