%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL026-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 02:00:42 PM UTC 2026
% Result : Unsatisfiable 3.33s 2.90s
% Output : Proof 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 55 unt; 0 def)
% Number of atoms : 67 ( 38 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 : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 121 ( 43 sgn 16 !; 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(f1,axiom,
is_a_theorem(implies(X,implies(Y,X))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_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(h0,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(f2,axiom,
is_a_theorem(implies(implies(implies(X,falsehood),falsehood),X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_5) ).
fof(f2_nnf,plain,
! [X] : is_a_theorem(implies(implies(implies(X,falsehood),falsehood),X)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : is_a_theorem(implies(implies(implies(X,falsehood),falsehood),X)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
is_a_theorem(implies(implies(implies(X0,falsehood),falsehood),X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
is_a_theorem(implies(implies(implies(X0,falsehood),falsehood),X0)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h1,plain,
is_a_theorem(implies(falsehood,falsehood)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi2]) ).
cnf(h3,plain,
is_a_theorem(implies(V0,implies(falsehood,falsehood))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1]) ).
cnf(h4,plain,
is_a_theorem(implies(V0,implies(V1,implies(falsehood,falsehood)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h3]) ).
cnf(h6,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,implies(falsehood,falsehood))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h4]) ).
cnf(h9,plain,
is_a_theorem(implies(V0,implies(V1,implies(V2,implies(V3,implies(falsehood,falsehood)))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h6]) ).
cnf(f3,axiom,
is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_6) ).
fof(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c3,plain,
is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h16,plain,
is_a_theorem(implies(implies(V0,V1),implies(V0,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi1]) ).
cnf(h21,plain,
is_a_theorem(implies(V0,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h16,h9]) ).
cnf(h22,plain,
is_a_theorem(implies(implies(implies(V0,V1),V0),implies(implies(V0,V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h21]) ).
cnf(h91,plain,
is_a_theorem(implies(implies(implies(V0,implies(V1,V0)),V2),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h22,h0]) ).
cnf(h132,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,implies(V2,V1)),V3),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h91]) ).
cnf(h340,plain,
is_a_theorem(implies(implies(V0,implies(implies(V1,implies(V2,V1)),V3)),implies(V0,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h132]) ).
cnf(h1043,plain,
is_a_theorem(implies(implies(V0,implies(implies(V1,V0),V2)),implies(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h340,hi3]) ).
cnf(h2,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,falsehood),falsehood),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi2]) ).
cnf(h14,plain,
is_a_theorem(implies(implies(V0,implies(implies(V1,falsehood),falsehood)),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h2]) ).
cnf(h51,plain,
is_a_theorem(implies(falsehood,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h14,hi1]) ).
cnf(h55,plain,
is_a_theorem(implies(V0,implies(falsehood,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h51]) ).
cnf(h57,plain,
is_a_theorem(implies(implies(V0,falsehood),implies(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h55]) ).
cnf(h66,plain,
is_a_theorem(implies(V0,implies(implies(V1,falsehood),implies(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h57]) ).
cnf(h72,plain,
is_a_theorem(implies(implies(V0,implies(V1,falsehood)),implies(V0,implies(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h66]) ).
cnf(h15,plain,
is_a_theorem(implies(implies(V0,V1),implies(V0,implies(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h0]) ).
cnf(h244,plain,
is_a_theorem(implies(implies(V0,implies(V1,falsehood)),implies(V2,implies(V0,implies(V1,V3))))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h15,h72]) ).
cnf(h1044,plain,
is_a_theorem(implies(V0,implies(implies(V1,implies(implies(V2,V1),falsehood)),implies(V1,V3)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h244,h1043]) ).
cnf(h1866,plain,
is_a_theorem(implies(implies(implies(V0,V1),falsehood),implies(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1043,h1044]) ).
cnf(h76,plain,
is_a_theorem(implies(V0,implies(implies(implies(V1,V2),V1),implies(implies(V1,V2),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h22]) ).
cnf(h1058,plain,
is_a_theorem(implies(V0,implies(implies(V0,V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1043,h76]) ).
cnf(h1127,plain,
is_a_theorem(implies(V0,implies(V1,implies(implies(V1,V2),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h1058]) ).
cnf(h1216,plain,
is_a_theorem(implies(implies(V0,V1),implies(V0,implies(implies(V1,V2),V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h1127]) ).
cnf(h1868,plain,
is_a_theorem(implies(implies(implies(V0,V1),falsehood),implies(implies(implies(V1,V2),V3),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1216,h1866]) ).
cnf(h75,plain,
is_a_theorem(implies(implies(implies(V0,falsehood),V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h14,h22]) ).
cnf(t7,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h75,h1868]) ).
cnf(t352,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f4,negated_conjecture,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c0_3) ).
fof(f4_nnf,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(implies(a,b),a),a)) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t352]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL026-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n009.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 21:39:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.33/2.90 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.33/2.90 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------