%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL416-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 02:01:57 PM UTC 2026
% Result : Unsatisfiable 8.71s 1.53s
% Output : Proof 8.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 36 unt; 0 def)
% Number of atoms : 48 ( 27 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 : 13 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 150 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f0_nnf,plain,
! [A,B] :
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,B)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( is_a_theorem(B)
| ~ is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,B)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(equivalent(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(is_a_theorem(equivalent(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(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xcb) ).
fof(f1_nnf,plain,
! [A,B,C] : is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] : is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X2))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),V2)),V3),equivalent(V4,V3)),V4)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,hi1]) ).
cnf(h1,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),V2)),V3),equivalent(V4,V3)),V4),V5),equivalent(V6,V5)),V6)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h0]) ).
cnf(h4,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),V2)),V3),equivalent(V4,V3)),V4),V5),V6),equivalent(V5,V6))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1,hi1]) ).
cnf(h2,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),V2)),V3),V4),equivalent(V3,V4))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,hi1]) ).
cnf(h6,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),V2)),V3),V4),equivalent(V3,V4)),V5),equivalent(V6,V5)),V6)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h2]) ).
cnf(h30,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),V2)),V3),V4),equivalent(V3,V4)),V5),V6),equivalent(V5,V6))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6,hi1]) ).
cnf(h112,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(equivalent(V1,equivalent(equivalent(equivalent(equivalent(V2,equivalent(equivalent(equivalent(V2,V3),equivalent(V4,V3)),V4)),V5),equivalent(V6,V5)),V6)),V1),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h30,h4]) ).
cnf(h180,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(equivalent(V1,equivalent(equivalent(equivalent(V1,V2),equivalent(V3,V2)),V3)),V4),equivalent(V5,V4)),V5)),V0),equivalent(V6,equivalent(equivalent(equivalent(V6,V7),equivalent(V8,V7)),V8)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h112,hi1]) ).
cnf(h5,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(equivalent(equivalent(equivalent(V1,equivalent(equivalent(equivalent(V1,V2),equivalent(V3,V2)),V3)),V4),equivalent(V5,V4)),V5),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h2]) ).
cnf(h13,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),V2)),V3),equivalent(V4,V3)),V4),equivalent(equivalent(equivalent(equivalent(V5,equivalent(equivalent(equivalent(V5,V6),equivalent(V7,V6)),V7)),V8),V9),equivalent(V8,V9)))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5,h2]) ).
cnf(h8,plain,
is_a_theorem(equivalent(equivalent(V0,equivalent(equivalent(equivalent(equivalent(V1,equivalent(equivalent(equivalent(V1,V2),equivalent(V3,V2)),V3)),V4),equivalent(V5,V4)),V5)),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h2,h0]) ).
cnf(h35,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(equivalent(V1,equivalent(equivalent(equivalent(V1,V2),equivalent(V3,V2)),V3)),V4),equivalent(V5,V4)),V5)),V0),V6),equivalent(V7,V6)),V7)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h8]) ).
cnf(h235,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),V2)),V3),equivalent(equivalent(equivalent(V3,V4),equivalent(V5,V4)),V5))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h35,h13]) ).
cnf(h279,plain,
is_a_theorem(equivalent(equivalent(V0,V1),equivalent(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0,h235]) ).
cnf(h314,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(V0,V1),equivalent(V0,V1)),V2),equivalent(V3,V2)),V3)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h279]) ).
cnf(h374,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(V0,V1),equivalent(V0,V1)),V2),V3),equivalent(V2,V3)),V4),equivalent(V5,V4)),V5)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h235,h314]) ).
cnf(h3613,plain,
is_a_theorem(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V0,V1),equivalent(V2,V1)),V2)),V3),V3)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h374,h180]) ).
cnf(h403,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(V0,V1),equivalent(V0,V1)),V2),V3),equivalent(V2,V3))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h314,hi1]) ).
cnf(h448,plain,
is_a_theorem(equivalent(V0,equivalent(equivalent(equivalent(V1,V2),equivalent(V1,V2)),V0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h403,h403]) ).
cnf(h528,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V1,V2),equivalent(V1,V2)),V0)),V3),equivalent(V4,V3)),V4)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi1,h448]) ).
cnf(h1329,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(V0,equivalent(equivalent(equivalent(V1,V2),equivalent(V1,V2)),V0)),V3),V4),equivalent(V3,V4))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h528,hi1]) ).
cnf(t0,plain,
is_a_theorem(equivalent(X1,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1329,h3613]) ).
cnf(t257,plain,
is_a_theorem(equivalent(X1,X1)) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f2,negated_conjecture,
~ is_a_theorem(equivalent(a,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_reflexivity) ).
fof(f2_nnf,plain,
~ is_a_theorem(equivalent(a,a)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ is_a_theorem(equivalent(a,a)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(equivalent(a,a)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(a,a)) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t257]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL416-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n020.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 23:15:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.71/1.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.71/1.53 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------