%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL096-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 02:00:56 PM UTC 2026
% Result : Unsatisfiable 7.10s 1.61s
% Output : Proof 7.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 28 unt; 0 def)
% Number of atoms : 40 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 102 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(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(equivalent(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(equivalent(X,Y)) ),
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(f3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),U),equivalent(equivalent(equivalent(X,V),Z),equivalent(equivalent(Y,V),U)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_4) ).
fof(f3_nnf,plain,
! [X,Y,Z,U,V] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),U),equivalent(equivalent(equivalent(X,V),Z),equivalent(equivalent(Y,V),U)))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z,U,V] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X,Y),Z),U),equivalent(equivalent(equivalent(X,V),Z),equivalent(equivalent(Y,V),U)))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X2),X3),equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),X3)))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X2),X3),equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),X3)))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_3) ).
fof(f2_nnf,plain,
! [X,Y,Z,U,V] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z,U,V] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h4,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(V0,V1),equivalent(V0,V2)),V3),V4),V5),equivalent(equivalent(equivalent(equivalent(V1,V2),V3),V4),V5))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi2]) ).
cnf(h40,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(V0,V1),V2),equivalent(equivalent(V3,V1),equivalent(equivalent(V0,V3),V2))),V4),V4)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h4,hi2]) ).
cnf(f1,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),U),U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_2) ).
fof(f1_nnf,plain,
! [X,Y,Z,U] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),U),U)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z,U] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z)),U),U)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),equivalent(X1,X2)),X3),X3)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),equivalent(X1,X2)),X3),X3)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h5,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(V0,V1),equivalent(V0,V2)),V3),V4),equivalent(equivalent(equivalent(V1,V2),V3),V4))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi1]) ).
cnf(t25,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3),X3)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5,h40]) ).
cnf(t407,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X2),X1)),X3),X3)) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(f4,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_1) ).
fof(f4_nnf,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t407]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL096-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.57 % Computer : n016.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Wed Sep 23 21:58:43 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.10/1.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.10/1.61 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------