%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL982+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 02:03:27 PM UTC 2026
% Result : Theorem 3.42s 0.87s
% Output : Proof 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 42 unt; 0 def)
% Number of atoms : 54 ( 32 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 : 14 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 252 ( 74 sgn 27 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X,Y] :
( 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(t1,plain,
ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t5,plain,
ifeq(is_a_theorem(implies(X1,X2)),true,ifeq(is_a_theorem(X1),true,is_a_theorem(X2),true),true) = true,
inference(orient,[status(thm)],[t1]) ).
fof(f1,axiom,
! [A,B,C,D,E] : is_a_theorem(implies(implies(A,B),implies(implies(implies(C,implies(D,E)),implies(B,implies(not(D),not(A)))),implies(A,D)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5) ).
fof(f1_nnf,plain,
! [A,B,C,D,E] : is_a_theorem(implies(implies(A,B),implies(implies(implies(C,implies(D,E)),implies(B,implies(not(D),not(A)))),implies(A,D)))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C,D,E] : is_a_theorem(implies(implies(A,B),implies(implies(implies(C,implies(D,E)),implies(B,implies(not(D),not(A)))),implies(A,D)))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X2,implies(X3,X4)),implies(X1,implies(not(X3),not(X0)))),implies(X0,X3)))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t2,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X3,implies(X4,X5)),implies(X2,implies(not(X4),not(X1)))),implies(X1,X4)))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t4,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X3,implies(X4,X5)),implies(X2,implies(not(X4),not(X1)))),implies(X1,X4)))) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t6,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(implies(X3,implies(X4,X5)),implies(X2,implies(not(X4),not(X1)))),implies(X1,X4))),true),true),
inference(cp,[status(thm)],[t5,t4]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t252,plain,
true = ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(implies(X3,implies(X4,X5)),implies(X2,implies(not(X4),not(X1)))),implies(X1,X4))),true),
inference(step,[status(thm)],[t6,t3]) ).
cnf(t9,plain,
ifeq(is_a_theorem(implies(X1,X2)),true,is_a_theorem(implies(implies(implies(X3,implies(X4,X5)),implies(X2,implies(not(X4),not(X1)))),implies(X1,X4))),true) = true,
inference(orient,[status(thm)],[t252]) ).
cnf(t10,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(Y6,implies(not(X5),not(Y7)))),implies(Y7,X5)),implies(not(X2),not(implies(Y7,Y6))))),implies(implies(Y7,Y6),X2))),true),
inference(cp,[status(thm)],[t9,t4]) ).
cnf(t254,plain,
true = is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(Y6,implies(not(X5),not(Y7)))),implies(Y7,X5)),implies(not(X2),not(implies(Y7,Y6))))),implies(implies(Y7,Y6),X2))),
inference(step,[status(thm)],[t10,t3]) ).
cnf(t19,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(Y6,implies(not(X5),not(Y7)))),implies(Y7,X5)),implies(not(X2),not(implies(Y7,Y6))))),implies(implies(Y7,Y6),X2))) = true,
inference(orient,[status(thm)],[t254]) ).
cnf(t20,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(Y6,implies(not(X5),not(Y7)))),implies(Y7,X5)),implies(not(X2),not(implies(Y7,Y6)))))),true,is_a_theorem(implies(implies(Y7,Y6),X2)),true),true),
inference(cp,[status(thm)],[t5,t19]) ).
cnf(t255,plain,
true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(Y6,implies(not(X5),not(Y7)))),implies(Y7,X5)),implies(not(X2),not(implies(Y7,Y6)))))),true,is_a_theorem(implies(implies(Y7,Y6),X2)),true),
inference(step,[status(thm)],[t20,t3]) ).
cnf(t27,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(Y6,implies(not(X5),not(Y7)))),implies(Y7,X5)),implies(not(X2),not(implies(Y7,Y6)))))),true,is_a_theorem(implies(implies(Y7,Y6),X2)),true) = true,
inference(orient,[status(thm)],[t255]) ).
cnf(t28,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X3,implies(X4,X5)),implies(implies(X1,Y5),implies(not(X4),not(implies(implies(Y6,implies(Y5,Y7)),implies(X2,implies(not(Y5),not(X1)))))))),implies(implies(implies(Y6,implies(Y5,Y7)),implies(X2,implies(not(Y5),not(X1)))),X4)))),true),
inference(cp,[status(thm)],[t27,t19]) ).
cnf(t257,plain,
true = is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X3,implies(X4,X5)),implies(implies(X1,Y5),implies(not(X4),not(implies(implies(Y6,implies(Y5,Y7)),implies(X2,implies(not(Y5),not(X1)))))))),implies(implies(implies(Y6,implies(Y5,Y7)),implies(X2,implies(not(Y5),not(X1)))),X4)))),
inference(step,[status(thm)],[t28,t3]) ).
cnf(t51,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X3,implies(X4,X5)),implies(implies(X1,Y5),implies(not(X4),not(implies(implies(Y6,implies(Y5,Y7)),implies(X2,implies(not(Y5),not(X1)))))))),implies(implies(implies(Y6,implies(Y5,Y7)),implies(X2,implies(not(Y5),not(X1)))),X4)))) = true,
inference(orient,[status(thm)],[t257]) ).
cnf(t55,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(implies(Y6,Y7),implies(not(X5),not(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))))))),implies(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))),X5)),implies(not(X2),not(implies(Y6,Y10))))),implies(implies(Y6,Y10),X2))),true),
inference(cp,[status(thm)],[t9,t51]) ).
cnf(t260,plain,
true = is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(implies(Y6,Y7),implies(not(X5),not(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))))))),implies(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))),X5)),implies(not(X2),not(implies(Y6,Y10))))),implies(implies(Y6,Y10),X2))),
inference(step,[status(thm)],[t55,t3]) ).
cnf(t108,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(implies(Y6,Y7),implies(not(X5),not(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))))))),implies(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))),X5)),implies(not(X2),not(implies(Y6,Y10))))),implies(implies(Y6,Y10),X2))) = true,
inference(orient,[status(thm)],[t260]) ).
cnf(t109,plain,
true = ifeq(true,true,ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(implies(Y6,Y7),implies(not(X5),not(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))))))),implies(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))),X5)),implies(not(X2),not(implies(Y6,Y10)))))),true,is_a_theorem(implies(implies(Y6,Y10),X2)),true),true),
inference(cp,[status(thm)],[t5,t108]) ).
cnf(t261,plain,
true = ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(implies(Y6,Y7),implies(not(X5),not(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))))))),implies(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))),X5)),implies(not(X2),not(implies(Y6,Y10)))))),true,is_a_theorem(implies(implies(Y6,Y10),X2)),true),
inference(step,[status(thm)],[t109,t3]) ).
cnf(t131,plain,
ifeq(is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(implies(implies(X4,implies(X5,Y5)),implies(implies(Y6,Y7),implies(not(X5),not(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))))))),implies(implies(implies(Y8,implies(Y7,Y9)),implies(Y10,implies(not(Y7),not(Y6)))),X5)),implies(not(X2),not(implies(Y6,Y10)))))),true,is_a_theorem(implies(implies(Y6,Y10),X2)),true) = true,
inference(orient,[status(thm)],[t261]) ).
cnf(t23,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(implies(X4,X5),Y5),implies(not(X2),not(implies(implies(Y6,implies(Y5,Y7)),implies(implies(implies(implies(Y8,implies(Y9,Y10)),implies(X5,implies(not(Y9),not(X4)))),implies(X4,Y9)),implies(not(Y5),not(implies(X4,X5))))))))),implies(implies(implies(Y6,implies(Y5,Y7)),implies(implies(implies(implies(Y8,implies(Y9,Y10)),implies(X5,implies(not(Y9),not(X4)))),implies(X4,Y9)),implies(not(Y5),not(implies(X4,X5))))),X2))),true),
inference(cp,[status(thm)],[t9,t19]) ).
cnf(t263,plain,
true = is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(implies(X4,X5),Y5),implies(not(X2),not(implies(implies(Y6,implies(Y5,Y7)),implies(implies(implies(implies(Y8,implies(Y9,Y10)),implies(X5,implies(not(Y9),not(X4)))),implies(X4,Y9)),implies(not(Y5),not(implies(X4,X5))))))))),implies(implies(implies(Y6,implies(Y5,Y7)),implies(implies(implies(implies(Y8,implies(Y9,Y10)),implies(X5,implies(not(Y9),not(X4)))),implies(X4,Y9)),implies(not(Y5),not(implies(X4,X5))))),X2))),
inference(step,[status(thm)],[t23,t3]) ).
cnf(t208,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),implies(implies(implies(X4,X5),Y5),implies(not(X2),not(implies(implies(Y6,implies(Y5,Y7)),implies(implies(implies(implies(Y8,implies(Y9,Y10)),implies(X5,implies(not(Y9),not(X4)))),implies(X4,Y9)),implies(not(Y5),not(implies(X4,X5))))))))),implies(implies(implies(Y6,implies(Y5,Y7)),implies(implies(implies(implies(Y8,implies(Y9,Y10)),implies(X5,implies(not(Y9),not(X4)))),implies(X4,Y9)),implies(not(Y5),not(implies(X4,X5))))),X2))) = true,
inference(orient,[status(thm)],[t263]) ).
cnf(t224,plain,
true = ifeq(true,true,is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),true),
inference(cp,[status(thm)],[t131,t208]) ).
cnf(t264,plain,
true = is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(step,[status(thm)],[t224,t3]) ).
cnf(t231,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) = true,
inference(orient,[status(thm)],[t264]) ).
fof(f2,conjecture,
! [A,B,C] : is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_1) ).
fof(f2_neg,negated_conjecture,
~ ! [A,B,C] : is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
? [A,B,C] : ~ is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
~ is_a_theorem(implies(implies(sk0,sk1),implies(implies(sk1,sk2),implies(sk0,sk2)))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f2_nnf]) ).
cnf(c2,plain,
~ is_a_theorem(implies(implies(sk0,sk1),implies(implies(sk1,sk2),implies(sk0,sk2)))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
is_a_theorem(implies(implies(sk0,sk1),implies(implies(sk1,sk2),implies(sk0,sk2)))) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t231]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL982+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 00:44:56 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.42/0.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.42/0.87 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------