%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL236-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 02:01:30 PM UTC 2026
% Result : Unsatisfiable 3.63s 0.87s
% Output : Proof 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 43 unt; 0 def)
% Number of atoms : 63 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 19 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 84 ( 5 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
fof(f6_nnf,plain,
! [X] :
( ~ axiom(X)
| theorem(X) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] :
( ~ axiom(X)
| theorem(X) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ axiom(X0)
| theorem(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(axiom(X0),true,theorem(X0),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f1,axiom,
axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f1_nnf,plain,
! [A,B] : axiom(implies(A,or(B,A))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : axiom(implies(A,or(B,A))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
axiom(implies(X0,or(X1,X0))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi2,axiom,
axiom(implies(X0,or(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f5,axiom,
implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
fof(f5_nnf,plain,
! [X,Y] : implies(X,Y) = or(not(X),Y),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] : implies(X,Y) = or(not(X),Y),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
implies(X0,X1) = or(not(X0),X1),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi1,axiom,
implies(X0,X1) = or(not(X0),X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h1,plain,
theorem(or(not(V0),or(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi2,hi1]) ).
cnf(f3,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f3_nnf,plain,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi4,axiom,
axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h3,plain,
theorem(or(not(or(V0,or(V1,V2))),or(V1,or(V0,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi4,hi1]) ).
cnf(f7,axiom,
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
fof(f7_nnf,plain,
! [X,Y] :
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ theorem(X1)
| ~ theorem(implies(X1,X0))
| theorem(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(theorem(implies(X0,X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h16,plain,
theorem(or(V0,or(not(V1),V1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h3,h1,hi1]) ).
cnf(h52,plain,
theorem(or(not(V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h16,h16,hi1]) ).
cnf(f2,axiom,
axiom(implies(or(A,B),or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f2_nnf,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
axiom(implies(or(X0,X1),or(X1,X0))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi3,axiom,
axiom(implies(or(X0,X1),or(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h2,plain,
theorem(or(not(or(V0,V1)),or(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3,hi1]) ).
cnf(t1,plain,
theorem(or(X1,not(X1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h2,h52,hi1]) ).
cnf(t160,plain,
theorem(or(X1,not(X1))) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(f9,negated_conjecture,
~ theorem(implies(or(not(p),not(q)),not(and(p,q)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f9_nnf,plain,
~ theorem(implies(or(not(p),not(q)),not(and(p,q)))),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ theorem(implies(or(not(p),not(q)),not(and(p,q)))),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ theorem(implies(or(not(p),not(q)),not(and(p,q)))),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(u6,negated_conjecture,
theorem(implies(or(not(p),not(q)),not(and(p,q)))) != true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(d0,axiom,
implies(X0,X1) = or(not(X0),X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f8,axiom,
and(P,Q) = not(or(not(P),not(Q))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_defn) ).
fof(f8_nnf,plain,
! [P,Q] : and(P,Q) = not(or(not(P),not(Q))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [P,Q] : and(P,Q) = not(or(not(P),not(Q))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
and(X0,X1) = not(or(not(X0),not(X1))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(d1,axiom,
and(X0,X1) = not(or(not(X0),not(X1))),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(goal_0,negated_conjecture,
theorem(or(not(or(not(p),not(q))),not(not(or(not(p),not(q)))))) != true,
inference(definition_unfolding,[status(thm)],[u6,d0,d1]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t160]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL236-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.33 % Computer : n005.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8046.5625MB
% 0.09/0.33 % OS : Linux 6.8.0-71-generic
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Wed Sep 23 22:30:02 UTC 2026
% 0.09/0.33 % CPUTime :
% 0.09/0.33 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.63/0.87 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.63/0.87 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------