%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL294-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 02:01:40 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.92s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 66 unt; 0 def)
% Number of atoms : 86 ( 45 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 : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 116 ( 5 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t4,plain,
or(not(X1),X2) = implies(X1,X2),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t102,plain,
or(not(X1),X2) = implies(X1,X2),
inference(orient,[status(thm)],[t4]) ).
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(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(f0,axiom,
axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f0_nnf,plain,
! [A] : axiom(implies(or(A,A),A)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A] : axiom(implies(or(A,A),A)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
axiom(implies(or(X0,X0),X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
axiom(implies(or(X0,X0),X0)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
theorem(or(not(or(V0,V0)),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi0,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(h10,plain,
theorem(or(V0,not(or(V0,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h2,h0,hi1]) ).
cnf(t41,plain,
theorem(not(or(not(or(not(X1),X1)),not(or(not(X1),X1))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h10,h52,hi1]) ).
cnf(t1191,plain,
theorem(not(implies(or(not(X1),X1),not(or(not(X1),X1))))) = true,
inference(step,[status(thm)],[t41,t102]) ).
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(t13,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t1057,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(step,[status(thm)],[t13,t102]) ).
cnf(t104,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(orient,[status(thm)],[t1057]) ).
cnf(t1192,plain,
theorem(and(or(not(X1),X1),or(not(X1),X1))) = true,
inference(step,[status(thm)],[t1191,t104]) ).
cnf(t1193,plain,
theorem(and(implies(X1,X1),or(not(X1),X1))) = true,
inference(step,[status(thm)],[t1192,t102]) ).
cnf(t1194,plain,
theorem(and(implies(X1,X1),implies(X1,X1))) = true,
inference(step,[status(thm)],[t1193,t102]) ).
cnf(t465,plain,
theorem(and(implies(X1,X1),implies(X1,X1))) = true,
inference(orient,[status(thm)],[t1194]) ).
cnf(f9,axiom,
equivalent(P,Q) = and(implies(P,Q),implies(Q,P)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalent_defn) ).
fof(f9_nnf,plain,
! [P,Q] : equivalent(P,Q) = and(implies(P,Q),implies(Q,P)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [P,Q] : equivalent(P,Q) = and(implies(P,Q),implies(Q,P)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t14,plain,
and(implies(X1,X2),implies(X2,X1)) = equivalent(X1,X2),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t804,plain,
and(implies(X1,X2),implies(X2,X1)) = equivalent(X1,X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t1227,plain,
theorem(equivalent(X1,X1)) = true,
inference(step,[status(thm)],[t465,t804]) ).
cnf(t810,plain,
theorem(equivalent(X1,X1)) = true,
inference(rw,[status(thm)],[t1227]) ).
cnf(t1051,plain,
theorem(equivalent(X1,X1)) = true,
inference(orient,[status(thm)],[t810]) ).
cnf(f10,negated_conjecture,
~ theorem(equivalent(implies(p,q),or(not(p),q))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f10_nnf,plain,
~ theorem(equivalent(implies(p,q),or(not(p),q))),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ theorem(equivalent(implies(p,q),or(not(p),q))),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ theorem(equivalent(implies(p,q),or(not(p),q))),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(goal_0,negated_conjecture,
theorem(equivalent(implies(p,q),or(not(p),q))) != true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(g0_0,plain,
theorem(equivalent(implies(p,q),implies(p,q))) != true,
inference(rw,[status(thm)],[goal_0,t102]) ).
cnf(g0_1,plain,
true != true,
inference(rw,[status(thm)],[g0_0,t1051]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL294-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.36 % Computer : n015.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Wed Sep 23 22:48:15 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/5.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.92 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------