%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL274-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 02:01:38 PM UTC 2026
% Result : Unsatisfiable 6.09s 1.21s
% Output : Proof 6.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t6,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(equality_encoding,[status(esa)],[c8]) ).
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(t3,plain,
or(not(X1),X2) = implies(X1,X2),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t13,plain,
or(not(X1),X2) = implies(X1,X2),
inference(orient,[status(thm)],[t3]) ).
cnf(t48,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(step,[status(thm)],[t6,t13]) ).
cnf(t40,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(orient,[status(thm)],[t48]) ).
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(t7,plain,
and(implies(X1,X2),implies(X2,X1)) = equivalent(X1,X2),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t44,plain,
and(implies(X1,X2),implies(X2,X1)) = equivalent(X1,X2),
inference(orient,[status(thm)],[t7]) ).
cnf(f10,negated_conjecture,
~ theorem(equivalent(or(p,q),or(q,p))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f10_nnf,plain,
~ theorem(equivalent(or(p,q),or(q,p))),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ theorem(equivalent(or(p,q),or(q,p))),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ theorem(equivalent(or(p,q),or(q,p))),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(goal_0,negated_conjecture,
theorem(equivalent(or(p,q),or(q,p))) != true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(g0_0,plain,
theorem(equivalent(or(p,q),or(q,p))) != theorem(not(implies(implies(or(p,q),or(q,p)),not(implies(or(q,p),or(p,q)))))),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
theorem(equivalent(or(p,q),or(q,p))) != theorem(and(implies(or(p,q),or(q,p)),implies(or(q,p),or(p,q)))),
inference(rw,[status(thm)],[g0_0,t40]) ).
cnf(g0_2,plain,
theorem(equivalent(or(p,q),or(q,p))) != theorem(equivalent(or(p,q),or(q,p))),
inference(rw,[status(thm)],[g0_1,t44]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL274-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 22:42:08 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.09/1.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.09/1.21 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------