%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL175-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 02:01:12 PM UTC 2026
% Result : Unsatisfiable 2.93s 0.87s
% Output : Proof 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 42 unt; 0 def)
% Number of atoms : 50 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 14 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 36 ( 7 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
sF0 = not(p),
introduced(definition) ).
cnf(t12,plain,
not(p) = sF0,
inference(orient,[status(thm)],[t8]) ).
cnf(t9,axiom,
sF1 = or(p,p),
introduced(definition) ).
cnf(t13,plain,
or(p,p) = sF1,
inference(orient,[status(thm)],[t9]) ).
cnf(t10,axiom,
sF2 = or(not(p),or(p,p)),
introduced(definition) ).
cnf(t34,plain,
sF2 = or(sF0,or(p,p)),
inference(step,[status(thm)],[t10,t12]) ).
cnf(t35,plain,
sF2 = or(sF0,sF1),
inference(step,[status(thm)],[t34,t13]) ).
cnf(t15,plain,
or(sF0,sF1) = sF2,
inference(orient,[status(thm)],[t35]) ).
cnf(f6,axiom,
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox2/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(t3,plain,
ifeq(axiom(X1),true,theorem(X1),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t26,plain,
ifeq(axiom(X1),true,theorem(X1),true) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f1,axiom,
axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox2/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(u1,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/sandbox2/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(d0,axiom,
implies(X0,X1) = or(not(X0),X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t1,plain,
axiom(or(not(X1),or(X2,X1))) = true,
inference(definition_unfolding,[status(thm)],[u1,d0]) ).
cnf(t16,plain,
axiom(or(not(X1),or(X2,X1))) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t18,plain,
true = axiom(or(not(p),sF1)),
inference(cp,[status(thm)],[t16,t13]) ).
cnf(t36,plain,
true = axiom(or(sF0,sF1)),
inference(step,[status(thm)],[t18,t12]) ).
cnf(t37,plain,
true = axiom(sF2),
inference(step,[status(thm)],[t36,t15]) ).
cnf(t20,plain,
axiom(sF2) = true,
inference(orient,[status(thm)],[t37]) ).
cnf(t28,plain,
true = ifeq(true,true,theorem(sF2),true),
inference(cp,[status(thm)],[t26,t20]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t38,plain,
true = theorem(sF2),
inference(step,[status(thm)],[t28,t14]) ).
cnf(t33,plain,
theorem(sF2) = true,
inference(orient,[status(thm)],[t38]) ).
cnf(f8,negated_conjecture,
~ theorem(implies(p,or(p,p))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f8_nnf,plain,
~ theorem(implies(p,or(p,p))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ theorem(implies(p,or(p,p))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ theorem(implies(p,or(p,p))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(u6,negated_conjecture,
theorem(implies(p,or(p,p))) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(goal_0,negated_conjecture,
theorem(or(not(p),or(p,p))) != true,
inference(definition_unfolding,[status(thm)],[u6,d0]) ).
cnf(g0_0,plain,
theorem(or(sF0,or(p,p))) != true,
inference(rw,[status(thm)],[goal_0,t12]) ).
cnf(g0_1,plain,
theorem(or(sF0,sF1)) != true,
inference(rw,[status(thm)],[g0_0,t13]) ).
cnf(g0_2,plain,
theorem(sF2) != true,
inference(rw,[status(thm)],[g0_1,t15]) ).
cnf(g0_3,plain,
true != true,
inference(rw,[status(thm)],[g0_2,t33]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL175-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 22:10:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.93/0.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.93/0.87 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------