%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL156-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 02:01:05 PM UTC 2026
% Result : Unsatisfiable 6.19s 1.31s
% Output : CNFRefutation 6.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 12
% Syntax : Number of clauses : 90 ( 90 unt; 0 nHn; 57 RR)
% Number of literals : 90 ( 89 equ; 9 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 43 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t64,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(orient,[status(thm)],[t3]) ).
cnf(t4,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t122,plain,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t4]) ).
cnf(t12,axiom,
sF0 = not(x),
introduced(definition) ).
cnf(t18,plain,
not(x) = sF0,
inference(orient,[status(thm)],[t12]) ).
cnf(t126,plain,
truth = implies(implies(not(X1),sF0),implies(x,X1)),
inference(cp,[status(thm)],[t122,t18]) ).
cnf(u1,axiom,
or(X,Y) = or(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(d0,axiom,
or(X,Y) = implies(not(X),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t2,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(definition_unfolding,[status(thm)],[u1,d0]) ).
cnf(t33,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(orient,[status(thm)],[t2]) ).
cnf(t13,axiom,
sF1 = not(not(x)),
introduced(definition) ).
cnf(t763,plain,
sF1 = not(sF0),
inference(step,[status(thm)],[t13,t18]) ).
cnf(t23,plain,
not(sF0) = sF1,
inference(orient,[status(thm)],[t763]) ).
cnf(t36,plain,
implies(not(X1),sF0) = implies(sF1,X1),
inference(cp,[status(thm)],[t33,t23]) ).
cnf(t55,plain,
implies(not(X1),sF0) = implies(sF1,X1),
inference(orient,[status(thm)],[t36]) ).
cnf(t799,plain,
truth = implies(implies(sF1,X1),implies(x,X1)),
inference(step,[status(thm)],[t126,t55]) ).
cnf(t517,plain,
implies(implies(sF1,X1),implies(x,X1)) = truth,
inference(orient,[status(thm)],[t799]) ).
cnf(t0,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t17,plain,
not(truth) = falsehood,
inference(orient,[status(thm)],[t0]) ).
cnf(t14,axiom,
sF2 = not(truth),
introduced(definition) ).
cnf(t760,plain,
sF2 = falsehood,
inference(step,[status(thm)],[t14,t17]) ).
cnf(t19,plain,
falsehood = sF2,
inference(orient,[status(thm)],[t760]) ).
cnf(t761,plain,
not(truth) = sF2,
inference(step,[status(thm)],[t17,t19]) ).
cnf(t20,plain,
not(truth) = sF2,
inference(orient,[status(thm)],[t761]) ).
cnf(t124,plain,
truth = implies(implies(not(X1),sF2),implies(truth,X1)),
inference(cp,[status(thm)],[t122,t20]) ).
cnf(t1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t22,plain,
implies(truth,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t779,plain,
truth = implies(implies(not(X1),sF2),X1),
inference(step,[status(thm)],[t124,t22]) ).
cnf(t174,plain,
implies(implies(not(X1),sF2),X1) = truth,
inference(orient,[status(thm)],[t779]) ).
cnf(t182,plain,
truth = implies(implies(not(sF2),X1),X1),
inference(cp,[status(thm)],[t174,t33]) ).
cnf(t198,plain,
implies(implies(not(sF2),X1),X1) = truth,
inference(orient,[status(thm)],[t182]) ).
cnf(t199,plain,
truth = implies(implies(X1,not(sF2)),not(sF2)),
inference(cp,[status(thm)],[t198,t64]) ).
cnf(t557,plain,
implies(implies(X1,not(sF2)),not(sF2)) = truth,
inference(orient,[status(thm)],[t199]) ).
cnf(t564,plain,
truth = implies(implies(implies(not(sF2),X1),X1),not(sF2)),
inference(cp,[status(thm)],[t557,t64]) ).
cnf(t802,plain,
truth = implies(truth,not(sF2)),
inference(step,[status(thm)],[t564,t198]) ).
cnf(t803,plain,
truth = not(sF2),
inference(step,[status(thm)],[t802,t22]) ).
cnf(t570,plain,
not(sF2) = truth,
inference(orient,[status(thm)],[t803]) ).
cnf(t575,plain,
implies(not(X1),sF2) = implies(truth,X1),
inference(cp,[status(thm)],[t33,t570]) ).
cnf(t833,plain,
implies(not(X1),sF2) = X1,
inference(step,[status(thm)],[t575,t22]) ).
cnf(t682,plain,
implies(not(X1),sF2) = X1,
inference(orient,[status(thm)],[t833]) ).
cnf(t835,plain,
implies(X1,X1) = truth,
inference(step,[status(thm)],[t174,t682]) ).
cnf(t684,plain,
implies(X1,X1) = truth,
inference(rw,[status(thm)],[t835]) ).
cnf(t692,plain,
implies(X1,X1) = truth,
inference(orient,[status(thm)],[t684]) ).
cnf(t712,plain,
truth = implies(truth,implies(x,sF1)),
inference(cp,[status(thm)],[t517,t692]) ).
cnf(t839,plain,
truth = implies(x,sF1),
inference(step,[status(thm)],[t712,t22]) ).
cnf(t734,plain,
implies(x,sF1) = truth,
inference(orient,[status(thm)],[t839]) ).
cnf(t736,plain,
implies(implies(sF1,x),x) = implies(truth,sF1),
inference(cp,[status(thm)],[t64,t734]) ).
cnf(t35,plain,
implies(not(X1),x) = implies(sF0,X1),
inference(cp,[status(thm)],[t33,t18]) ).
cnf(t50,plain,
implies(not(X1),x) = implies(sF0,X1),
inference(orient,[status(thm)],[t35]) ).
cnf(t51,plain,
implies(sF0,sF0) = implies(sF1,x),
inference(cp,[status(thm)],[t50,t23]) ).
cnf(t54,plain,
implies(sF1,x) = implies(sF0,sF0),
inference(orient,[status(thm)],[t51]) ).
cnf(t177,plain,
truth = implies(implies(sF1,sF2),sF0),
inference(cp,[status(thm)],[t174,t23]) ).
cnf(t15,axiom,
sF3 = implies(not(not(x)),not(truth)),
introduced(definition) ).
cnf(t764,plain,
sF3 = implies(not(sF0),not(truth)),
inference(step,[status(thm)],[t15,t18]) ).
cnf(t765,plain,
sF3 = implies(sF1,not(truth)),
inference(step,[status(thm)],[t764,t23]) ).
cnf(t766,plain,
sF3 = implies(sF1,sF2),
inference(step,[status(thm)],[t765,t20]) ).
cnf(t24,plain,
implies(sF1,sF2) = sF3,
inference(orient,[status(thm)],[t766]) ).
cnf(t780,plain,
truth = implies(sF3,sF0),
inference(step,[status(thm)],[t177,t24]) ).
cnf(t186,plain,
implies(sF3,sF0) = truth,
inference(orient,[status(thm)],[t780]) ).
cnf(t578,plain,
implies(sF1,sF2) = implies(truth,sF0),
inference(cp,[status(thm)],[t55,t570]) ).
cnf(t806,plain,
sF3 = implies(truth,sF0),
inference(step,[status(thm)],[t578,t24]) ).
cnf(t807,plain,
sF3 = sF0,
inference(step,[status(thm)],[t806,t22]) ).
cnf(t589,plain,
sF3 = sF0,
inference(orient,[status(thm)],[t807]) ).
cnf(t810,plain,
implies(sF0,sF0) = truth,
inference(step,[status(thm)],[t186,t589]) ).
cnf(t594,plain,
implies(sF0,sF0) = truth,
inference(rw,[status(thm)],[t810]) ).
cnf(t643,plain,
implies(sF0,sF0) = truth,
inference(orient,[status(thm)],[t594]) ).
cnf(t831,plain,
implies(sF1,x) = truth,
inference(step,[status(thm)],[t54,t643]) ).
cnf(t644,plain,
implies(sF1,x) = truth,
inference(orient,[status(thm)],[t831]) ).
cnf(t840,plain,
implies(truth,x) = implies(truth,sF1),
inference(step,[status(thm)],[t736,t644]) ).
cnf(t841,plain,
x = implies(truth,sF1),
inference(step,[status(thm)],[t840,t22]) ).
cnf(t842,plain,
x = sF1,
inference(step,[status(thm)],[t841,t22]) ).
cnf(t739,plain,
x = sF1,
inference(orient,[status(thm)],[t842]) ).
cnf(t843,plain,
not(sF1) = sF0,
inference(step,[status(thm)],[t18,t739]) ).
cnf(t740,plain,
not(sF1) = sF0,
inference(rw,[status(thm)],[t843]) ).
cnf(t750,plain,
not(sF1) = sF0,
inference(orient,[status(thm)],[t740]) ).
cnf(t808,plain,
implies(sF1,sF2) = sF0,
inference(step,[status(thm)],[t24,t589]) ).
cnf(t590,plain,
implies(sF1,sF2) = sF0,
inference(orient,[status(thm)],[t808]) ).
cnf(u10,negated_conjecture,
and_star(x,truth) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(u4,axiom,
and_star(X,Y) = not(or(not(X),not(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(d3,axiom,
and_star(X,Y) = not(implies(not(not(X)),not(Y))),
inference(definition_unfolding,[status(thm)],[u4,d0]) ).
cnf(goal_0,negated_conjecture,
not(implies(not(not(x)),not(truth))) != x,
inference(definition_unfolding,[status(thm)],[u10,d3]) ).
cnf(g0_0,plain,
not(implies(not(not(sF1)),not(truth))) != x,
inference(rw,[status(thm)],[goal_0,t739]) ).
cnf(g0_1,plain,
not(implies(not(sF0),not(truth))) != x,
inference(rw,[status(thm)],[g0_0,t750]) ).
cnf(g0_2,plain,
not(implies(sF1,not(truth))) != x,
inference(rw,[status(thm)],[g0_1,t23]) ).
cnf(g0_3,plain,
not(implies(sF1,sF2)) != x,
inference(rw,[status(thm)],[g0_2,t20]) ).
cnf(g0_4,plain,
not(sF0) != x,
inference(rw,[status(thm)],[g0_3,t590]) ).
cnf(g0_5,plain,
sF1 != x,
inference(rw,[status(thm)],[g0_4,t23]) ).
cnf(g0_6,plain,
sF1 != sF1,
inference(rw,[status(thm)],[g0_5,t739]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL156-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 22:08:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.19/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.19/1.31 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------