%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 02:01:06 PM UTC 2026
% Result : Unsatisfiable 11.50s 2.24s
% Output : CNFRefutation 11.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 14
% Syntax : Number of clauses : 202 ( 202 unt; 0 nHn; 12 RR)
% Number of literals : 202 ( 201 equ; 5 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 320 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t5,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t75,plain,
xor(X1,X2) = xor(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t11,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t17,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t14,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
inference(orient,[status(thm)],[t14]) ).
cnf(t1,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t16,plain,
implies(truth,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t20,plain,
truth = implies(X1,implies(implies(X1,X2),implies(truth,X2))),
inference(cp,[status(thm)],[t19,t16]) ).
cnf(t3943,plain,
truth = implies(X1,implies(implies(X1,X2),X2)),
inference(step,[status(thm)],[t20,t16]) ).
cnf(t102,plain,
implies(X1,implies(implies(X1,X2),X2)) = truth,
inference(orient,[status(thm)],[t3943]) ).
cnf(t18,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(cp,[status(thm)],[t17,t16]) ).
cnf(t106,plain,
truth = implies(implies(truth,X1),X1),
inference(cp,[status(thm)],[t102,t16]) ).
cnf(t3944,plain,
truth = implies(X1,X1),
inference(step,[status(thm)],[t106,t16]) ).
cnf(t118,plain,
implies(X1,X1) = truth,
inference(orient,[status(thm)],[t3944]) ).
cnf(t3959,plain,
implies(implies(X1,truth),truth) = truth,
inference(step,[status(thm)],[t18,t118]) ).
cnf(t349,plain,
implies(implies(X1,truth),truth) = truth,
inference(orient,[status(thm)],[t3959]) ).
cnf(t356,plain,
truth = implies(X1,truth),
inference(cp,[status(thm)],[t102,t349]) ).
cnf(t357,plain,
implies(X1,truth) = truth,
inference(orient,[status(thm)],[t356]) ).
cnf(t361,plain,
truth = implies(truth,implies(implies(truth,X1),implies(X2,X1))),
inference(cp,[status(thm)],[t19,t357]) ).
cnf(t3978,plain,
truth = implies(implies(truth,X1),implies(X2,X1)),
inference(step,[status(thm)],[t361,t16]) ).
cnf(t3979,plain,
truth = implies(X1,implies(X2,X1)),
inference(step,[status(thm)],[t3978,t16]) ).
cnf(t388,plain,
implies(X1,implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t3979]) ).
cnf(t6,axiom,
implies(not(X1),X2) = or(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t40,plain,
implies(not(X1),X2) = or(X1,X2),
inference(orient,[status(thm)],[t6]) ).
cnf(t392,plain,
truth = implies(X1,or(X2,X1)),
inference(cp,[status(thm)],[t388,t40]) ).
cnf(t396,plain,
implies(X1,or(X2,X1)) = truth,
inference(orient,[status(thm)],[t392]) ).
cnf(t404,plain,
implies(implies(or(X1,X2),X2),X2) = implies(truth,or(X1,X2)),
inference(cp,[status(thm)],[t17,t396]) ).
cnf(t3991,plain,
implies(implies(or(X1,X2),X2),X2) = or(X1,X2),
inference(step,[status(thm)],[t404,t16]) ).
cnf(t665,plain,
implies(implies(or(X1,X2),X2),X2) = or(X1,X2),
inference(orient,[status(thm)],[t3991]) ).
cnf(t4,axiom,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t57,plain,
or(X1,X2) = or(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t401,plain,
truth = implies(X1,or(X1,X2)),
inference(cp,[status(thm)],[t396,t57]) ).
cnf(t405,plain,
implies(X1,or(X1,X2)) = truth,
inference(orient,[status(thm)],[t401]) ).
cnf(t412,plain,
implies(implies(or(X1,X2),X1),X1) = implies(truth,or(X1,X2)),
inference(cp,[status(thm)],[t17,t405]) ).
cnf(t3992,plain,
implies(implies(or(X1,X2),X1),X1) = or(X1,X2),
inference(step,[status(thm)],[t412,t16]) ).
cnf(t676,plain,
implies(implies(or(X1,X2),X1),X1) = or(X1,X2),
inference(orient,[status(thm)],[t3992]) ).
cnf(t12,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t31,plain,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t12]) ).
cnf(t3930,plain,
implies(or(X1,not(X2)),implies(X2,X1)) = truth,
inference(step,[status(thm)],[t31,t40]) ).
cnf(t45,plain,
implies(or(X1,not(X2)),implies(X2,X1)) = truth,
inference(rw,[status(thm)],[t3930]) ).
cnf(t723,plain,
implies(or(X1,not(X2)),implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t45]) ).
cnf(t0,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t53,plain,
not(truth) = falsehood,
inference(orient,[status(thm)],[t0]) ).
cnf(t730,plain,
truth = implies(or(X1,falsehood),implies(truth,X1)),
inference(cp,[status(thm)],[t723,t53]) ).
cnf(t3995,plain,
truth = implies(or(X1,falsehood),X1),
inference(step,[status(thm)],[t730,t16]) ).
cnf(t742,plain,
implies(or(X1,falsehood),X1) = truth,
inference(orient,[status(thm)],[t3995]) ).
cnf(t749,plain,
or(X1,falsehood) = implies(truth,X1),
inference(cp,[status(thm)],[t676,t742]) ).
cnf(t3996,plain,
or(X1,falsehood) = X1,
inference(step,[status(thm)],[t749,t16]) ).
cnf(t751,plain,
or(X1,falsehood) = X1,
inference(orient,[status(thm)],[t3996]) ).
cnf(t758,plain,
or(X1,falsehood) = implies(implies(X1,falsehood),falsehood),
inference(cp,[status(thm)],[t665,t751]) ).
cnf(t4049,plain,
X1 = implies(implies(X1,falsehood),falsehood),
inference(step,[status(thm)],[t758,t751]) ).
cnf(t922,plain,
implies(implies(X1,falsehood),falsehood) = X1,
inference(orient,[status(thm)],[t4049]) ).
cnf(t923,plain,
not(X1) = implies(or(X1,falsehood),falsehood),
inference(cp,[status(thm)],[t922,t40]) ).
cnf(t4050,plain,
not(X1) = implies(X1,falsehood),
inference(step,[status(thm)],[t923,t751]) ).
cnf(t929,plain,
implies(X1,falsehood) = not(X1),
inference(orient,[status(thm)],[t4050]) ).
cnf(t395,plain,
implies(implies(implies(X1,X2),X2),X2) = implies(truth,implies(X1,X2)),
inference(cp,[status(thm)],[t17,t388]) ).
cnf(t3990,plain,
implies(implies(implies(X1,X2),X2),X2) = implies(X1,X2),
inference(step,[status(thm)],[t395,t16]) ).
cnf(t657,plain,
implies(implies(implies(X1,X2),X2),X2) = implies(X1,X2),
inference(orient,[status(thm)],[t3990]) ).
cnf(t933,plain,
not(implies(implies(X1,falsehood),falsehood)) = implies(X1,falsehood),
inference(cp,[status(thm)],[t929,t657]) ).
cnf(t954,plain,
xor(truth,X1) = not(X1),
inference(orient,[status(thm)],[t933]) ).
cnf(t955,plain,
not(X1) = xor(X1,truth),
inference(cp,[status(thm)],[t954,t75]) ).
cnf(t956,plain,
xor(X1,truth) = not(X1),
inference(orient,[status(thm)],[t955]) ).
cnf(t15,axiom,
or(and(X1,not(X2)),and(not(X1),X2)) = xor(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,axiom,
not(or(not(X1),not(X2))) = and_star(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t7,axiom,
not(or(not(X1),not(X2))) = and(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t46,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(orient,[status(thm)],[t7]) ).
cnf(t3931,plain,
and(X1,X2) = and_star(X1,X2),
inference(step,[status(thm)],[t8,t46]) ).
cnf(t50,plain,
and(X1,X2) = and_star(X1,X2),
inference(orient,[status(thm)],[t3931]) ).
cnf(t3934,plain,
or(and_star(X1,not(X2)),and(not(X1),X2)) = xor(X1,X2),
inference(step,[status(thm)],[t15,t50]) ).
cnf(t3935,plain,
or(and_star(X1,not(X2)),and_star(not(X1),X2)) = xor(X1,X2),
inference(step,[status(thm)],[t3934,t50]) ).
cnf(t62,plain,
or(and_star(X1,not(X2)),and_star(not(X1),X2)) = xor(X1,X2),
inference(orient,[status(thm)],[t3935]) ).
cnf(t3932,plain,
not(or(not(X1),not(X2))) = and_star(X1,X2),
inference(step,[status(thm)],[t46,t50]) ).
cnf(t51,plain,
not(or(not(X1),not(X2))) = and_star(X1,X2),
inference(orient,[status(thm)],[t3932]) ).
cnf(t55,plain,
and_star(truth,X1) = not(or(falsehood,not(X1))),
inference(cp,[status(thm)],[t51,t53]) ).
cnf(t81,plain,
not(or(falsehood,not(X1))) = and_star(truth,X1),
inference(orient,[status(thm)],[t55]) ).
cnf(t84,plain,
or(or(falsehood,not(X1)),X2) = implies(and_star(truth,X1),X2),
inference(cp,[status(thm)],[t40,t81]) ).
cnf(t13,axiom,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t59,plain,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t3984,plain,
or(falsehood,or(not(X1),X2)) = implies(and_star(truth,X1),X2),
inference(step,[status(thm)],[t84,t59]) ).
cnf(t497,plain,
or(falsehood,or(not(X1),X2)) = implies(and_star(truth,X1),X2),
inference(orient,[status(thm)],[t3984]) ).
cnf(t507,plain,
implies(and_star(truth,X1),X2) = or(falsehood,or(X2,not(X1))),
inference(cp,[status(thm)],[t497,t57]) ).
cnf(t619,plain,
or(falsehood,or(X1,not(X2))) = implies(and_star(truth,X2),X1),
inference(orient,[status(thm)],[t507]) ).
cnf(t753,plain,
X1 = or(falsehood,X1),
inference(cp,[status(thm)],[t751,t57]) ).
cnf(t776,plain,
or(falsehood,X1) = X1,
inference(orient,[status(thm)],[t753]) ).
cnf(t4009,plain,
or(X1,not(X2)) = implies(and_star(truth,X2),X1),
inference(step,[status(thm)],[t619,t776]) ).
cnf(t785,plain,
or(X1,not(X2)) = implies(and_star(truth,X2),X1),
inference(rw,[status(thm)],[t4009]) ).
cnf(t105,plain,
truth = or(X1,implies(implies(not(X1),X2),X2)),
inference(cp,[status(thm)],[t102,t40]) ).
cnf(t3958,plain,
truth = or(X1,implies(or(X1,X2),X2)),
inference(step,[status(thm)],[t105,t40]) ).
cnf(t327,plain,
or(X1,implies(or(X1,X2),X2)) = truth,
inference(orient,[status(thm)],[t3958]) ).
cnf(t343,plain,
truth = or(X1,implies(or(X2,X1),X2)),
inference(cp,[status(thm)],[t327,t57]) ).
cnf(t427,plain,
or(X1,implies(or(X2,X1),X2)) = truth,
inference(orient,[status(thm)],[t343]) ).
cnf(t121,plain,
truth = or(X1,not(X1)),
inference(cp,[status(thm)],[t118,t40]) ).
cnf(t125,plain,
or(X1,not(X1)) = truth,
inference(orient,[status(thm)],[t121]) ).
cnf(t130,plain,
or(X1,or(not(X1),X2)) = or(truth,X2),
inference(cp,[status(thm)],[t59,t125]) ).
cnf(t157,plain,
or(X1,or(not(X1),X2)) = or(truth,X2),
inference(orient,[status(thm)],[t130]) ).
cnf(t360,plain,
truth = or(X1,truth),
inference(cp,[status(thm)],[t357,t40]) ).
cnf(t376,plain,
or(X1,truth) = truth,
inference(orient,[status(thm)],[t360]) ).
cnf(t379,plain,
truth = or(truth,X1),
inference(cp,[status(thm)],[t376,t57]) ).
cnf(t381,plain,
or(truth,X1) = truth,
inference(orient,[status(thm)],[t379]) ).
cnf(t3974,plain,
or(X1,or(not(X1),X2)) = truth,
inference(step,[status(thm)],[t157,t381]) ).
cnf(t384,plain,
or(X1,or(not(X1),X2)) = truth,
inference(orient,[status(thm)],[t3974]) ).
cnf(t433,plain,
truth = or(or(not(X1),X2),implies(truth,X1)),
inference(cp,[status(thm)],[t427,t384]) ).
cnf(t3980,plain,
truth = or(not(X1),or(X2,implies(truth,X1))),
inference(step,[status(thm)],[t433,t59]) ).
cnf(t3981,plain,
truth = or(not(X1),or(X2,X1)),
inference(step,[status(thm)],[t3980,t16]) ).
cnf(t442,plain,
or(not(X1),or(X2,X1)) = truth,
inference(orient,[status(thm)],[t3981]) ).
cnf(t132,plain,
and_star(X1,not(X1)) = not(truth),
inference(cp,[status(thm)],[t51,t125]) ).
cnf(t3946,plain,
and_star(X1,not(X1)) = falsehood,
inference(step,[status(thm)],[t132,t53]) ).
cnf(t135,plain,
and_star(X1,not(X1)) = falsehood,
inference(orient,[status(thm)],[t3946]) ).
cnf(t141,plain,
xor(X1,X1) = or(falsehood,and_star(not(X1),X1)),
inference(cp,[status(thm)],[t62,t135]) ).
cnf(t2,axiom,
and(X1,X2) = and(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t3936,plain,
and_star(X1,X2) = and(X2,X1),
inference(step,[status(thm)],[t2,t50]) ).
cnf(t3937,plain,
and_star(X1,X2) = and_star(X2,X1),
inference(step,[status(thm)],[t3936,t50]) ).
cnf(t68,plain,
and_star(X1,X2) = and_star(X2,X1),
inference(orient,[status(thm)],[t3937]) ).
cnf(t3947,plain,
xor(X1,X1) = or(falsehood,and_star(X1,not(X1))),
inference(step,[status(thm)],[t141,t68]) ).
cnf(t3948,plain,
xor(X1,X1) = or(falsehood,falsehood),
inference(step,[status(thm)],[t3947,t135]) ).
cnf(t187,plain,
xor(X1,X1) = or(falsehood,falsehood),
inference(orient,[status(thm)],[t3948]) ).
cnf(t450,plain,
truth = or(not(falsehood),xor(X1,X1)),
inference(cp,[status(thm)],[t442,t187]) ).
cnf(t460,plain,
or(not(falsehood),xor(X1,X1)) = truth,
inference(orient,[status(thm)],[t450]) ).
cnf(t192,plain,
or(falsehood,or(falsehood,X1)) = or(xor(X2,X2),X1),
inference(cp,[status(thm)],[t59,t187]) ).
cnf(t235,plain,
or(xor(X1,X1),X2) = or(falsehood,or(falsehood,X2)),
inference(orient,[status(thm)],[t192]) ).
cnf(t752,plain,
xor(X1,X1) = or(falsehood,or(falsehood,falsehood)),
inference(cp,[status(thm)],[t751,t235]) ).
cnf(t3998,plain,
xor(X1,X1) = or(falsehood,falsehood),
inference(step,[status(thm)],[t752,t751]) ).
cnf(t3999,plain,
xor(X1,X1) = falsehood,
inference(step,[status(thm)],[t3998,t751]) ).
cnf(t762,plain,
xor(X1,X1) = falsehood,
inference(orient,[status(thm)],[t3999]) ).
cnf(t4000,plain,
or(not(falsehood),falsehood) = truth,
inference(step,[status(thm)],[t460,t762]) ).
cnf(t4001,plain,
not(falsehood) = truth,
inference(step,[status(thm)],[t4000,t751]) ).
cnf(t763,plain,
not(falsehood) = truth,
inference(rw,[status(thm)],[t4001]) ).
cnf(t767,plain,
not(falsehood) = truth,
inference(orient,[status(thm)],[t763]) ).
cnf(t774,plain,
and_star(falsehood,X1) = not(or(truth,not(X1))),
inference(cp,[status(thm)],[t51,t767]) ).
cnf(t4014,plain,
and_star(falsehood,X1) = not(truth),
inference(step,[status(thm)],[t774,t381]) ).
cnf(t4015,plain,
and_star(falsehood,X1) = falsehood,
inference(step,[status(thm)],[t4014,t53]) ).
cnf(t857,plain,
and_star(falsehood,X1) = falsehood,
inference(orient,[status(thm)],[t4015]) ).
cnf(t868,plain,
xor(falsehood,X1) = or(falsehood,and_star(not(falsehood),X1)),
inference(cp,[status(thm)],[t62,t857]) ).
cnf(t4030,plain,
xor(falsehood,X1) = and_star(not(falsehood),X1),
inference(step,[status(thm)],[t868,t776]) ).
cnf(t4031,plain,
xor(falsehood,X1) = and_star(truth,X1),
inference(step,[status(thm)],[t4030,t767]) ).
cnf(t894,plain,
and_star(truth,X1) = xor(falsehood,X1),
inference(orient,[status(thm)],[t4031]) ).
cnf(t930,plain,
not(implies(or(X1,falsehood),falsehood)) = or(X1,falsehood),
inference(cp,[status(thm)],[t929,t665]) ).
cnf(t4054,plain,
not(not(or(X1,falsehood))) = or(X1,falsehood),
inference(step,[status(thm)],[t930,t929]) ).
cnf(t4013,plain,
not(not(X1)) = and_star(truth,X1),
inference(step,[status(thm)],[t81,t776]) ).
cnf(t788,plain,
not(not(X1)) = and_star(truth,X1),
inference(rw,[status(thm)],[t4013]) ).
cnf(t875,plain,
not(not(X1)) = and_star(truth,X1),
inference(orient,[status(thm)],[t788]) ).
cnf(t4032,plain,
not(not(X1)) = xor(falsehood,X1),
inference(step,[status(thm)],[t875,t894]) ).
cnf(t895,plain,
not(not(X1)) = xor(falsehood,X1),
inference(orient,[status(thm)],[t4032]) ).
cnf(t4055,plain,
xor(falsehood,or(X1,falsehood)) = or(X1,falsehood),
inference(step,[status(thm)],[t4054,t895]) ).
cnf(t4056,plain,
xor(falsehood,X1) = or(X1,falsehood),
inference(step,[status(thm)],[t4055,t751]) ).
cnf(t4057,plain,
xor(falsehood,X1) = X1,
inference(step,[status(thm)],[t4056,t751]) ).
cnf(t944,plain,
xor(falsehood,X1) = X1,
inference(orient,[status(thm)],[t4057]) ).
cnf(t4060,plain,
and_star(truth,X1) = X1,
inference(step,[status(thm)],[t894,t944]) ).
cnf(t947,plain,
and_star(truth,X1) = X1,
inference(orient,[status(thm)],[t4060]) ).
cnf(t4068,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(step,[status(thm)],[t785,t947]) ).
cnf(t966,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(orient,[status(thm)],[t4068]) ).
cnf(t968,plain,
implies(X1,X2) = or(not(X1),X2),
inference(cp,[status(thm)],[t966,t57]) ).
cnf(t978,plain,
or(not(X1),X2) = implies(X1,X2),
inference(orient,[status(thm)],[t968]) ).
cnf(t4069,plain,
not(implies(X2,not(X1))) = and_star(X1,X2),
inference(step,[status(thm)],[t51,t966]) ).
cnf(t977,plain,
not(implies(X2,not(X1))) = and_star(X1,X2),
inference(rw,[status(thm)],[t4069]) ).
cnf(t987,plain,
not(implies(X1,not(X2))) = and_star(X2,X1),
inference(orient,[status(thm)],[t977]) ).
cnf(t990,plain,
and_star(X1,not(X2)) = not(or(X2,not(X1))),
inference(cp,[status(thm)],[t987,t40]) ).
cnf(t4070,plain,
and_star(X1,not(X2)) = not(implies(X1,X2)),
inference(step,[status(thm)],[t990,t966]) ).
cnf(t1006,plain,
not(implies(X1,X2)) = and_star(X1,not(X2)),
inference(orient,[status(thm)],[t4070]) ).
cnf(t1021,plain,
implies(implies(X1,X2),X3) = or(and_star(X1,not(X2)),X3),
inference(cp,[status(thm)],[t978,t1006]) ).
cnf(t1389,plain,
or(and_star(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(orient,[status(thm)],[t1021]) ).
cnf(t4094,plain,
implies(implies(X1,X2),and_star(not(X1),X2)) = xor(X1,X2),
inference(step,[status(thm)],[t62,t1389]) ).
cnf(t1405,plain,
implies(implies(X1,X2),and_star(not(X1),X2)) = xor(X1,X2),
inference(rw,[status(thm)],[t4094]) ).
cnf(t2141,plain,
implies(implies(X1,X2),and_star(not(X1),X2)) = xor(X1,X2),
inference(orient,[status(thm)],[t1405]) ).
cnf(t4058,plain,
not(not(X1)) = X1,
inference(step,[status(thm)],[t895,t944]) ).
cnf(t945,plain,
not(not(X1)) = X1,
inference(orient,[status(thm)],[t4058]) ).
cnf(t1023,plain,
implies(X1,X2) = not(and_star(X1,not(X2))),
inference(cp,[status(thm)],[t945,t1006]) ).
cnf(t1031,plain,
not(and_star(X1,not(X2))) = implies(X1,X2),
inference(orient,[status(thm)],[t1023]) ).
cnf(t1035,plain,
implies(X1,not(X2)) = not(and_star(X1,X2)),
inference(cp,[status(thm)],[t1031,t945]) ).
cnf(t1046,plain,
not(and_star(X1,X2)) = implies(X1,not(X2)),
inference(orient,[status(thm)],[t1035]) ).
cnf(t1049,plain,
or(and_star(X1,X2),X3) = implies(implies(X1,not(X2)),X3),
inference(cp,[status(thm)],[t40,t1046]) ).
cnf(t1420,plain,
implies(implies(X1,not(X2)),X3) = or(and_star(X1,X2),X3),
inference(orient,[status(thm)],[t1049]) ).
cnf(t2142,plain,
xor(X1,not(X2)) = or(and_star(X1,X2),and_star(not(X1),not(X2))),
inference(cp,[status(thm)],[t2141,t1420]) ).
cnf(t1022,plain,
implies(implies(X1,X2),X3) = or(X3,and_star(X1,not(X2))),
inference(cp,[status(thm)],[t966,t1006]) ).
cnf(t1406,plain,
or(X1,and_star(X2,not(X3))) = implies(implies(X2,X3),X1),
inference(orient,[status(thm)],[t1022]) ).
cnf(t1411,plain,
implies(implies(X1,X2),X3) = or(X3,and_star(not(X2),X1)),
inference(cp,[status(thm)],[t1406,t68]) ).
cnf(t1564,plain,
or(X1,and_star(not(X2),X3)) = implies(implies(X3,X2),X1),
inference(orient,[status(thm)],[t1411]) ).
cnf(t4202,plain,
xor(X1,not(X2)) = implies(implies(not(X2),X1),and_star(X1,X2)),
inference(step,[status(thm)],[t2142,t1564]) ).
cnf(t4203,plain,
xor(X1,not(X2)) = implies(or(X2,X1),and_star(X1,X2)),
inference(step,[status(thm)],[t4202,t40]) ).
cnf(t3758,plain,
implies(or(X1,X2),and_star(X2,X1)) = xor(X2,not(X1)),
inference(orient,[status(thm)],[t4203]) ).
cnf(t1014,plain,
and_star(not(X1),not(X2)) = not(or(X1,X2)),
inference(cp,[status(thm)],[t1006,t40]) ).
cnf(t1075,plain,
and_star(not(X1),not(X2)) = not(or(X1,X2)),
inference(orient,[status(thm)],[t1014]) ).
cnf(t3821,plain,
xor(not(X1),not(not(X2))) = implies(or(not(X2),not(X1)),not(or(X1,X2))),
inference(cp,[status(thm)],[t3758,t1075]) ).
cnf(t3773,plain,
xor(not(X1),not(X2)) = implies(implies(X1,X2),and_star(not(X1),X2)),
inference(cp,[status(thm)],[t3758,t966]) ).
cnf(t4204,plain,
xor(not(X1),not(X2)) = xor(X1,X2),
inference(step,[status(thm)],[t3773,t2141]) ).
cnf(t3862,plain,
xor(not(X1),not(X2)) = xor(X1,X2),
inference(orient,[status(thm)],[t4204]) ).
cnf(t4211,plain,
xor(X1,not(X2)) = implies(or(not(X2),not(X1)),not(or(X1,X2))),
inference(step,[status(thm)],[t3821,t3862]) ).
cnf(t979,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(cp,[status(thm)],[t978,t966]) ).
cnf(t1252,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(orient,[status(thm)],[t979]) ).
cnf(t4212,plain,
xor(X1,not(X2)) = implies(or(X1,X2),not(or(not(X2),not(X1)))),
inference(step,[status(thm)],[t4211,t1252]) ).
cnf(t4213,plain,
xor(X1,not(X2)) = implies(or(X1,X2),not(implies(X2,not(X1)))),
inference(step,[status(thm)],[t4212,t978]) ).
cnf(t4214,plain,
xor(X1,not(X2)) = implies(or(X1,X2),and_star(X2,not(not(X1)))),
inference(step,[status(thm)],[t4213,t1006]) ).
cnf(t4215,plain,
xor(X1,not(X2)) = implies(or(X1,X2),and_star(X2,X1)),
inference(step,[status(thm)],[t4214,t945]) ).
cnf(t4216,plain,
xor(X1,not(X2)) = xor(X2,not(X1)),
inference(step,[status(thm)],[t4215,t3758]) ).
cnf(t3917,plain,
xor(X1,not(X2)) = xor(X2,not(X1)),
inference(orient,[status(thm)],[t4216]) ).
cnf(goal_0,negated_conjecture,
xor(xor(x,truth),y) != xor(x,xor(truth,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
xor(y,xor(x,truth)) != xor(x,xor(truth,y)),
inference(rw,[status(thm)],[goal_0,t75]) ).
cnf(g0_1,plain,
xor(y,not(x)) != xor(x,xor(truth,y)),
inference(rw,[status(thm)],[g0_0,t956]) ).
cnf(g0_2,plain,
xor(y,not(x)) != xor(x,not(y)),
inference(rw,[status(thm)],[g0_1,t954]) ).
cnf(g0_3,plain,
xor(y,not(x)) != xor(y,not(x)),
inference(rw,[status(thm)],[g0_2,t3917]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL159-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.74 % Computer : n009.cluster.edu
% 0.10/0.74 % Model : x86_64 x86_64
% 0.10/0.74 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.74 % Memory : 8046.5625MB
% 0.10/0.74 % OS : Linux 6.8.0-71-generic
% 0.10/0.74 % CPULimit : 300
% 0.10/0.74 % WCLimit : 300
% 0.10/0.74 % DateTime : Wed Sep 23 22:07:15 UTC 2026
% 0.10/0.74 % CPUTime :
% 0.10/0.75 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.50/2.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.50/2.24 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------