%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL157-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 0.07s 16.82s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 14
% Syntax : Number of clauses : 123 ( 123 unt; 0 nHn; 17 RR)
% Number of literals : 123 ( 122 equ; 7 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 181 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
and(X1,X2) = and(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t8,axiom,
not(or(not(X1),not(X2))) = and_star(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t7,axiom,
not(or(not(X1),not(X2))) = and(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t46,plain,
not(or(not(X1),not(X2))) = and(X1,X2),
inference(orient,[status(thm)],[t7]) ).
cnf(t872,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)],[t872]) ).
cnf(t877,plain,
and_star(X1,X2) = and(X2,X1),
inference(step,[status(thm)],[t2,t50]) ).
cnf(t878,plain,
and_star(X1,X2) = and_star(X2,X1),
inference(step,[status(thm)],[t877,t50]) ).
cnf(t68,plain,
and_star(X1,X2) = and_star(X2,X1),
inference(orient,[status(thm)],[t878]) ).
cnf(t873,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)],[t873]) ).
cnf(t0,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t53,plain,
not(truth) = falsehood,
inference(orient,[status(thm)],[t0]) ).
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(t14,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
file('/export/starexec/sandbox2/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/sandbox2/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(t884,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)],[t884]) ).
cnf(t106,plain,
truth = implies(implies(truth,X1),X1),
inference(cp,[status(thm)],[t102,t16]) ).
cnf(t885,plain,
truth = implies(X1,X1),
inference(step,[status(thm)],[t106,t16]) ).
cnf(t118,plain,
implies(X1,X1) = truth,
inference(orient,[status(thm)],[t885]) ).
cnf(t6,axiom,
implies(not(X1),X2) = or(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t40,plain,
implies(not(X1),X2) = or(X1,X2),
inference(orient,[status(thm)],[t6]) ).
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(t131,plain,
and_star(truth,falsehood) = not(truth),
inference(cp,[status(thm)],[t81,t125]) ).
cnf(t886,plain,
and_star(truth,falsehood) = falsehood,
inference(step,[status(thm)],[t131,t53]) ).
cnf(t133,plain,
and_star(truth,falsehood) = falsehood,
inference(orient,[status(thm)],[t886]) ).
cnf(t9,axiom,
and(and(X1,X2),X3) = and(X1,and(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t879,plain,
and_star(and(X1,X2),X3) = and(X1,and(X2,X3)),
inference(step,[status(thm)],[t9,t50]) ).
cnf(t880,plain,
and_star(and_star(X1,X2),X3) = and(X1,and(X2,X3)),
inference(step,[status(thm)],[t879,t50]) ).
cnf(t881,plain,
and_star(and_star(X1,X2),X3) = and_star(X1,and(X2,X3)),
inference(step,[status(thm)],[t880,t50]) ).
cnf(t882,plain,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
inference(step,[status(thm)],[t881,t50]) ).
cnf(t71,plain,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
inference(orient,[status(thm)],[t882]) ).
cnf(t105,plain,
truth = or(X1,implies(implies(not(X1),X2),X2)),
inference(cp,[status(thm)],[t102,t40]) ).
cnf(t899,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)],[t899]) ).
cnf(t4,axiom,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t57,plain,
or(X1,X2) = or(X2,X1),
inference(orient,[status(thm)],[t4]) ).
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(t13,axiom,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t59,plain,
or(or(X1,X2),X3) = or(X1,or(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
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(t11,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t17,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(orient,[status(thm)],[t11]) ).
cnf(t18,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(cp,[status(thm)],[t17,t16]) ).
cnf(t900,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)],[t900]) ).
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(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(t915,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)],[t915]) ).
cnf(t433,plain,
truth = or(or(not(X1),X2),implies(truth,X1)),
inference(cp,[status(thm)],[t427,t384]) ).
cnf(t921,plain,
truth = or(not(X1),or(X2,implies(truth,X1))),
inference(step,[status(thm)],[t433,t59]) ).
cnf(t922,plain,
truth = or(not(X1),or(X2,X1)),
inference(step,[status(thm)],[t921,t16]) ).
cnf(t442,plain,
or(not(X1),or(X2,X1)) = truth,
inference(orient,[status(thm)],[t922]) ).
cnf(t15,axiom,
or(and(X1,not(X2)),and(not(X1),X2)) = xor(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t875,plain,
or(and_star(X1,not(X2)),and(not(X1),X2)) = xor(X1,X2),
inference(step,[status(thm)],[t15,t50]) ).
cnf(t876,plain,
or(and_star(X1,not(X2)),and_star(not(X1),X2)) = xor(X1,X2),
inference(step,[status(thm)],[t875,t50]) ).
cnf(t62,plain,
or(and_star(X1,not(X2)),and_star(not(X1),X2)) = xor(X1,X2),
inference(orient,[status(thm)],[t876]) ).
cnf(t132,plain,
and_star(X1,not(X1)) = not(truth),
inference(cp,[status(thm)],[t51,t125]) ).
cnf(t887,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)],[t887]) ).
cnf(t141,plain,
xor(X1,X1) = or(falsehood,and_star(not(X1),X1)),
inference(cp,[status(thm)],[t62,t135]) ).
cnf(t888,plain,
xor(X1,X1) = or(falsehood,and_star(X1,not(X1))),
inference(step,[status(thm)],[t141,t68]) ).
cnf(t889,plain,
xor(X1,X1) = or(falsehood,falsehood),
inference(step,[status(thm)],[t888,t135]) ).
cnf(t187,plain,
xor(X1,X1) = or(falsehood,falsehood),
inference(orient,[status(thm)],[t889]) ).
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(t361,plain,
truth = implies(truth,implies(implies(truth,X1),implies(X2,X1))),
inference(cp,[status(thm)],[t19,t357]) ).
cnf(t919,plain,
truth = implies(implies(truth,X1),implies(X2,X1)),
inference(step,[status(thm)],[t361,t16]) ).
cnf(t920,plain,
truth = implies(X1,implies(X2,X1)),
inference(step,[status(thm)],[t919,t16]) ).
cnf(t388,plain,
implies(X1,implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t920]) ).
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(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(t933,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)],[t933]) ).
cnf(t12,axiom,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t31,plain,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t12]) ).
cnf(t871,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)],[t871]) ).
cnf(t723,plain,
implies(or(X1,not(X2)),implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t45]) ).
cnf(t730,plain,
truth = implies(or(X1,falsehood),implies(truth,X1)),
inference(cp,[status(thm)],[t723,t53]) ).
cnf(t936,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)],[t936]) ).
cnf(t749,plain,
or(X1,falsehood) = implies(truth,X1),
inference(cp,[status(thm)],[t676,t742]) ).
cnf(t937,plain,
or(X1,falsehood) = X1,
inference(step,[status(thm)],[t749,t16]) ).
cnf(t751,plain,
or(X1,falsehood) = X1,
inference(orient,[status(thm)],[t937]) ).
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(t939,plain,
xor(X1,X1) = or(falsehood,falsehood),
inference(step,[status(thm)],[t752,t751]) ).
cnf(t940,plain,
xor(X1,X1) = falsehood,
inference(step,[status(thm)],[t939,t751]) ).
cnf(t762,plain,
xor(X1,X1) = falsehood,
inference(orient,[status(thm)],[t940]) ).
cnf(t941,plain,
or(not(falsehood),falsehood) = truth,
inference(step,[status(thm)],[t460,t762]) ).
cnf(t942,plain,
not(falsehood) = truth,
inference(step,[status(thm)],[t941,t751]) ).
cnf(t763,plain,
not(falsehood) = truth,
inference(rw,[status(thm)],[t942]) ).
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(t955,plain,
and_star(falsehood,X1) = not(truth),
inference(step,[status(thm)],[t774,t381]) ).
cnf(t956,plain,
and_star(falsehood,X1) = falsehood,
inference(step,[status(thm)],[t955,t53]) ).
cnf(t857,plain,
and_star(falsehood,X1) = falsehood,
inference(orient,[status(thm)],[t956]) ).
cnf(goal_0,negated_conjecture,
and_star(x,falsehood) != falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
and_star(falsehood,x) != falsehood,
inference(rw,[status(thm)],[goal_0,t68]) ).
cnf(g0_1,plain,
and_star(and_star(truth,falsehood),x) != falsehood,
inference(rw,[status(thm)],[g0_0,t133]) ).
cnf(g0_2,plain,
and_star(and_star(falsehood,truth),x) != falsehood,
inference(rw,[status(thm)],[g0_1,t68]) ).
cnf(g0_3,plain,
and_star(falsehood,and_star(truth,x)) != falsehood,
inference(rw,[status(thm)],[g0_2,t71]) ).
cnf(g0_4,plain,
and_star(falsehood,and_star(x,truth)) != falsehood,
inference(rw,[status(thm)],[g0_3,t68]) ).
cnf(g0_5,plain,
falsehood != falsehood,
inference(rw,[status(thm)],[g0_4,t857]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL157-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.05/16.15 % Computer : n012.cluster.edu
% 0.05/16.15 % Model : x86_64 x86_64
% 0.05/16.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/16.15 % Memory : 8046.5625MB
% 0.05/16.15 % OS : Linux 6.8.0-71-generic
% 0.05/16.15 % CPULimit : 300
% 0.05/16.15 % WCLimit : 300
% 0.05/16.15 % DateTime : Wed Sep 23 22:07:02 UTC 2026
% 0.05/16.15 % CPUTime :
% 0.05/16.16 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/16.82 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/16.82 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------