%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL158-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 5.18s 6.06s
% Output : CNFRefutation 5.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 11
% Syntax : Number of clauses : 80 ( 80 unt; 0 nHn; 7 RR)
% Number of literals : 80 ( 79 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 119 ( 12 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(t957,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)],[t957]) ).
cnf(t962,plain,
and_star(X1,X2) = and(X2,X1),
inference(step,[status(thm)],[t2,t50]) ).
cnf(t963,plain,
and_star(X1,X2) = and_star(X2,X1),
inference(step,[status(thm)],[t962,t50]) ).
cnf(t68,plain,
and_star(X1,X2) = and_star(X2,X1),
inference(orient,[status(thm)],[t963]) ).
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(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(t969,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)],[t969]) ).
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(t970,plain,
truth = implies(X1,X1),
inference(step,[status(thm)],[t106,t16]) ).
cnf(t118,plain,
implies(X1,X1) = truth,
inference(orient,[status(thm)],[t970]) ).
cnf(t985,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)],[t985]) ).
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(t1004,plain,
truth = implies(implies(truth,X1),implies(X2,X1)),
inference(step,[status(thm)],[t361,t16]) ).
cnf(t1005,plain,
truth = implies(X1,implies(X2,X1)),
inference(step,[status(thm)],[t1004,t16]) ).
cnf(t388,plain,
implies(X1,implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t1005]) ).
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(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(t1017,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)],[t1017]) ).
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(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(t1018,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)],[t1018]) ).
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(t956,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)],[t956]) ).
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/sandbox2/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(t1021,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)],[t1021]) ).
cnf(t749,plain,
or(X1,falsehood) = implies(truth,X1),
inference(cp,[status(thm)],[t676,t742]) ).
cnf(t1022,plain,
or(X1,falsehood) = X1,
inference(step,[status(thm)],[t749,t16]) ).
cnf(t751,plain,
or(X1,falsehood) = X1,
inference(orient,[status(thm)],[t1022]) ).
cnf(t758,plain,
or(X1,falsehood) = implies(implies(X1,falsehood),falsehood),
inference(cp,[status(thm)],[t665,t751]) ).
cnf(t1075,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)],[t1075]) ).
cnf(t923,plain,
not(X1) = implies(or(X1,falsehood),falsehood),
inference(cp,[status(thm)],[t922,t40]) ).
cnf(t1076,plain,
not(X1) = implies(X1,falsehood),
inference(step,[status(thm)],[t923,t751]) ).
cnf(t929,plain,
implies(X1,falsehood) = not(X1),
inference(orient,[status(thm)],[t1076]) ).
cnf(t395,plain,
implies(implies(implies(X1,X2),X2),X2) = implies(truth,implies(X1,X2)),
inference(cp,[status(thm)],[t17,t388]) ).
cnf(t1016,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)],[t1016]) ).
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(t958,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)],[t958]) ).
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(t132,plain,
and_star(X1,not(X1)) = not(truth),
inference(cp,[status(thm)],[t51,t125]) ).
cnf(t972,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)],[t972]) ).
cnf(goal_0,negated_conjecture,
and_star(xor(truth,x),x) != falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
and_star(x,xor(truth,x)) != falsehood,
inference(rw,[status(thm)],[goal_0,t68]) ).
cnf(g0_1,plain,
and_star(x,not(x)) != falsehood,
inference(rw,[status(thm)],[g0_0,t954]) ).
cnf(g0_2,plain,
falsehood != falsehood,
inference(rw,[status(thm)],[g0_1,t135]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL158-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.38 % Computer : n026.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Wed Sep 23 22:09:44 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.18/6.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.18/6.06 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------