%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 16.90s 2.63s
% Output : CNFRefutation 16.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 13
% Syntax : Number of clauses : 110 ( 110 unt; 0 nHn; 10 RR)
% Number of literals : 110 ( 109 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 184 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t10,axiom,
xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t28,plain,
xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2),
inference(orient,[status(thm)],[t10]) ).
cnf(t5,axiom,
xor(X1,truth) = not(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t24,plain,
xor(X1,truth) = not(X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t8,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t15,plain,
xor(X1,X2) = xor(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t26,plain,
not(X1) = xor(truth,X1),
inference(cp,[status(thm)],[t24,t15]) ).
cnf(t77,plain,
xor(truth,X1) = not(X1),
inference(orient,[status(thm)],[t26]) ).
cnf(t9816,plain,
not(and_star(X1,xor(truth,X2))) = implies(X1,X2),
inference(step,[status(thm)],[t28,t77]) ).
cnf(t9817,plain,
not(and_star(X1,not(X2))) = implies(X1,X2),
inference(step,[status(thm)],[t9816,t77]) ).
cnf(t80,plain,
not(and_star(X1,not(X2))) = implies(X1,X2),
inference(rw,[status(thm)],[t9817]) ).
cnf(t84,plain,
not(and_star(X1,not(X2))) = implies(X1,X2),
inference(orient,[status(thm)],[t80]) ).
cnf(t6,axiom,
and_star(X1,X2) = and_star(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t34,plain,
and_star(X1,X2) = and_star(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t87,plain,
implies(X1,X2) = not(and_star(not(X2),X1)),
inference(cp,[status(thm)],[t84,t34]) ).
cnf(t102,plain,
not(and_star(not(X1),X2)) = implies(X2,X1),
inference(orient,[status(thm)],[t87]) ).
cnf(t2,axiom,
and_star(X1,truth) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t14,plain,
and_star(X1,truth) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t35,plain,
and_star(truth,X1) = X1,
inference(cp,[status(thm)],[t34,t14]) ).
cnf(t69,plain,
and_star(truth,X1) = X1,
inference(orient,[status(thm)],[t35]) ).
cnf(t85,plain,
implies(truth,X1) = not(not(X1)),
inference(cp,[status(thm)],[t84,t69]) ).
cnf(t94,plain,
not(not(X1)) = implies(truth,X1),
inference(orient,[status(thm)],[t85]) ).
cnf(t98,plain,
implies(X1,not(X2)) = not(and_star(X1,implies(truth,X2))),
inference(cp,[status(thm)],[t84,t94]) ).
cnf(t11,axiom,
xor(xor(X1,truth),X2) = xor(X1,xor(truth,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t18,plain,
xor(xor(X1,truth),X2) = xor(X1,xor(truth,X2)),
inference(orient,[status(thm)],[t11]) ).
cnf(t9805,plain,
xor(not(X1),X2) = xor(X1,xor(truth,X2)),
inference(step,[status(thm)],[t18,t24]) ).
cnf(t27,plain,
xor(not(X1),X2) = xor(X1,xor(truth,X2)),
inference(rw,[status(thm)],[t9805]) ).
cnf(t9824,plain,
xor(not(X1),X2) = xor(X1,not(X2)),
inference(step,[status(thm)],[t27,t77]) ).
cnf(t136,plain,
xor(not(X1),X2) = xor(X1,not(X2)),
inference(orient,[status(thm)],[t9824]) ).
cnf(t138,plain,
xor(X1,not(truth)) = not(not(X1)),
inference(cp,[status(thm)],[t136,t24]) ).
cnf(t0,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t65,plain,
not(truth) = falsehood,
inference(orient,[status(thm)],[t0]) ).
cnf(t9825,plain,
xor(X1,falsehood) = not(not(X1)),
inference(step,[status(thm)],[t138,t65]) ).
cnf(t4,axiom,
xor(X1,falsehood) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t13,plain,
xor(X1,falsehood) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t9826,plain,
X1 = not(not(X1)),
inference(step,[status(thm)],[t9825,t13]) ).
cnf(t9827,plain,
X1 = implies(truth,X1),
inference(step,[status(thm)],[t9826,t94]) ).
cnf(t145,plain,
implies(truth,X1) = X1,
inference(orient,[status(thm)],[t9827]) ).
cnf(t9835,plain,
implies(X1,not(X2)) = not(and_star(X1,X2)),
inference(step,[status(thm)],[t98,t145]) ).
cnf(t169,plain,
not(and_star(X1,X2)) = implies(X1,not(X2)),
inference(orient,[status(thm)],[t9835]) ).
cnf(t9836,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(step,[status(thm)],[t102,t169]) ).
cnf(t178,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[t9836]) ).
cnf(t180,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(orient,[status(thm)],[t178]) ).
cnf(t95,plain,
implies(truth,and_star(X1,not(X2))) = not(implies(X1,X2)),
inference(cp,[status(thm)],[t94,t84]) ).
cnf(t9834,plain,
and_star(X1,not(X2)) = not(implies(X1,X2)),
inference(step,[status(thm)],[t95,t145]) ).
cnf(t162,plain,
not(implies(X1,X2)) = and_star(X1,not(X2)),
inference(orient,[status(thm)],[t9834]) ).
cnf(t182,plain,
implies(X1,implies(X2,X3)) = implies(and_star(X2,not(X3)),not(X1)),
inference(cp,[status(thm)],[t180,t162]) ).
cnf(t9,axiom,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t37,plain,
and_star(and_star(X1,X2),X3) = and_star(X1,and_star(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t172,plain,
implies(and_star(X1,X2),not(X3)) = not(and_star(X1,and_star(X2,X3))),
inference(cp,[status(thm)],[t169,t37]) ).
cnf(t9860,plain,
implies(and_star(X1,X2),not(X3)) = implies(X1,not(and_star(X2,X3))),
inference(step,[status(thm)],[t172,t169]) ).
cnf(t9861,plain,
implies(and_star(X1,X2),not(X3)) = implies(X1,implies(X2,not(X3))),
inference(step,[status(thm)],[t9860,t169]) ).
cnf(t464,plain,
implies(and_star(X1,X2),not(X3)) = implies(X1,implies(X2,not(X3))),
inference(orient,[status(thm)],[t9861]) ).
cnf(t9863,plain,
implies(X1,implies(X2,X3)) = implies(X2,implies(not(X3),not(X1))),
inference(step,[status(thm)],[t182,t464]) ).
cnf(t9864,plain,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
inference(step,[status(thm)],[t9863,t180]) ).
cnf(t562,plain,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
inference(orient,[status(thm)],[t9864]) ).
cnf(t12,axiom,
and_star(xor(and_star(xor(truth,X1),X2),truth),X2) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t9806,plain,
and_star(X2,xor(and_star(xor(truth,X1),X2),truth)) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1),
inference(step,[status(thm)],[t12,t34]) ).
cnf(t9807,plain,
and_star(X2,not(and_star(xor(truth,X1),X2))) = and_star(xor(and_star(xor(truth,X2),X1),truth),X1),
inference(step,[status(thm)],[t9806,t24]) ).
cnf(t9808,plain,
and_star(X2,not(and_star(xor(truth,X1),X2))) = and_star(X1,xor(and_star(xor(truth,X2),X1),truth)),
inference(step,[status(thm)],[t9807,t34]) ).
cnf(t9809,plain,
and_star(X2,not(and_star(xor(truth,X1),X2))) = and_star(X1,not(and_star(xor(truth,X2),X1))),
inference(step,[status(thm)],[t9808,t24]) ).
cnf(t45,plain,
and_star(X1,not(and_star(xor(truth,X2),X1))) = and_star(X2,not(and_star(xor(truth,X1),X2))),
inference(orient,[status(thm)],[t9809]) ).
cnf(t9813,plain,
and_star(X1,not(and_star(not(X2),X1))) = and_star(X2,not(and_star(xor(truth,X1),X2))),
inference(step,[status(thm)],[t45,t77]) ).
cnf(t9814,plain,
and_star(X1,not(and_star(not(X2),X1))) = and_star(X2,not(and_star(not(X1),X2))),
inference(step,[status(thm)],[t9813,t77]) ).
cnf(t78,plain,
and_star(X1,not(and_star(not(X2),X1))) = and_star(X2,not(and_star(not(X1),X2))),
inference(rw,[status(thm)],[t9814]) ).
cnf(t9896,plain,
and_star(X1,implies(not(X2),not(X1))) = and_star(X2,not(and_star(not(X1),X2))),
inference(step,[status(thm)],[t78,t169]) ).
cnf(t9897,plain,
and_star(X1,implies(X1,X2)) = and_star(X2,not(and_star(not(X1),X2))),
inference(step,[status(thm)],[t9896,t180]) ).
cnf(t9898,plain,
and_star(X1,implies(X1,X2)) = and_star(X2,implies(not(X1),not(X2))),
inference(step,[status(thm)],[t9897,t169]) ).
cnf(t9899,plain,
and_star(X1,implies(X1,X2)) = and_star(X2,implies(X2,X1)),
inference(step,[status(thm)],[t9898,t180]) ).
cnf(t1306,plain,
and_star(X1,implies(X1,X2)) = and_star(X2,implies(X2,X1)),
inference(orient,[status(thm)],[t9899]) ).
cnf(t1312,plain,
and_star(not(X1),implies(not(X1),not(X2))) = and_star(not(X2),implies(X1,X2)),
inference(cp,[status(thm)],[t1306,t180]) ).
cnf(t10018,plain,
and_star(not(X1),implies(X2,X1)) = and_star(not(X2),implies(X1,X2)),
inference(step,[status(thm)],[t1312,t180]) ).
cnf(t6181,plain,
and_star(not(X1),implies(X2,X1)) = and_star(not(X2),implies(X1,X2)),
inference(orient,[status(thm)],[t10018]) ).
cnf(t6259,plain,
implies(not(X1),not(implies(X2,X1))) = not(and_star(not(X2),implies(X1,X2))),
inference(cp,[status(thm)],[t169,t6181]) ).
cnf(t10062,plain,
implies(implies(X2,X1),X1) = not(and_star(not(X2),implies(X1,X2))),
inference(step,[status(thm)],[t6259,t180]) ).
cnf(t10063,plain,
implies(implies(X2,X1),X1) = implies(not(X2),not(implies(X1,X2))),
inference(step,[status(thm)],[t10062,t169]) ).
cnf(t10064,plain,
implies(implies(X2,X1),X1) = implies(implies(X1,X2),X2),
inference(step,[status(thm)],[t10063,t180]) ).
cnf(t9602,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(orient,[status(thm)],[t10064]) ).
cnf(t7,axiom,
and_star(xor(truth,X1),X1) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t9810,plain,
and_star(X1,xor(truth,X1)) = falsehood,
inference(step,[status(thm)],[t7,t34]) ).
cnf(t57,plain,
and_star(X1,xor(truth,X1)) = falsehood,
inference(orient,[status(thm)],[t9810]) ).
cnf(t9815,plain,
and_star(X1,not(X1)) = falsehood,
inference(step,[status(thm)],[t57,t77]) ).
cnf(t79,plain,
and_star(X1,not(X1)) = falsehood,
inference(rw,[status(thm)],[t9815]) ).
cnf(t81,plain,
and_star(X1,not(X1)) = falsehood,
inference(orient,[status(thm)],[t79]) ).
cnf(t83,plain,
and_star(X1,and_star(not(X1),X2)) = and_star(falsehood,X2),
inference(cp,[status(thm)],[t37,t81]) ).
cnf(t1,axiom,
and_star(X1,falsehood) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t42,plain,
and_star(X1,falsehood) = falsehood,
inference(orient,[status(thm)],[t1]) ).
cnf(t43,plain,
falsehood = and_star(falsehood,X1),
inference(cp,[status(thm)],[t42,t34]) ).
cnf(t72,plain,
and_star(falsehood,X1) = falsehood,
inference(orient,[status(thm)],[t43]) ).
cnf(t9823,plain,
and_star(X1,and_star(not(X1),X2)) = falsehood,
inference(step,[status(thm)],[t83,t72]) ).
cnf(t113,plain,
and_star(X1,and_star(not(X1),X2)) = falsehood,
inference(orient,[status(thm)],[t9823]) ).
cnf(t115,plain,
falsehood = and_star(X1,and_star(X2,not(X1))),
inference(cp,[status(thm)],[t113,t34]) ).
cnf(t127,plain,
and_star(X1,and_star(X2,not(X1))) = falsehood,
inference(orient,[status(thm)],[t115]) ).
cnf(t171,plain,
implies(X1,not(and_star(X2,not(X1)))) = not(falsehood),
inference(cp,[status(thm)],[t169,t127]) ).
cnf(t9837,plain,
implies(X1,implies(X2,X1)) = not(falsehood),
inference(step,[status(thm)],[t171,t84]) ).
cnf(t16,plain,
xor(falsehood,X1) = X1,
inference(cp,[status(thm)],[t15,t13]) ).
cnf(t66,plain,
xor(falsehood,X1) = X1,
inference(orient,[status(thm)],[t16]) ).
cnf(t67,plain,
truth = not(falsehood),
inference(cp,[status(thm)],[t66,t24]) ).
cnf(t68,plain,
not(falsehood) = truth,
inference(orient,[status(thm)],[t67]) ).
cnf(t9838,plain,
implies(X1,implies(X2,X1)) = truth,
inference(step,[status(thm)],[t9837,t68]) ).
cnf(t179,plain,
implies(X1,implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t9838]) ).
cnf(t578,plain,
truth = implies(implies(X1,X2),implies(X1,implies(X3,X2))),
inference(cp,[status(thm)],[t179,t562]) ).
cnf(t9869,plain,
truth = implies(X1,implies(implies(X1,X2),implies(X3,X2))),
inference(step,[status(thm)],[t578,t562]) ).
cnf(t772,plain,
implies(X1,implies(implies(X1,X2),implies(X3,X2))) = truth,
inference(orient,[status(thm)],[t9869]) ).
cnf(goal_0,negated_conjecture,
implies(implies(x,y),implies(implies(y,z),implies(x,z))) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
implies(implies(x,y),implies(x,implies(implies(y,z),z))) != truth,
inference(rw,[status(thm)],[goal_0,t562]) ).
cnf(g0_1,plain,
implies(x,implies(implies(x,y),implies(implies(y,z),z))) != truth,
inference(rw,[status(thm)],[g0_0,t562]) ).
cnf(g0_2,plain,
implies(x,implies(implies(x,y),implies(implies(z,y),y))) != truth,
inference(rw,[status(thm)],[g0_1,t9602]) ).
cnf(g0_3,plain,
truth != truth,
inference(rw,[status(thm)],[g0_2,t772]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 22:07:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.90/2.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.90/2.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------