%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 02:00:57 PM UTC 2026
% Result : Unsatisfiable 21.34s 3.41s
% Output : CNFRefutation 21.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 17
% Syntax : Number of clauses : 126 ( 126 unt; 0 nHn; 65 RR)
% Number of literals : 126 ( 125 equ; 10 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 114 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t10,axiom,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t55,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(orient,[status(thm)],[t10]) ).
cnf(t9,axiom,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t31,plain,
implies(X1,implies(X2,X3)) = implies(X2,implies(X1,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t57,plain,
implies(implies(implies(X1,X2),X3),X3) = implies(X1,implies(implies(X3,implies(X1,X2)),X2)),
inference(cp,[status(thm)],[t55,t31]) ).
cnf(t13098,plain,
implies(implies(implies(X1,X2),X3),X3) = implies(X1,implies(implies(X3,implies(X1,X2)),X2)),
inference(orient,[status(thm)],[t57]) ).
cnf(t15,axiom,
sFlat0 = implies(a,b),
introduced(definition) ).
cnf(t164,plain,
implies(a,b) = sFlat0,
inference(orient,[status(thm)],[t15]) ).
cnf(t174,plain,
implies(a,implies(X1,b)) = implies(X1,sFlat0),
inference(cp,[status(thm)],[t31,t164]) ).
cnf(t416,plain,
implies(a,implies(X1,b)) = implies(X1,sFlat0),
inference(orient,[status(thm)],[t174]) ).
cnf(t16,axiom,
sFlat1 = implies(b,a),
introduced(definition) ).
cnf(t152,plain,
implies(b,a) = sFlat1,
inference(orient,[status(thm)],[t16]) ).
cnf(t17,axiom,
sFlat2 = implies(implies(a,b),implies(b,a)),
introduced(definition) ).
cnf(t16841,plain,
sFlat2 = implies(b,implies(implies(a,b),a)),
inference(step,[status(thm)],[t17,t31]) ).
cnf(t140,plain,
implies(b,implies(implies(a,b),a)) = sFlat2,
inference(orient,[status(thm)],[t16841]) ).
cnf(t16843,plain,
implies(b,implies(sFlat0,a)) = sFlat2,
inference(step,[status(thm)],[t140,t164]) ).
cnf(t176,plain,
implies(b,implies(sFlat0,a)) = sFlat2,
inference(rw,[status(thm)],[t16843]) ).
cnf(t16849,plain,
implies(sFlat0,implies(b,a)) = sFlat2,
inference(step,[status(thm)],[t176,t31]) ).
cnf(t16850,plain,
implies(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t16849,t152]) ).
cnf(t259,plain,
implies(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t16850]) ).
cnf(t18,axiom,
sFlat3 = implies(implies(implies(a,b),implies(b,a)),implies(b,a)),
introduced(definition) ).
cnf(t16836,plain,
sFlat3 = implies(implies(implies(b,a),implies(a,b)),implies(a,b)),
inference(step,[status(thm)],[t18,t55]) ).
cnf(t16837,plain,
sFlat3 = implies(a,implies(implies(implies(b,a),implies(a,b)),b)),
inference(step,[status(thm)],[t16836,t31]) ).
cnf(t16838,plain,
sFlat3 = implies(a,implies(implies(a,implies(implies(b,a),b)),b)),
inference(step,[status(thm)],[t16837,t31]) ).
cnf(t114,plain,
implies(a,implies(implies(a,implies(implies(b,a),b)),b)) = sFlat3,
inference(orient,[status(thm)],[t16838]) ).
cnf(t16842,plain,
implies(a,implies(implies(a,implies(sFlat1,b)),b)) = sFlat3,
inference(step,[status(thm)],[t114,t152]) ).
cnf(t163,plain,
implies(a,implies(implies(a,implies(sFlat1,b)),b)) = sFlat3,
inference(rw,[status(thm)],[t16842]) ).
cnf(t17082,plain,
implies(implies(a,implies(sFlat1,b)),sFlat0) = sFlat3,
inference(step,[status(thm)],[t163,t416]) ).
cnf(t17083,plain,
implies(implies(sFlat1,sFlat0),sFlat0) = sFlat3,
inference(step,[status(thm)],[t17082,t416]) ).
cnf(t17084,plain,
implies(implies(sFlat0,sFlat1),sFlat1) = sFlat3,
inference(step,[status(thm)],[t17083,t55]) ).
cnf(t17085,plain,
implies(sFlat2,sFlat1) = sFlat3,
inference(step,[status(thm)],[t17084,t259]) ).
cnf(t10583,plain,
implies(sFlat2,sFlat1) = sFlat3,
inference(orient,[status(thm)],[t17085]) ).
cnf(t7,axiom,
implies(not(X1),not(X2)) = implies(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t25,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t60,plain,
implies(implies(not(X1),not(X2)),not(X2)) = implies(implies(X1,X2),not(X1)),
inference(cp,[status(thm)],[t55,t25]) ).
cnf(t3,axiom,
not(not(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t20,plain,
not(not(X1)) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t26,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(cp,[status(thm)],[t25,t20]) ).
cnf(t588,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(orient,[status(thm)],[t26]) ).
cnf(t17205,plain,
implies(X2,not(implies(not(X1),not(X2)))) = implies(implies(X1,X2),not(X1)),
inference(step,[status(thm)],[t60,t588]) ).
cnf(t17206,plain,
implies(X2,not(implies(X2,X1))) = implies(implies(X1,X2),not(X1)),
inference(step,[status(thm)],[t17205,t25]) ).
cnf(t17207,plain,
implies(X2,not(implies(X2,X1))) = implies(X1,not(implies(X1,X2))),
inference(step,[status(thm)],[t17206,t588]) ).
cnf(t14827,plain,
implies(X1,not(implies(X1,X2))) = implies(X2,not(implies(X2,X1))),
inference(orient,[status(thm)],[t17207]) ).
cnf(t14,axiom,
implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t16835,plain,
implies(implies(X1,X2),implies(X3,implies(implies(X3,X1),X2))) = truth,
inference(step,[status(thm)],[t14,t31]) ).
cnf(t66,plain,
implies(implies(X1,X2),implies(X3,implies(implies(X3,X1),X2))) = truth,
inference(orient,[status(thm)],[t16835]) ).
cnf(t5,axiom,
implies(X1,implies(X2,X1)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t38,plain,
implies(X1,implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t5]) ).
cnf(t70,plain,
truth = implies(truth,implies(X1,implies(implies(X1,X2),implies(X3,X2)))),
inference(cp,[status(thm)],[t66,t38]) ).
cnf(t2,axiom,
implies(truth,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
implies(truth,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t17078,plain,
truth = implies(X1,implies(implies(X1,X2),implies(X3,X2))),
inference(step,[status(thm)],[t70,t19]) ).
cnf(t9983,plain,
implies(X1,implies(implies(X1,X2),implies(X3,X2))) = truth,
inference(orient,[status(thm)],[t17078]) ).
cnf(t42,plain,
truth = implies(not(X1),implies(X1,X2)),
inference(cp,[status(thm)],[t38,t25]) ).
cnf(t16860,plain,
truth = implies(X1,implies(not(X1),X2)),
inference(step,[status(thm)],[t42,t31]) ).
cnf(t505,plain,
implies(X1,implies(not(X1),X2)) = truth,
inference(orient,[status(thm)],[t16860]) ).
cnf(t162,plain,
implies(b,implies(X1,a)) = implies(X1,sFlat1),
inference(cp,[status(thm)],[t31,t152]) ).
cnf(t397,plain,
implies(b,implies(X1,a)) = implies(X1,sFlat1),
inference(orient,[status(thm)],[t162]) ).
cnf(t508,plain,
truth = implies(not(b),sFlat1),
inference(cp,[status(thm)],[t505,t397]) ).
cnf(t545,plain,
implies(not(b),sFlat1) = truth,
inference(orient,[status(thm)],[t508]) ).
cnf(t556,plain,
implies(not(b),implies(X1,sFlat1)) = implies(X1,truth),
inference(cp,[status(thm)],[t31,t545]) ).
cnf(t1,axiom,
implies(X1,truth) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t48,plain,
implies(X1,truth) = truth,
inference(orient,[status(thm)],[t1]) ).
cnf(t16864,plain,
implies(not(b),implies(X1,sFlat1)) = truth,
inference(step,[status(thm)],[t556,t48]) ).
cnf(t619,plain,
implies(not(b),implies(X1,sFlat1)) = truth,
inference(orient,[status(thm)],[t16864]) ).
cnf(t10600,plain,
truth = implies(not(b),sFlat3),
inference(cp,[status(thm)],[t619,t10583]) ).
cnf(t27,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(cp,[status(thm)],[t25,t20]) ).
cnf(t1002,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(orient,[status(thm)],[t27]) ).
cnf(t17097,plain,
truth = implies(not(sFlat3),b),
inference(step,[status(thm)],[t10600,t1002]) ).
cnf(t10878,plain,
implies(not(sFlat3),b) = truth,
inference(orient,[status(thm)],[t17097]) ).
cnf(t10889,plain,
truth = implies(not(sFlat3),implies(truth,implies(X1,b))),
inference(cp,[status(thm)],[t9983,t10878]) ).
cnf(t17122,plain,
truth = implies(not(sFlat3),implies(X1,b)),
inference(step,[status(thm)],[t10889,t19]) ).
cnf(t11776,plain,
implies(not(sFlat3),implies(X1,b)) = truth,
inference(orient,[status(thm)],[t17122]) ).
cnf(t13,axiom,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t87,plain,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
inference(orient,[status(thm)],[t13]) ).
cnf(t165,plain,
truth = implies(b,sFlat0),
inference(cp,[status(thm)],[t38,t164]) ).
cnf(t229,plain,
implies(b,sFlat0) = truth,
inference(orient,[status(thm)],[t165]) ).
cnf(t235,plain,
truth = implies(truth,implies(implies(sFlat0,X1),implies(b,X1))),
inference(cp,[status(thm)],[t87,t229]) ).
cnf(t16878,plain,
truth = implies(implies(sFlat0,X1),implies(b,X1)),
inference(step,[status(thm)],[t235,t19]) ).
cnf(t16879,plain,
truth = implies(b,implies(implies(sFlat0,X1),X1)),
inference(step,[status(thm)],[t16878,t31]) ).
cnf(t875,plain,
implies(b,implies(implies(sFlat0,X1),X1)) = truth,
inference(orient,[status(thm)],[t16879]) ).
cnf(t272,plain,
implies(sFlat0,implies(X1,sFlat1)) = implies(X1,sFlat2),
inference(cp,[status(thm)],[t31,t259]) ).
cnf(t434,plain,
implies(sFlat0,implies(X1,sFlat1)) = implies(X1,sFlat2),
inference(orient,[status(thm)],[t272]) ).
cnf(t10601,plain,
implies(sFlat2,sFlat2) = implies(sFlat0,sFlat3),
inference(cp,[status(thm)],[t434,t10583]) ).
cnf(t0,axiom,
implies(X1,X1) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t30,plain,
implies(X1,X1) = truth,
inference(orient,[status(thm)],[t0]) ).
cnf(t17092,plain,
truth = implies(sFlat0,sFlat3),
inference(step,[status(thm)],[t10601,t30]) ).
cnf(t10651,plain,
implies(sFlat0,sFlat3) = truth,
inference(orient,[status(thm)],[t17092]) ).
cnf(t10674,plain,
truth = implies(b,implies(truth,sFlat3)),
inference(cp,[status(thm)],[t875,t10651]) ).
cnf(t17095,plain,
truth = implies(truth,implies(b,sFlat3)),
inference(step,[status(thm)],[t10674,t31]) ).
cnf(t17096,plain,
truth = implies(b,sFlat3),
inference(step,[status(thm)],[t17095,t19]) ).
cnf(t10768,plain,
implies(b,sFlat3) = truth,
inference(orient,[status(thm)],[t17096]) ).
cnf(t10794,plain,
implies(implies(sFlat3,b),b) = implies(truth,sFlat3),
inference(cp,[status(thm)],[t55,t10768]) ).
cnf(t17118,plain,
implies(implies(sFlat3,b),b) = sFlat3,
inference(step,[status(thm)],[t10794,t19]) ).
cnf(t11297,plain,
implies(implies(sFlat3,b),b) = sFlat3,
inference(orient,[status(thm)],[t17118]) ).
cnf(t11777,plain,
truth = implies(not(sFlat3),sFlat3),
inference(cp,[status(thm)],[t11776,t11297]) ).
cnf(t11809,plain,
implies(not(sFlat3),sFlat3) = truth,
inference(orient,[status(thm)],[t11777]) ).
cnf(t14856,plain,
implies(sFlat3,not(implies(sFlat3,not(sFlat3)))) = implies(not(sFlat3),not(truth)),
inference(cp,[status(thm)],[t14827,t11809]) ).
cnf(t17258,plain,
implies(sFlat3,not(implies(sFlat3,not(sFlat3)))) = implies(truth,sFlat3),
inference(step,[status(thm)],[t14856,t25]) ).
cnf(t17259,plain,
implies(sFlat3,not(implies(sFlat3,not(sFlat3)))) = sFlat3,
inference(step,[status(thm)],[t17258,t19]) ).
cnf(t16056,plain,
implies(sFlat3,not(implies(sFlat3,not(sFlat3)))) = sFlat3,
inference(orient,[status(thm)],[t17259]) ).
cnf(t12,axiom,
ifeq(implies(X1,X2),implies(X2,X3),implies(X1,X3),truth) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t177,plain,
ifeq(implies(X1,X2),implies(X2,X3),implies(X1,X3),truth) = truth,
inference(orient,[status(thm)],[t12]) ).
cnf(t187,plain,
truth = ifeq(X1,implies(X1,X2),implies(truth,X2),truth),
inference(cp,[status(thm)],[t177,t19]) ).
cnf(t16867,plain,
truth = ifeq(X1,implies(X1,X2),X2,truth),
inference(step,[status(thm)],[t187,t19]) ).
cnf(t711,plain,
ifeq(X1,implies(X1,X2),X2,truth) = truth,
inference(orient,[status(thm)],[t16867]) ).
cnf(t16062,plain,
truth = ifeq(sFlat3,sFlat3,not(implies(sFlat3,not(sFlat3))),truth),
inference(cp,[status(thm)],[t711,t16056]) ).
cnf(t4,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t17260,plain,
truth = not(implies(sFlat3,not(sFlat3))),
inference(step,[status(thm)],[t16062,t21]) ).
cnf(t16088,plain,
not(implies(sFlat3,not(sFlat3))) = truth,
inference(orient,[status(thm)],[t17260]) ).
cnf(t17261,plain,
implies(sFlat3,truth) = sFlat3,
inference(step,[status(thm)],[t16056,t16088]) ).
cnf(t17262,plain,
truth = sFlat3,
inference(step,[status(thm)],[t17261,t48]) ).
cnf(t16130,plain,
truth = sFlat3,
inference(rw,[status(thm)],[t17262]) ).
cnf(t16131,plain,
truth = sFlat3,
inference(orient,[status(thm)],[t16130]) ).
cnf(goal_0,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
implies(a,implies(implies(implies(b,a),implies(a,b)),b)) != truth,
inference(rw,[status(thm)],[goal_0,t13098]) ).
cnf(g0_1,plain,
implies(implies(implies(b,a),implies(a,b)),sFlat0) != truth,
inference(rw,[status(thm)],[g0_0,t416]) ).
cnf(g0_2,plain,
implies(implies(a,implies(implies(b,a),b)),sFlat0) != truth,
inference(rw,[status(thm)],[g0_1,t31]) ).
cnf(g0_3,plain,
implies(implies(implies(b,a),sFlat0),sFlat0) != truth,
inference(rw,[status(thm)],[g0_2,t416]) ).
cnf(g0_4,plain,
implies(implies(sFlat1,sFlat0),sFlat0) != truth,
inference(rw,[status(thm)],[g0_3,t152]) ).
cnf(g0_5,plain,
implies(implies(sFlat0,sFlat1),sFlat1) != truth,
inference(rw,[status(thm)],[g0_4,t55]) ).
cnf(g0_6,plain,
implies(sFlat2,sFlat1) != truth,
inference(rw,[status(thm)],[g0_5,t259]) ).
cnf(g0_7,plain,
sFlat3 != truth,
inference(rw,[status(thm)],[g0_6,t10583]) ).
cnf(g0_8,plain,
sFlat3 != sFlat3,
inference(rw,[status(thm)],[g0_7,t16131]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % 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 21:58:04 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 21.34/3.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.34/3.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------