%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL145-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 02:01:04 PM UTC 2026
% Result : Unsatisfiable 6.91s 1.32s
% Output : Proof 6.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 7
% Syntax : Number of formulae : 123 ( 123 unt; 0 def)
% Number of atoms : 123 ( 122 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 203 ( 35 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
big_hat(X,Y) = not(big_V(not(X),not(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_hat_definition) ).
fof(f5_nnf,plain,
! [X,Y] : big_hat(X,Y) = not(big_V(not(X),not(Y))),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] : big_hat(X,Y) = not(big_V(not(X),not(Y))),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
big_hat(X0,X1) = not(big_V(not(X0),not(X1))),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t5,plain,
not(big_V(not(X1),not(X2))) = big_hat(X1,X2),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t48,plain,
not(big_V(not(X1),not(X2))) = big_hat(X1,X2),
inference(orient,[status(thm)],[t5]) ).
cnf(f4,axiom,
big_V(X,Y) = implies(implies(X,Y),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',big_V_definition) ).
fof(f4_nnf,plain,
! [X,Y] : big_V(X,Y) = implies(implies(X,Y),Y),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : big_V(X,Y) = implies(implies(X,Y),Y),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
big_V(X0,X1) = implies(implies(X0,X1),X1),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t4,plain,
implies(implies(X1,X2),X2) = big_V(X1,X2),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t17,plain,
implies(implies(X1,X2),X2) = big_V(X1,X2),
inference(orient,[status(thm)],[t4]) ).
cnf(f1,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
fof(f1_nnf,plain,
! [X,Y,Z] : implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t11,plain,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t21,plain,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
inference(orient,[status(thm)],[t11]) ).
cnf(f0,axiom,
implies(truth,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
fof(f0_nnf,plain,
! [X] : implies(truth,X) = X,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : implies(truth,X) = X,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
implies(truth,X0) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t0,plain,
implies(truth,X1) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t13,plain,
implies(truth,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t22,plain,
truth = implies(X1,implies(implies(X1,X2),implies(truth,X2))),
inference(cp,[status(thm)],[t21,t13]) ).
cnf(t1670,plain,
truth = implies(X1,implies(implies(X1,X2),X2)),
inference(step,[status(thm)],[t22,t13]) ).
cnf(t1671,plain,
truth = implies(X1,big_V(X1,X2)),
inference(step,[status(thm)],[t1670,t17]) ).
cnf(t79,plain,
implies(X1,big_V(X1,X2)) = truth,
inference(orient,[status(thm)],[t1671]) ).
cnf(t84,plain,
truth = implies(truth,implies(implies(big_V(X1,X2),X3),implies(X1,X3))),
inference(cp,[status(thm)],[t21,t79]) ).
cnf(t1692,plain,
truth = implies(implies(big_V(X1,X2),X3),implies(X1,X3)),
inference(step,[status(thm)],[t84,t13]) ).
cnf(t251,plain,
implies(implies(big_V(X1,X2),X3),implies(X1,X3)) = truth,
inference(orient,[status(thm)],[t1692]) ).
cnf(f2,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f2_nnf,plain,
! [X,Y] : implies(implies(X,Y),Y) = implies(implies(Y,X),X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : implies(implies(X,Y),Y) = implies(implies(Y,X),X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t8,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t15,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t1668,plain,
big_V(X1,X2) = implies(implies(X2,X1),X1),
inference(step,[status(thm)],[t15,t17]) ).
cnf(t1669,plain,
big_V(X1,X2) = big_V(X2,X1),
inference(step,[status(thm)],[t1668,t17]) ).
cnf(t20,plain,
big_V(X1,X2) = big_V(X2,X1),
inference(rw,[status(thm)],[t1669]) ).
cnf(t105,plain,
big_V(X1,X2) = big_V(X2,X1),
inference(orient,[status(thm)],[t20]) ).
cnf(t108,plain,
truth = implies(X1,big_V(X2,X1)),
inference(cp,[status(thm)],[t79,t105]) ).
cnf(t122,plain,
implies(X1,big_V(X2,X1)) = truth,
inference(orient,[status(thm)],[t108]) ).
cnf(t254,plain,
truth = implies(truth,implies(X1,big_V(X2,big_V(X1,X3)))),
inference(cp,[status(thm)],[t251,t122]) ).
cnf(t1695,plain,
truth = implies(X1,big_V(X2,big_V(X1,X3))),
inference(step,[status(thm)],[t254,t13]) ).
cnf(t297,plain,
implies(X1,big_V(X2,big_V(X1,X3))) = truth,
inference(orient,[status(thm)],[t1695]) ).
cnf(t80,plain,
truth = big_V(truth,X1),
inference(cp,[status(thm)],[t79,t13]) ).
cnf(t92,plain,
big_V(truth,X1) = truth,
inference(orient,[status(thm)],[t80]) ).
cnf(t106,plain,
big_V(X1,truth) = truth,
inference(cp,[status(thm)],[t105,t92]) ).
cnf(t110,plain,
big_V(X1,truth) = truth,
inference(orient,[status(thm)],[t106]) ).
cnf(t112,plain,
truth = implies(X1,truth),
inference(cp,[status(thm)],[t79,t110]) ).
cnf(t116,plain,
implies(X1,truth) = truth,
inference(orient,[status(thm)],[t112]) ).
cnf(t117,plain,
truth = implies(truth,implies(implies(truth,X1),implies(X2,X1))),
inference(cp,[status(thm)],[t21,t116]) ).
cnf(t1677,plain,
truth = implies(implies(truth,X1),implies(X2,X1)),
inference(step,[status(thm)],[t117,t13]) ).
cnf(t1678,plain,
truth = implies(X1,implies(X2,X1)),
inference(step,[status(thm)],[t1677,t13]) ).
cnf(t128,plain,
implies(X1,implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t1678]) ).
cnf(t129,plain,
big_V(X1,implies(X2,X1)) = implies(truth,implies(X2,X1)),
inference(cp,[status(thm)],[t17,t128]) ).
cnf(t1683,plain,
big_V(X1,implies(X2,X1)) = implies(X2,X1),
inference(step,[status(thm)],[t129,t13]) ).
cnf(t150,plain,
big_V(X1,implies(X2,X1)) = implies(X2,X1),
inference(orient,[status(thm)],[t1683]) ).
cnf(t298,plain,
truth = implies(X1,big_V(X2,implies(X3,X1))),
inference(cp,[status(thm)],[t297,t150]) ).
cnf(t410,plain,
implies(X1,big_V(X2,implies(X3,X1))) = truth,
inference(orient,[status(thm)],[t298]) ).
cnf(f3,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).
fof(f3_nnf,plain,
! [X,Y] : implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t9,plain,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t33,plain,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t9]) ).
cnf(t34,plain,
truth = implies(implies(not(X1),not(truth)),X1),
inference(cp,[status(thm)],[t33,t13]) ).
cnf(t176,plain,
implies(implies(not(X1),not(truth)),X1) = truth,
inference(orient,[status(thm)],[t34]) ).
cnf(t180,plain,
big_V(implies(not(X1),not(truth)),X1) = implies(truth,X1),
inference(cp,[status(thm)],[t17,t176]) ).
cnf(t1690,plain,
big_V(X1,implies(not(X1),not(truth))) = implies(truth,X1),
inference(step,[status(thm)],[t180,t105]) ).
cnf(t1691,plain,
big_V(X1,implies(not(X1),not(truth))) = X1,
inference(step,[status(thm)],[t1690,t13]) ).
cnf(t214,plain,
big_V(X1,implies(not(X1),not(truth))) = X1,
inference(orient,[status(thm)],[t1691]) ).
cnf(t411,plain,
truth = implies(not(truth),X1),
inference(cp,[status(thm)],[t410,t214]) ).
cnf(t423,plain,
implies(not(truth),X1) = truth,
inference(orient,[status(thm)],[t411]) ).
cnf(t424,plain,
big_V(not(truth),X1) = implies(truth,X1),
inference(cp,[status(thm)],[t17,t423]) ).
cnf(t1699,plain,
big_V(not(truth),X1) = X1,
inference(step,[status(thm)],[t424,t13]) ).
cnf(t435,plain,
big_V(not(truth),X1) = X1,
inference(orient,[status(thm)],[t1699]) ).
cnf(t442,plain,
big_hat(truth,X1) = not(not(X1)),
inference(cp,[status(thm)],[t48,t435]) ).
cnf(t443,plain,
not(not(X1)) = big_hat(truth,X1),
inference(orient,[status(thm)],[t442]) ).
cnf(t456,plain,
big_hat(X1,not(X2)) = not(big_V(not(X1),big_hat(truth,X2))),
inference(cp,[status(thm)],[t48,t443]) ).
cnf(t625,plain,
not(big_V(not(X1),big_hat(truth,X2))) = big_hat(X1,not(X2)),
inference(orient,[status(thm)],[t456]) ).
cnf(t132,plain,
truth = implies(truth,implies(implies(implies(X1,X2),X3),implies(X2,X3))),
inference(cp,[status(thm)],[t21,t128]) ).
cnf(t1731,plain,
truth = implies(implies(implies(X1,X2),X3),implies(X2,X3)),
inference(step,[status(thm)],[t132,t13]) ).
cnf(t1178,plain,
implies(implies(implies(X1,X2),X3),implies(X2,X3)) = truth,
inference(orient,[status(thm)],[t1731]) ).
cnf(t1181,plain,
truth = implies(truth,implies(not(X1),implies(X1,X2))),
inference(cp,[status(thm)],[t1178,t33]) ).
cnf(t1732,plain,
truth = implies(not(X1),implies(X1,X2)),
inference(step,[status(thm)],[t1181,t13]) ).
cnf(t1210,plain,
implies(not(X1),implies(X1,X2)) = truth,
inference(orient,[status(thm)],[t1732]) ).
cnf(t1224,plain,
truth = implies(not(implies(X1,X2)),big_V(X1,X2)),
inference(cp,[status(thm)],[t1210,t17]) ).
cnf(t1361,plain,
implies(not(implies(X1,X2)),big_V(X1,X2)) = truth,
inference(orient,[status(thm)],[t1224]) ).
cnf(t437,plain,
X1 = big_V(X1,not(truth)),
inference(cp,[status(thm)],[t435,t105]) ).
cnf(t461,plain,
big_V(X1,not(truth)) = X1,
inference(orient,[status(thm)],[t437]) ).
cnf(t1365,plain,
truth = implies(not(implies(X1,not(truth))),X1),
inference(cp,[status(thm)],[t1361,t461]) ).
cnf(t1383,plain,
implies(not(implies(X1,not(truth))),X1) = truth,
inference(orient,[status(thm)],[t1365]) ).
cnf(t1398,plain,
truth = implies(truth,implies(X1,implies(not(X1),not(truth)))),
inference(cp,[status(thm)],[t33,t1383]) ).
cnf(t1738,plain,
truth = implies(X1,implies(not(X1),not(truth))),
inference(step,[status(thm)],[t1398,t13]) ).
cnf(t1426,plain,
implies(X1,implies(not(X1),not(truth))) = truth,
inference(orient,[status(thm)],[t1738]) ).
cnf(t1438,plain,
big_V(X1,implies(not(X1),not(truth))) = implies(truth,implies(not(X1),not(truth))),
inference(cp,[status(thm)],[t17,t1426]) ).
cnf(t1739,plain,
X1 = implies(truth,implies(not(X1),not(truth))),
inference(step,[status(thm)],[t1438,t214]) ).
cnf(t1740,plain,
X1 = implies(not(X1),not(truth)),
inference(step,[status(thm)],[t1739,t13]) ).
cnf(t1455,plain,
implies(not(X1),not(truth)) = X1,
inference(orient,[status(thm)],[t1740]) ).
cnf(t1467,plain,
big_V(not(X1),not(truth)) = implies(X1,not(truth)),
inference(cp,[status(thm)],[t17,t1455]) ).
cnf(t1741,plain,
not(X1) = implies(X1,not(truth)),
inference(step,[status(thm)],[t1467,t461]) ).
cnf(t1498,plain,
implies(X1,not(truth)) = not(X1),
inference(orient,[status(thm)],[t1741]) ).
cnf(t1499,plain,
not(implies(X1,not(truth))) = big_V(X1,not(truth)),
inference(cp,[status(thm)],[t1498,t17]) ).
cnf(t1753,plain,
not(not(X1)) = big_V(X1,not(truth)),
inference(step,[status(thm)],[t1499,t1498]) ).
cnf(t1754,plain,
big_hat(truth,X1) = big_V(X1,not(truth)),
inference(step,[status(thm)],[t1753,t443]) ).
cnf(t1755,plain,
big_hat(truth,X1) = X1,
inference(step,[status(thm)],[t1754,t461]) ).
cnf(t1528,plain,
big_hat(truth,X1) = X1,
inference(orient,[status(thm)],[t1755]) ).
cnf(t1764,plain,
not(big_V(not(X1),X2)) = big_hat(X1,not(X2)),
inference(step,[status(thm)],[t625,t1528]) ).
cnf(t1538,plain,
not(big_V(not(X1),X2)) = big_hat(X1,not(X2)),
inference(rw,[status(thm)],[t1764]) ).
cnf(t1570,plain,
not(big_V(not(X1),X2)) = big_hat(X1,not(X2)),
inference(orient,[status(thm)],[t1538]) ).
cnf(t1756,plain,
not(not(X1)) = X1,
inference(step,[status(thm)],[t443,t1528]) ).
cnf(t1529,plain,
not(not(X1)) = X1,
inference(orient,[status(thm)],[t1756]) ).
cnf(t1585,plain,
big_hat(not(X1),not(X2)) = not(big_V(X1,X2)),
inference(cp,[status(thm)],[t1570,t1529]) ).
cnf(t1662,plain,
big_hat(not(X1),not(X2)) = not(big_V(X1,X2)),
inference(orient,[status(thm)],[t1585]) ).
cnf(f8,negated_conjecture,
not(big_V(x,y)) != big_hat(not(x),not(y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
fof(f8_nnf,plain,
not(big_V(x,y)) != big_hat(not(x),not(y)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
not(big_V(x,y)) != big_hat(not(x),not(y)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
not(big_V(x,y)) != big_hat(not(x),not(y)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
big_hat(not(x),not(y)) != not(big_V(x,y)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
not(big_V(x,y)) != not(big_V(x,y)),
inference(rw,[status(thm)],[goal_0,t1662]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL145-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 22:07:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.91/1.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.91/1.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------