%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : Sun Sep 27 07:53:51 AM UTC 2026
% Result : Unsatisfiable 5.34s 24.01s
% Output : CNFRefutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of clauses : 101 ( 68 unt; 0 nHn; 28 RR)
% Number of literals : 135 ( 86 equ; 36 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 165 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_wajsberg_theorem,negated_conjecture,
not('big$uhat'(x,y)) != 'big$uV'(not(x),not(y)) ).
cnf(wajsberg_1,axiom,
implies(truth,X0) = X0 ).
cnf(wajsberg_2,axiom,
implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth ).
cnf(big_V_definition,axiom,
'big$uV'(X0,X1) = implies(implies(X0,X1),X1) ).
cnf(big_hat_definition,axiom,
'big$uhat'(X0,X1) = not('big$uV'(not(X0),not(X1))) ).
cnf(partial_order_definition1,axiom,
( implies(X0,X1) = truth
| ~ ordered(X0,X1) ) ).
cnf(partial_order_definition2,axiom,
( ordered(X0,X1)
| implies(X0,X1) != truth ) ).
cnf(c0,plain,
not('big$uhat'(x,y)) != 'big$uV'(not(x),not(y)),
inference(clausification,[status(esa)],[prove_wajsberg_theorem]) ).
cnf(c1,plain,
implies(truth,X0) = X0,
inference(clausification,[status(esa)],[wajsberg_1]) ).
cnf(c2,plain,
implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(clausification,[status(esa)],[wajsberg_2]) ).
cnf(c3,plain,
implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(clausification,[status(esa)],[wajsberg_3]) ).
cnf(c4,plain,
implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(clausification,[status(esa)],[wajsberg_4]) ).
cnf(c5,plain,
'big$uV'(X0,X1) = implies(implies(X0,X1),X1),
inference(clausification,[status(esa)],[big_V_definition]) ).
cnf(c6,plain,
'big$uhat'(X0,X1) = not('big$uV'(not(X0),not(X1))),
inference(clausification,[status(esa)],[big_hat_definition]) ).
cnf(c7,plain,
( implies(X0,X1) = truth
| ~ ordered(X0,X1) ),
inference(clausification,[status(esa)],[partial_order_definition1]) ).
cnf(c8,plain,
( ordered(X0,X1)
| implies(X0,X1) != truth ),
inference(clausification,[status(esa)],[partial_order_definition2]) ).
cnf(d0,plain,
'big$uV'(X0,X1) = implies(implies(X1,X0),X0),
inference(demodulation,[status(thm)],[c3,c5]) ).
cnf(d1,plain,
'big$uV'(X0,X1) = 'big$uV'(X1,X0),
inference(superposition,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
( ~ ordered(X0,X1)
| 'big$uV'(X0,X1) = implies(truth,X1) ),
inference(superposition,[status(thm)],[c7,c5]) ).
cnf(d3,plain,
( ~ ordered(X1,X0)
| 'big$uV'(X1,X0) = X0 ),
inference(demodulation,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
( ~ ordered(X0,X1)
| 'big$uV'(X1,X0) = X1 ),
inference(superposition,[status(thm)],[d1,d3]) ).
cnf(d5,plain,
( ~ ordered(X1,X0)
| X0 = 'big$uV'(X1,X0) ),
inference(superposition,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d7,plain,
implies(X1,implies(implies(X1,X0),X0)) = truth,
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
implies(X0,'big$uV'(X0,X1)) = truth,
inference(demodulation,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
truth = 'big$uV'(truth,X0),
inference(superposition,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
truth = 'big$uV'(X0,truth),
inference(superposition,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
implies(X0,truth) = truth,
inference(superposition,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
implies(implies(X1,truth),implies(X0,implies(X1,X0))) = truth,
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d13,plain,
implies(truth,implies(X1,implies(X0,X1))) = truth,
inference(demodulation,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
implies(X0,implies(X1,X0)) = truth,
inference(demodulation,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
( ordered(X0,implies(X1,X0))
| truth != truth ),
inference(superposition,[status(thm)],[d14,c8]) ).
cnf(d16,plain,
'big$uV'(truth,X0) = implies(X0,X0),
inference(superposition,[status(thm)],[c1,c5]) ).
cnf(d17,plain,
'big$uV'(X0,X0) = implies('big$uV'(truth,X0),X0),
inference(superposition,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
'big$uV'(X0,X0) = implies(implies(X0,X0),X0),
inference(superposition,[status(thm)],[d16,d17]) ).
cnf(d19,plain,
'big$uV'(X0,X0) = 'big$uV'(X0,X0),
inference(demodulation,[status(thm)],[d18,c5]) ).
cnf(d20,plain,
implies(truth,truth) = 'big$uV'(truth,truth),
inference(superposition,[status(thm)],[d16,d19]) ).
cnf(d21,plain,
truth = 'big$uV'(truth,truth),
inference(demodulation,[status(thm)],[d20,c1]) ).
cnf(d22,plain,
truth = implies(truth,truth),
inference(demodulation,[status(thm)],[d21,d16]) ).
cnf(d23,plain,
truth = truth,
inference(demodulation,[status(thm)],[d22,c1]) ).
cnf(d24,plain,
ordered(X0,implies(X1,X0)),
inference(resolution,[status(thm)],[d23,d15]) ).
cnf(d25,plain,
( ~ ordered(X1,X0)
| ~ ordered(X0,X1)
| X0 = X1 ),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d26,plain,
( ~ ordered(implies(X1,X0),X0)
| X0 = implies(X1,X0) ),
inference(resolution,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
( ordered(X0,'big$uV'(X0,X1))
| truth != truth ),
inference(superposition,[status(thm)],[d8,c8]) ).
cnf(d28,plain,
ordered(X0,'big$uV'(X0,X1)),
inference(resolution,[status(thm)],[d23,d27]) ).
cnf(d29,plain,
ordered(X0,'big$uV'(X1,X0)),
inference(superposition,[status(thm)],[d1,d28]) ).
cnf(d30,plain,
'big$uV'(implies(X0,X1),X1) = implies('big$uV'(X0,X1),X1),
inference(superposition,[status(thm)],[c5,c5]) ).
cnf(d31,plain,
'big$uV'(X1,implies(X0,X1)) = implies('big$uV'(X0,X1),X1),
inference(demodulation,[status(thm)],[d30,d1]) ).
cnf(d32,plain,
ordered(implies(X1,X0),implies('big$uV'(X1,X0),X0)),
inference(superposition,[status(thm)],[d31,d29]) ).
cnf(d33,plain,
( ~ ordered(X0,X1)
| implies(truth,implies(implies(X1,X2),implies(X0,X2))) = truth ),
inference(superposition,[status(thm)],[c7,c2]) ).
cnf(d34,plain,
( ~ ordered(X2,X0)
| implies(implies(X0,X1),implies(X2,X1)) = truth ),
inference(demodulation,[status(thm)],[d33,c1]) ).
cnf(d35,plain,
( ~ ordered(truth,X1)
| implies(implies(X1,X0),X0) = truth ),
inference(superposition,[status(thm)],[c1,d34]) ).
cnf(d36,plain,
( ~ ordered(truth,X0)
| 'big$uV'(X0,X1) = truth ),
inference(demodulation,[status(thm)],[d35,c5]) ).
cnf(d37,plain,
( ~ ordered(truth,X0)
| ordered(implies(X0,X1),implies(truth,X1)) ),
inference(superposition,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
( ~ ordered(truth,X1)
| ordered(implies(X1,X0),X0) ),
inference(demodulation,[status(thm)],[d37,c1]) ).
cnf(d39,plain,
( X1 = implies(X0,X1)
| ~ ordered(truth,X0) ),
inference(resolution,[status(thm)],[d38,d26]) ).
cnf(d40,plain,
( ~ ordered(truth,implies(X0,X1))
| 'big$uV'(X0,X1) = X1 ),
inference(superposition,[status(thm)],[d39,c5]) ).
cnf(d41,plain,
( ordered(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))
| truth != truth ),
inference(superposition,[status(thm)],[c2,c8]) ).
cnf(d42,plain,
ordered(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(resolution,[status(thm)],[d23,d41]) ).
cnf(d43,plain,
ordered(implies(X2,implies(not(X0),not(X1))),implies(truth,implies(X2,implies(X1,X0)))),
inference(superposition,[status(thm)],[c4,d42]) ).
cnf(d44,plain,
ordered(implies(X0,implies(not(X2),not(X1))),implies(X0,implies(X1,X2))),
inference(demodulation,[status(thm)],[d43,c1]) ).
cnf(d45,plain,
implies(implies(X2,implies(not(X0),not(X1))),implies(truth,implies(X2,implies(X1,X0)))) = truth,
inference(superposition,[status(thm)],[c4,c2]) ).
cnf(d46,plain,
implies(implies(X0,implies(not(X2),not(X1))),implies(X0,implies(X1,X2))) = truth,
inference(demodulation,[status(thm)],[d45,c1]) ).
cnf(d47,plain,
implies(truth,implies(not(X0),implies(X0,X1))) = truth,
inference(superposition,[status(thm)],[d14,d46]) ).
cnf(d48,plain,
implies(not(X0),implies(X0,X1)) = truth,
inference(demodulation,[status(thm)],[d47,c1]) ).
cnf(d49,plain,
ordered(truth,implies(not(not(X0)),implies(X1,X0))),
inference(superposition,[status(thm)],[d48,d44]) ).
cnf(d50,plain,
'big$uV'(X0,X0) = implies(truth,X0),
inference(demodulation,[status(thm)],[d17,d9]) ).
cnf(d51,plain,
'big$uV'(X0,X0) = X0,
inference(demodulation,[status(thm)],[d50,c1]) ).
cnf(d52,plain,
truth = implies(X0,X0),
inference(demodulation,[status(thm)],[d16,d9]) ).
cnf(d53,plain,
'big$uV'(X0,X0) = implies(truth,X0),
inference(superposition,[status(thm)],[d52,d0]) ).
cnf(d54,plain,
X0 = implies(truth,X0),
inference(demodulation,[status(thm)],[d53,d51]) ).
cnf(d55,plain,
ordered(truth,implies(not(not(X0)),X0)),
inference(superposition,[status(thm)],[d54,d49]) ).
cnf(d56,plain,
'big$uV'(not(not(X0)),X0) = X0,
inference(resolution,[status(thm)],[d55,d40]) ).
cnf(d57,plain,
'big$uV'(X0,not(not(X0))) = X0,
inference(demodulation,[status(thm)],[d56,d1]) ).
cnf(d58,plain,
( ~ ordered(X0,not(not(X0)))
| not(not(X0)) = X0 ),
inference(superposition,[status(thm)],[d57,d5]) ).
cnf(d59,plain,
( ~ ordered(not(X0),not(X1))
| implies(truth,implies(X1,X0)) = truth ),
inference(superposition,[status(thm)],[c7,c4]) ).
cnf(d60,plain,
( ~ ordered(not(X1),not(X0))
| implies(X0,X1) = truth ),
inference(demodulation,[status(thm)],[d59,c1]) ).
cnf(d61,plain,
ordered(not(not(X0)),X0),
inference(superposition,[status(thm)],[d57,d29]) ).
cnf(d62,plain,
implies(X0,not(not(X0))) = truth,
inference(resolution,[status(thm)],[d61,d60]) ).
cnf(d63,plain,
( ordered(X0,not(not(X0)))
| truth != truth ),
inference(superposition,[status(thm)],[d62,c8]) ).
cnf(d64,plain,
( ~ ordered(X0,X0)
| 'big$uV'(truth,X0) = truth ),
inference(superposition,[status(thm)],[d16,c7]) ).
cnf(d65,plain,
( ~ ordered(X0,X0)
| truth = implies(X0,X0) ),
inference(superposition,[status(thm)],[d64,d16]) ).
cnf(d66,plain,
( ~ ordered(X0,X0)
| truth = 'big$uV'(truth,X0) ),
inference(superposition,[status(thm)],[d16,d65]) ).
cnf(d67,plain,
( ~ ordered(X0,X0)
| 'big$uV'(X0,X0) = implies(truth,X0) ),
inference(superposition,[status(thm)],[d66,d17]) ).
cnf(d68,plain,
( ~ ordered(X0,X0)
| X0 = implies(truth,X0) ),
inference(demodulation,[status(thm)],[d67,d51]) ).
cnf(d69,plain,
( ~ ordered(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d68,c1]) ).
cnf(d70,plain,
( ordered(X0,X0)
| 'big$uV'(truth,X0) != truth ),
inference(superposition,[status(thm)],[d16,c8]) ).
cnf(d71,plain,
( ordered(X0,X0)
| truth != truth ),
inference(demodulation,[status(thm)],[d70,d9]) ).
cnf(d72,plain,
ordered(X0,X0),
inference(resolution,[status(thm)],[d23,d71]) ).
cnf(d73,plain,
X0 = X0,
inference(resolution,[status(thm)],[d72,d69]) ).
cnf(d74,plain,
ordered(X0,not(not(X0))),
inference(resolution,[status(thm)],[d73,d63]) ).
cnf(d75,plain,
not(not(X0)) = X0,
inference(resolution,[status(thm)],[d74,d58]) ).
cnf(d76,plain,
'big$uhat'(X0,X0) = not(not(X0)),
inference(superposition,[status(thm)],[d51,c6]) ).
cnf(d77,plain,
'big$uhat'('big$uV'(not(X0),not(X1)),X2) = not('big$uV'('big$uhat'(X0,X1),not(X2))),
inference(superposition,[status(thm)],[c6,c6]) ).
cnf(d78,plain,
not('big$uV'('big$uhat'(X0,X1),not('big$uV'(not(X0),not(X1))))) = not(not('big$uV'(not(X0),not(X1)))),
inference(superposition,[status(thm)],[d77,d76]) ).
cnf(d79,plain,
not('big$uV'('big$uhat'(X0,X1),'big$uhat'(X0,X1))) = not(not('big$uV'(not(X0),not(X1)))),
inference(demodulation,[status(thm)],[d78,c6]) ).
cnf(d80,plain,
not('big$uhat'(X0,X1)) = not(not('big$uV'(not(X0),not(X1)))),
inference(demodulation,[status(thm)],[d79,d51]) ).
cnf(d81,plain,
not('big$uhat'(X0,X1)) = 'big$uV'(not(X0),not(X1)),
inference(demodulation,[status(thm)],[d80,d75]) ).
cnf(d82,plain,
$false,
inference(resolution,[status(thm)],[d81,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL146-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.45 % Computer : n005.cluster.edu
% 0.16/5.45 % Model : x86_64 x86_64
% 0.16/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.45 % Memory : 8046.5625MB
% 0.16/5.45 % OS : Linux 6.8.0-71-generic
% 0.16/5.45 % CPULimit : 300
% 0.16/5.45 % WCLimit : 300
% 0.16/5.45 % DateTime : Fri Sep 25 21:55:37 UTC 2026
% 0.16/5.46 % CPUTime :
% 0.16/5.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.34/24.01 % SZS status Unsatisfiable for theBenchmark.p
% 5.34/24.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------