%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 07:58:06 AM UTC 2026
% Result : Unsatisfiable 13.12s 2.14s
% Output : CNFRefutation 13.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 32 unt; 0 def)
% Number of atoms : 76 ( 38 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 36 ( 14 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 7 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(wajsberg_1,axiom,
! [VAR_0] : implies(truth,VAR_0) = VAR_0,
file('theBenchmark.p',wajsberg_1) ).
cnf(c_1,plain,
implies(truth,A) = A,
inference(clausify,[status(thm)],[wajsberg_1]) ).
fof(wajsberg_2,axiom,
! [VAR_0,VAR_1,VAR_2] : implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2))) = truth,
file('theBenchmark.p',wajsberg_2) ).
cnf(c_2,plain,
implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth,
inference(clausify,[status(thm)],[wajsberg_2]) ).
fof(wajsberg_3,axiom,
! [VAR_0,VAR_1] : implies(implies(VAR_0,VAR_1),VAR_1) = implies(implies(VAR_1,VAR_0),VAR_0),
file('theBenchmark.p',wajsberg_3) ).
cnf(c_3,plain,
implies(implies(A,B),B) = implies(implies(B,A),A),
inference(clausify,[status(thm)],[wajsberg_3]) ).
fof(partial_order_definition1,axiom,
! [VAR_0,VAR_1] :
( implies(VAR_0,VAR_1) = truth
| ~ ordered(VAR_0,VAR_1) ),
file('theBenchmark.p',partial_order_definition1) ).
cnf(c_8,plain,
( implies(A,B) = truth
| ~ ordered(A,B) ),
inference(clausify,[status(thm)],[partial_order_definition1]) ).
fof(partial_order_definition2,axiom,
! [VAR_0,VAR_1] :
( ordered(VAR_0,VAR_1)
| implies(VAR_0,VAR_1) != truth ),
file('theBenchmark.p',partial_order_definition2) ).
cnf(c_9,plain,
( ordered(A,B)
| implies(A,B) != truth ),
inference(clausify,[status(thm)],[partial_order_definition2]) ).
fof(antecedent,axiom,
( ordered(y,implies(x,z))
| ordered(x,implies(y,z)) ),
file('theBenchmark.p',antecedent) ).
cnf(c_10,plain,
( ordered(y,implies(x,z))
| ordered(x,implies(y,z)) ),
inference(clausify,[status(thm)],[antecedent]) ).
fof(prove_wajsberg_theorem,axiom,
( ~ ordered(y,implies(x,z))
| ~ ordered(x,implies(y,z)) ),
file('theBenchmark.p',prove_wajsberg_theorem) ).
cnf(c_11,plain,
( ~ ordered(y,implies(x,z))
| ~ ordered(x,implies(y,z)) ),
inference(clausify,[status(thm)],[prove_wajsberg_theorem]) ).
cnf(c_2085,plain,
implies(A,implies(implies(A,B),implies(truth,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_12,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(paramod,[status(thm)],[c_1,c_2085]) ).
cnf(c_13,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_2086,plain,
implies(A,A) = implies(implies(A,truth),truth),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_15,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(copy,[status(thm)],[c_2086]) ).
cnf(c_2087,plain,
( ordered(truth,A)
| A != truth ),
inference(paramod,[status(thm)],[c_1,c_9]) ).
cnf(c_22,plain,
( ordered(truth,A)
| truth != A ),
inference(copy,[status(thm)],[c_2087]) ).
cnf(c_24,plain,
( implies(x,implies(y,z)) = truth
| ordered(y,implies(x,z)) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_25,plain,
( implies(y,implies(x,z)) = truth
| ordered(x,implies(y,z)) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_2088,plain,
truth = implies(implies(truth,A),A),
inference(paramod,[status(thm)],[c_12,c_1]) ).
cnf(c_2089,plain,
truth = implies(A,A),
inference(paramod,[status(thm)],[c_1,c_2088]) ).
cnf(c_27,plain,
implies(A,A) = truth,
inference(copy,[status(thm)],[c_2089]) ).
cnf(c_30,plain,
implies(implies(A,truth),truth) = truth,
inference(paramod,[status(thm)],[c_27,c_15]) ).
cnf(c_60,plain,
implies(A,truth) = truth,
inference(paramod,[status(thm)],[c_30,c_12]) ).
cnf(c_2090,plain,
implies(truth,implies(B,implies(A,B))) = truth,
inference(paramod,[status(thm)],[c_60,c_13]) ).
cnf(c_63,plain,
implies(A,implies(B,A)) = truth,
inference(paramod,[status(thm)],[c_1,c_2090]) ).
cnf(c_2091,plain,
implies(truth,implies(implies(implies(A,B),C),implies(B,C))) = truth,
inference(paramod,[status(thm)],[c_63,c_2]) ).
cnf(c_73,plain,
implies(implies(implies(A,B),C),implies(B,C)) = truth,
inference(paramod,[status(thm)],[c_1,c_2091]) ).
cnf(c_2092,plain,
( implies(truth,implies(implies(implies(y,z),A),implies(x,A))) = truth
| ordered(y,implies(x,z)) ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_84,plain,
( implies(implies(implies(y,z),A),implies(x,A)) = truth
| ordered(y,implies(x,z)) ),
inference(paramod,[status(thm)],[c_1,c_2092]) ).
cnf(c_2093,plain,
( ordered(truth,A)
| A != truth ),
inference(copy,[status(thm)],[c_22]) ).
cnf(c_90,plain,
( ordered(truth,implies(y,implies(x,z)))
| ordered(x,implies(y,z)) ),
inference(resolve,[status(thm)],[c_25,c_2093]) ).
cnf(c_2094,plain,
( implies(truth,implies(implies(implies(x,z),A),implies(y,A))) = truth
| ordered(x,implies(y,z)) ),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_91,plain,
( implies(implies(implies(x,z),A),implies(y,A)) = truth
| ordered(x,implies(y,z)) ),
inference(paramod,[status(thm)],[c_1,c_2094]) ).
cnf(c_99,plain,
( ~ ordered(y,implies(x,z))
| ordered(truth,implies(y,implies(x,z))) ),
inference(resolve,[status(thm)],[c_90,c_11]) ).
cnf(c_192,plain,
ordered(implies(implies(A,B),C),implies(B,C)),
inference(resolve,[status(thm)],[c_73,c_9]) ).
cnf(c_267,plain,
ordered(implies(implies(implies(A,B),B),C),implies(A,C)),
inference(paramod,[status(thm)],[c_3,c_192]) ).
cnf(c_1903,plain,
( ordered(truth,implies(y,implies(x,z)))
| ordered(y,implies(x,z)) ),
inference(paramod,[status(thm)],[c_84,c_267]) ).
cnf(c_1905,plain,
( ordered(truth,implies(x,implies(y,z)))
| ordered(x,implies(y,z)) ),
inference(paramod,[status(thm)],[c_91,c_267]) ).
cnf(c_2095,plain,
( ordered(truth,implies(y,implies(x,z)))
| ordered(truth,implies(y,implies(x,z))) ),
inference(resolve,[status(thm)],[c_1903,c_99]) ).
cnf(c_1950,plain,
ordered(truth,implies(y,implies(x,z))),
inference(copy,[status(thm)],[c_2095]) ).
cnf(c_2096,plain,
implies(truth,implies(y,implies(x,z))) = truth,
inference(resolve,[status(thm)],[c_1950,c_8]) ).
cnf(c_1954,plain,
implies(y,implies(x,z)) = truth,
inference(paramod,[status(thm)],[c_1,c_2096]) ).
cnf(c_1961,plain,
ordered(y,implies(x,z)),
inference(resolve,[status(thm)],[c_1954,c_9]) ).
cnf(c_1987,plain,
~ ordered(x,implies(y,z)),
inference(resolve,[status(thm)],[c_1961,c_11]) ).
cnf(c_1993,plain,
ordered(truth,implies(x,implies(y,z))),
inference(resolve,[status(thm)],[c_1987,c_1905]) ).
cnf(c_2043,plain,
implies(x,implies(y,z)) != truth,
inference(resolve,[status(thm)],[c_9,c_1987]) ).
cnf(c_2097,plain,
implies(truth,implies(x,implies(y,z))) = truth,
inference(resolve,[status(thm)],[c_1993,c_8]) ).
cnf(c_2098,plain,
implies(x,implies(y,z)) = truth,
inference(paramod,[status(thm)],[c_1,c_2097]) ).
cnf(c_2084,plain,
$false,
inference(resolve,[status(thm)],[c_2043,c_2098]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n016.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 21:59:44 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3393766 was started by sandbox on n016,
% 0.19/0.45 % Fri Sep 25 21:59:44 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 13.12/2.14
% 13.12/2.14 % SZS status Unsatisfiable for theBenchmark
% 13.12/2.14
% 13.12/2.14 % Proof 1 at 0.96 (+ 0.54) seconds.
% 13.12/2.14 % Length of proof is 33.
% 13.12/2.14 % Level of proof is 15.
% 13.12/2.14 % Maximum clause weight is 30.000.
% 13.12/2.14 % Given clauses 356.
% 13.12/2.14
% 13.12/2.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------