%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 07:58:08 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.44s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [VAR_0] : xor(VAR_0,falsehood) = VAR_0,
file('theBenchmark.p',axiom_2) ).
cnf(c_2,plain,
xor(A,falsehood) = A,
inference(clausify,[status(thm)],[axiom_2]) ).
fof(axiom_3,axiom,
! [VAR_0] : xor(VAR_0,VAR_0) = falsehood,
file('theBenchmark.p',axiom_3) ).
cnf(c_3,plain,
xor(A,A) = falsehood,
inference(clausify,[status(thm)],[axiom_3]) ).
fof(axiom_4,axiom,
! [VAR_0] : and_star(VAR_0,truth) = VAR_0,
file('theBenchmark.p',axiom_4) ).
cnf(c_4,plain,
and_star(A,truth) = A,
inference(clausify,[status(thm)],[axiom_4]) ).
fof(axiom_7,axiom,
! [VAR_0,VAR_1] : xor(VAR_0,xor(truth,VAR_1)) = xor(xor(VAR_0,truth),VAR_1),
file('theBenchmark.p',axiom_7) ).
cnf(c_7,plain,
xor(A,xor(truth,B)) = xor(xor(A,truth),B),
inference(clausify,[status(thm)],[axiom_7]) ).
cnf(c_8,plain,
xor(xor(A,truth),B) = xor(A,xor(truth,B)),
inference(copy,[status(thm)],[c_7]) ).
fof(xor_commutativity,axiom,
! [VAR_0,VAR_1] : xor(VAR_0,VAR_1) = xor(VAR_1,VAR_0),
file('theBenchmark.p',xor_commutativity) ).
cnf(c_10,plain,
xor(A,B) = xor(B,A),
inference(clausify,[status(thm)],[xor_commutativity]) ).
fof(and_star_commutativity,axiom,
! [VAR_0,VAR_1] : and_star(VAR_0,VAR_1) = and_star(VAR_1,VAR_0),
file('theBenchmark.p',and_star_commutativity) ).
cnf(c_12,plain,
and_star(A,B) = and_star(B,A),
inference(clausify,[status(thm)],[and_star_commutativity]) ).
fof(implies_definition,axiom,
! [VAR_0,VAR_1] : implies(VAR_0,VAR_1) = xor(truth,and_star(VAR_0,xor(truth,VAR_1))),
file('theBenchmark.p',implies_definition) ).
cnf(c_14,plain,
implies(A,B) = xor(truth,and_star(A,xor(truth,B))),
inference(clausify,[status(thm)],[implies_definition]) ).
fof(prove_wajsberg_axiom,axiom,
implies(truth,x) != x,
file('theBenchmark.p',prove_wajsberg_axiom) ).
cnf(c_15,plain,
implies(truth,x) != x,
inference(clausify,[status(thm)],[prove_wajsberg_axiom]) ).
cnf(c_16,plain,
xor(truth,and_star(truth,xor(truth,x))) != x,
inference(paramod,[status(thm)],[c_14,c_15]) ).
cnf(c_21,plain,
xor(falsehood,A) = xor(truth,xor(truth,A)),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_37,plain,
xor(falsehood,A) = A,
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_24,plain,
xor(truth,xor(truth,A)) = A,
inference(paramod,[status(thm)],[c_21,c_37]) ).
cnf(c_33,plain,
and_star(truth,A) = A,
inference(paramod,[status(thm)],[c_12,c_4]) ).
cnf(c_38,plain,
xor(truth,xor(truth,x)) != x,
inference(paramod,[status(thm)],[c_33,c_16]) ).
cnf(c_39,plain,
x != x,
inference(paramod,[status(thm)],[c_24,c_38]) ).
cnf(c_36,plain,
$false,
inference(copy,[status(thm)],[c_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.42 % Computer : n004.cluster.edu
% 0.07/0.42 % Model : x86_64 x86_64
% 0.07/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.42 % Memory : 8046.5625MB
% 0.07/0.42 % OS : Linux 6.8.0-71-generic
% 0.07/0.42 % CPULimit : 300
% 0.07/0.42 % WCLimit : 300
% 0.07/0.42 % DateTime : Fri Sep 25 21:56:22 UTC 2026
% 0.07/0.43 % CPUTime :
% 0.07/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.43 % Process 56879 was started by sandbox2 on n004,
% 0.07/0.43 % Fri Sep 25 21:56:22 2026
% 0.07/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.43
% 0.07/0.43 % From the command line: assign(max_seconds, 300).
% 0.07/0.44
% 0.07/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.44
% 0.07/0.44 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.07/0.44 % Length of proof is 14.
% 0.07/0.44 % Level of proof is 4.
% 0.07/0.44 % Maximum clause weight is 11.000.
% 0.07/0.44 % Given clauses 9.
% 0.07/0.44
% 0.07/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------