%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL163-1 : 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 : n009.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 0.12s 0.48s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 47 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 13 ( 13 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
! [VAR_0] : not(VAR_0) = xor(VAR_0,truth),
file('theBenchmark.p',axiom_1) ).
cnf(c_1,plain,
not(A) = xor(A,truth),
inference(clausify,[status(thm)],[axiom_1]) ).
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_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(axiom_8,axiom,
! [VAR_0,VAR_1] : and_star(xor(and_star(xor(truth,VAR_0),VAR_1),truth),VAR_1) = and_star(xor(and_star(xor(truth,VAR_1),VAR_0),truth),VAR_0),
file('theBenchmark.p',axiom_8) ).
cnf(c_9,plain,
and_star(xor(and_star(xor(truth,A),B),truth),B) = and_star(xor(and_star(xor(truth,B),A),truth),A),
inference(clausify,[status(thm)],[axiom_8]) ).
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(implies(x,y),y) != implies(implies(y,x),x),
file('theBenchmark.p',prove_wajsberg_axiom) ).
cnf(c_15,plain,
implies(implies(x,y),y) != implies(implies(y,x),x),
inference(clausify,[status(thm)],[prove_wajsberg_axiom]) ).
cnf(c_261,plain,
implies(xor(truth,and_star(x,xor(truth,y))),y) != implies(implies(y,x),x),
inference(paramod,[status(thm)],[c_14,c_15]) ).
cnf(c_262,plain,
xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,y))) != implies(implies(y,x),x),
inference(paramod,[status(thm)],[c_14,c_261]) ).
cnf(c_263,plain,
xor(truth,and_star(xor(truth,y),xor(truth,and_star(x,xor(truth,y))))) != implies(implies(y,x),x),
inference(paramod,[status(thm)],[c_12,c_262]) ).
cnf(c_264,plain,
xor(truth,and_star(xor(truth,y),xor(truth,and_star(x,xor(truth,y))))) != implies(xor(truth,and_star(y,xor(truth,x))),x),
inference(paramod,[status(thm)],[c_14,c_263]) ).
cnf(c_265,plain,
xor(truth,and_star(xor(truth,y),xor(truth,and_star(x,xor(truth,y))))) != xor(truth,and_star(xor(truth,and_star(y,xor(truth,x))),xor(truth,x))),
inference(paramod,[status(thm)],[c_14,c_264]) ).
cnf(c_16,plain,
xor(truth,and_star(xor(truth,y),xor(truth,and_star(x,xor(truth,y))))) != xor(truth,and_star(xor(truth,x),xor(truth,and_star(y,xor(truth,x))))),
inference(paramod,[status(thm)],[c_12,c_265]) ).
cnf(c_266,plain,
and_star(xor(truth,and_star(xor(truth,A),B)),B) = and_star(xor(and_star(xor(truth,B),A),truth),A),
inference(paramod,[status(thm)],[c_10,c_9]) ).
cnf(c_267,plain,
and_star(B,xor(truth,and_star(xor(truth,A),B))) = and_star(xor(and_star(xor(truth,B),A),truth),A),
inference(paramod,[status(thm)],[c_12,c_266]) ).
cnf(c_268,plain,
and_star(B,xor(truth,and_star(xor(truth,A),B))) = and_star(xor(truth,and_star(xor(truth,B),A)),A),
inference(paramod,[status(thm)],[c_10,c_267]) ).
cnf(c_17,plain,
and_star(A,xor(truth,and_star(xor(truth,B),A))) = and_star(B,xor(truth,and_star(xor(truth,A),B))),
inference(paramod,[status(thm)],[c_12,c_268]) ).
cnf(c_269,plain,
not(xor(A,truth)) = xor(A,xor(truth,truth)),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_270,plain,
xor(xor(A,truth),truth) = xor(A,xor(truth,truth)),
inference(paramod,[status(thm)],[c_1,c_269]) ).
cnf(c_271,plain,
xor(truth,xor(A,truth)) = xor(A,xor(truth,truth)),
inference(paramod,[status(thm)],[c_10,c_270]) ).
cnf(c_272,plain,
xor(truth,xor(A,truth)) = xor(A,falsehood),
inference(paramod,[status(thm)],[c_3,c_271]) ).
cnf(c_19,plain,
xor(truth,xor(A,truth)) = A,
inference(paramod,[status(thm)],[c_2,c_272]) ).
cnf(c_21,plain,
xor(falsehood,A) = xor(truth,xor(truth,A)),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_273,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_273]) ).
cnf(c_274,plain,
and_star(A,xor(truth,and_star(A,xor(truth,B)))) = and_star(B,xor(truth,and_star(xor(truth,A),B))),
inference(paramod,[status(thm)],[c_12,c_17]) ).
cnf(c_40,plain,
and_star(A,xor(truth,and_star(xor(truth,B),A))) = and_star(B,xor(truth,and_star(B,xor(truth,A)))),
inference(copy,[status(thm)],[c_274]) ).
cnf(c_275,plain,
and_star(A,xor(truth,and_star(B,A))) = and_star(xor(B,truth),xor(truth,and_star(xor(B,truth),xor(truth,A)))),
inference(paramod,[status(thm)],[c_19,c_40]) ).
cnf(c_85,plain,
and_star(xor(A,truth),xor(truth,and_star(xor(A,truth),xor(truth,B)))) = and_star(B,xor(truth,and_star(A,B))),
inference(copy,[status(thm)],[c_275]) ).
cnf(c_276,plain,
xor(truth,and_star(xor(x,truth),xor(truth,and_star(xor(x,truth),xor(truth,xor(truth,y)))))) != xor(truth,and_star(xor(truth,x),xor(truth,and_star(y,xor(truth,x))))),
inference(paramod,[status(thm)],[c_85,c_16]) ).
cnf(c_277,plain,
xor(truth,and_star(xor(truth,x),xor(truth,and_star(xor(x,truth),xor(truth,xor(truth,y)))))) != xor(truth,and_star(xor(truth,x),xor(truth,and_star(y,xor(truth,x))))),
inference(paramod,[status(thm)],[c_10,c_276]) ).
cnf(c_278,plain,
xor(truth,and_star(xor(truth,x),xor(truth,and_star(xor(truth,x),xor(truth,xor(truth,y)))))) != xor(truth,and_star(xor(truth,x),xor(truth,and_star(y,xor(truth,x))))),
inference(paramod,[status(thm)],[c_10,c_277]) ).
cnf(c_279,plain,
xor(truth,and_star(xor(truth,x),xor(truth,and_star(xor(truth,x),y)))) != xor(truth,and_star(xor(truth,x),xor(truth,and_star(y,xor(truth,x))))),
inference(paramod,[status(thm)],[c_24,c_278]) ).
cnf(c_280,plain,
xor(truth,and_star(xor(truth,x),xor(truth,and_star(y,xor(truth,x))))) != xor(truth,and_star(xor(truth,x),xor(truth,and_star(y,xor(truth,x))))),
inference(paramod,[status(thm)],[c_12,c_279]) ).
cnf(c_260,plain,
$false,
inference(copy,[status(thm)],[c_280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL163-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 21:56:44 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2646469 was started by sandbox2 on n009,
% 0.08/0.35 % Fri Sep 25 21:56:44 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.48
% 0.12/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.48
% 0.12/0.48 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.12/0.48 % Length of proof is 18.
% 0.12/0.48 % Level of proof is 4.
% 0.12/0.48 % Maximum clause weight is 57.000.
% 0.12/0.48 % Given clauses 55.
% 0.12/0.48
% 0.12/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------