%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL109-6 : 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 : n015.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 07:58:00 AM UTC 2026
% Result : Unsatisfiable 38.00s 5.18s
% Output : CNFRefutation 38.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 12
% Syntax : Number of formulae : 84 ( 84 unt; 0 def)
% Number of atoms : 84 ( 83 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 19 ( 19 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 116 ( 5 sgn 18 !; 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_5,axiom,
! [VAR_0] : and_star(VAR_0,falsehood) = falsehood,
file('theBenchmark.p',axiom_5) ).
cnf(c_5,plain,
and_star(A,falsehood) = falsehood,
inference(clausify,[status(thm)],[axiom_5]) ).
fof(axiom_6,axiom,
! [VAR_0] : and_star(xor(truth,VAR_0),VAR_0) = falsehood,
file('theBenchmark.p',axiom_6) ).
cnf(c_6,plain,
and_star(xor(truth,A),A) = falsehood,
inference(clausify,[status(thm)],[axiom_6]) ).
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_associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : and_star(and_star(VAR_0,VAR_1),VAR_2) = and_star(VAR_0,and_star(VAR_1,VAR_2)),
file('theBenchmark.p',and_star_associativity) ).
cnf(c_11,plain,
and_star(and_star(A,B),C) = and_star(A,and_star(B,C)),
inference(clausify,[status(thm)],[and_star_associativity]) ).
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_mv_4,axiom,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
file('theBenchmark.p',prove_wajsberg_mv_4) ).
cnf(c_15,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
inference(clausify,[status(thm)],[prove_wajsberg_mv_4]) ).
cnf(c_3557,plain,
implies(implies(xor(truth,and_star(a,xor(truth,b))),implies(b,a)),implies(b,a)) != truth,
inference(paramod,[status(thm)],[c_14,c_15]) ).
cnf(c_3558,plain,
implies(implies(xor(truth,and_star(a,xor(truth,b))),xor(truth,and_star(b,xor(truth,a)))),implies(b,a)) != truth,
inference(paramod,[status(thm)],[c_14,c_3557]) ).
cnf(c_3559,plain,
implies(xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))),implies(b,a)) != truth,
inference(paramod,[status(thm)],[c_14,c_3558]) ).
cnf(c_3560,plain,
implies(xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))),xor(truth,and_star(b,xor(truth,a)))) != truth,
inference(paramod,[status(thm)],[c_14,c_3559]) ).
cnf(c_3561,plain,
xor(truth,and_star(xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))) != truth,
inference(paramod,[status(thm)],[c_14,c_3560]) ).
cnf(c_16,plain,
xor(truth,and_star(xor(truth,xor(truth,and_star(b,xor(truth,a)))),xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))))) != truth,
inference(paramod,[status(thm)],[c_12,c_3561]) ).
cnf(c_3562,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_3563,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_3562]) ).
cnf(c_3564,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_3563]) ).
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_3564]) ).
cnf(c_18,plain,
and_star(A,xor(truth,A)) = falsehood,
inference(paramod,[status(thm)],[c_12,c_6]) ).
cnf(c_3565,plain,
xor(falsehood,A) = xor(truth,xor(truth,A)),
inference(paramod,[status(thm)],[c_3,c_8]) ).
cnf(c_21,plain,
xor(truth,xor(truth,A)) = xor(falsehood,A),
inference(copy,[status(thm)],[c_3565]) ).
cnf(c_3566,plain,
xor(truth,and_star(xor(falsehood,and_star(b,xor(truth,a))),xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(truth,xor(truth,and_star(b,xor(truth,a)))))))) != truth,
inference(paramod,[status(thm)],[c_21,c_16]) ).
cnf(c_24,plain,
xor(truth,and_star(xor(falsehood,and_star(b,xor(truth,a))),xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(falsehood,and_star(b,xor(truth,a))))))) != truth,
inference(paramod,[status(thm)],[c_21,c_3566]) ).
cnf(c_25,plain,
xor(falsehood,A) = A,
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_3567,plain,
xor(truth,and_star(and_star(b,xor(truth,a)),xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),xor(falsehood,and_star(b,xor(truth,a))))))) != truth,
inference(paramod,[status(thm)],[c_25,c_24]) ).
cnf(c_3568,plain,
xor(truth,and_star(and_star(b,xor(truth,a)),xor(truth,and_star(xor(truth,and_star(a,xor(truth,b))),and_star(b,xor(truth,a)))))) != truth,
inference(paramod,[status(thm)],[c_25,c_3567]) ).
cnf(c_3569,plain,
xor(truth,and_star(and_star(b,xor(truth,a)),xor(truth,and_star(and_star(b,xor(truth,a)),xor(truth,and_star(a,xor(truth,b))))))) != truth,
inference(paramod,[status(thm)],[c_12,c_3568]) ).
cnf(c_3570,plain,
xor(truth,and_star(and_star(b,xor(truth,a)),xor(truth,and_star(b,and_star(xor(truth,a),xor(truth,and_star(a,xor(truth,b)))))))) != truth,
inference(paramod,[status(thm)],[c_11,c_3569]) ).
cnf(c_29,plain,
xor(truth,and_star(b,and_star(xor(truth,a),xor(truth,and_star(b,and_star(xor(truth,a),xor(truth,and_star(a,xor(truth,b))))))))) != truth,
inference(paramod,[status(thm)],[c_11,c_3570]) ).
cnf(c_30,plain,
xor(truth,xor(truth,A)) = A,
inference(paramod,[status(thm)],[c_25,c_21]) ).
cnf(c_35,plain,
and_star(truth,A) = A,
inference(paramod,[status(thm)],[c_12,c_4]) ).
cnf(c_36,plain,
and_star(falsehood,A) = falsehood,
inference(paramod,[status(thm)],[c_12,c_5]) ).
cnf(c_3571,plain,
and_star(and_star(A,B),C) = and_star(B,and_star(A,C)),
inference(paramod,[status(thm)],[c_12,c_11]) ).
cnf(c_37,plain,
and_star(A,and_star(B,C)) = and_star(B,and_star(A,C)),
inference(paramod,[status(thm)],[c_11,c_3571]) ).
cnf(c_3572,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_42,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_3572]) ).
cnf(c_3573,plain,
and_star(falsehood,A) = and_star(B,and_star(xor(truth,B),A)),
inference(paramod,[status(thm)],[c_18,c_11]) ).
cnf(c_3574,plain,
falsehood = and_star(B,and_star(xor(truth,B),A)),
inference(paramod,[status(thm)],[c_36,c_3573]) ).
cnf(c_46,plain,
and_star(A,and_star(xor(truth,A),B)) = falsehood,
inference(copy,[status(thm)],[c_3574]) ).
cnf(c_3575,plain,
falsehood = and_star(A,and_star(B,xor(truth,and_star(A,B)))),
inference(paramod,[status(thm)],[c_18,c_11]) ).
cnf(c_47,plain,
and_star(A,and_star(B,xor(truth,and_star(A,B)))) = falsehood,
inference(copy,[status(thm)],[c_3575]) ).
cnf(c_3576,plain,
and_star(A,xor(truth,and_star(B,A))) = and_star(xor(truth,B),xor(truth,and_star(xor(truth,A),xor(truth,B)))),
inference(paramod,[status(thm)],[c_30,c_17]) ).
cnf(c_50,plain,
and_star(xor(truth,A),xor(truth,and_star(xor(truth,B),xor(truth,A)))) = and_star(B,xor(truth,and_star(A,B))),
inference(copy,[status(thm)],[c_3576]) ).
cnf(c_52,plain,
and_star(A,and_star(B,xor(truth,A))) = falsehood,
inference(paramod,[status(thm)],[c_12,c_46]) ).
cnf(c_70,plain,
and_star(A,and_star(B,xor(truth,and_star(xor(truth,C),B)))) = and_star(C,and_star(A,xor(truth,and_star(xor(truth,B),C)))),
inference(paramod,[status(thm)],[c_17,c_37]) ).
cnf(c_3577,plain,
and_star(and_star(xor(truth,A),xor(truth,B)),xor(truth,and_star(xor(truth,xor(truth,B)),and_star(xor(truth,A),xor(truth,B))))) = and_star(xor(truth,B),xor(truth,and_star(A,xor(truth,and_star(B,A))))),
inference(paramod,[status(thm)],[c_50,c_42]) ).
cnf(c_3578,plain,
and_star(and_star(xor(truth,A),xor(truth,B)),xor(truth,and_star(B,and_star(xor(truth,A),xor(truth,B))))) = and_star(xor(truth,B),xor(truth,and_star(A,xor(truth,and_star(B,A))))),
inference(paramod,[status(thm)],[c_30,c_3577]) ).
cnf(c_3579,plain,
and_star(and_star(xor(truth,A),xor(truth,B)),xor(truth,falsehood)) = and_star(xor(truth,B),xor(truth,and_star(A,xor(truth,and_star(B,A))))),
inference(paramod,[status(thm)],[c_52,c_3578]) ).
cnf(c_3580,plain,
and_star(and_star(xor(truth,A),xor(truth,B)),truth) = and_star(xor(truth,B),xor(truth,and_star(A,xor(truth,and_star(B,A))))),
inference(paramod,[status(thm)],[c_2,c_3579]) ).
cnf(c_3581,plain,
and_star(truth,and_star(xor(truth,A),xor(truth,B))) = and_star(xor(truth,B),xor(truth,and_star(A,xor(truth,and_star(B,A))))),
inference(paramod,[status(thm)],[c_12,c_3580]) ).
cnf(c_3582,plain,
and_star(xor(truth,A),xor(truth,B)) = and_star(xor(truth,B),xor(truth,and_star(A,xor(truth,and_star(B,A))))),
inference(paramod,[status(thm)],[c_35,c_3581]) ).
cnf(c_411,plain,
and_star(xor(truth,A),xor(truth,and_star(B,xor(truth,and_star(A,B))))) = and_star(xor(truth,B),xor(truth,A)),
inference(copy,[status(thm)],[c_3582]) ).
cnf(c_3583,plain,
and_star(xor(truth,A),and_star(B,xor(truth,and_star(xor(truth,xor(truth,and_star(A,xor(truth,B)))),B)))) = and_star(xor(truth,and_star(A,xor(truth,B))),and_star(xor(truth,xor(truth,B)),xor(truth,A))),
inference(paramod,[status(thm)],[c_411,c_70]) ).
cnf(c_3584,plain,
and_star(xor(truth,A),and_star(B,xor(truth,and_star(and_star(A,xor(truth,B)),B)))) = and_star(xor(truth,and_star(A,xor(truth,B))),and_star(xor(truth,xor(truth,B)),xor(truth,A))),
inference(paramod,[status(thm)],[c_30,c_3583]) ).
cnf(c_3585,plain,
and_star(xor(truth,A),and_star(B,xor(truth,and_star(B,and_star(A,xor(truth,B)))))) = and_star(xor(truth,and_star(A,xor(truth,B))),and_star(xor(truth,xor(truth,B)),xor(truth,A))),
inference(paramod,[status(thm)],[c_12,c_3584]) ).
cnf(c_3586,plain,
and_star(xor(truth,A),and_star(B,xor(truth,falsehood))) = and_star(xor(truth,and_star(A,xor(truth,B))),and_star(xor(truth,xor(truth,B)),xor(truth,A))),
inference(paramod,[status(thm)],[c_52,c_3585]) ).
cnf(c_3587,plain,
and_star(xor(truth,A),and_star(B,truth)) = and_star(xor(truth,and_star(A,xor(truth,B))),and_star(xor(truth,xor(truth,B)),xor(truth,A))),
inference(paramod,[status(thm)],[c_2,c_3586]) ).
cnf(c_3588,plain,
and_star(xor(truth,A),B) = and_star(xor(truth,and_star(A,xor(truth,B))),and_star(xor(truth,xor(truth,B)),xor(truth,A))),
inference(paramod,[status(thm)],[c_4,c_3587]) ).
cnf(c_3589,plain,
and_star(xor(truth,A),B) = and_star(xor(truth,and_star(A,xor(truth,B))),and_star(B,xor(truth,A))),
inference(paramod,[status(thm)],[c_30,c_3588]) ).
cnf(c_3590,plain,
and_star(xor(truth,A),B) = and_star(and_star(B,xor(truth,A)),xor(truth,and_star(A,xor(truth,B)))),
inference(paramod,[status(thm)],[c_12,c_3589]) ).
cnf(c_3591,plain,
and_star(xor(truth,A),B) = and_star(B,and_star(xor(truth,A),xor(truth,and_star(A,xor(truth,B))))),
inference(paramod,[status(thm)],[c_11,c_3590]) ).
cnf(c_3552,plain,
and_star(A,and_star(xor(truth,B),xor(truth,and_star(B,xor(truth,A))))) = and_star(xor(truth,B),A),
inference(copy,[status(thm)],[c_3591]) ).
cnf(c_3592,plain,
xor(truth,and_star(b,and_star(xor(truth,a),xor(truth,and_star(xor(truth,a),b))))) != truth,
inference(paramod,[status(thm)],[c_3552,c_29]) ).
cnf(c_3593,plain,
xor(truth,and_star(b,and_star(xor(truth,a),xor(truth,and_star(b,xor(truth,a)))))) != truth,
inference(paramod,[status(thm)],[c_12,c_3592]) ).
cnf(c_3594,plain,
xor(truth,falsehood) != truth,
inference(paramod,[status(thm)],[c_47,c_3593]) ).
cnf(c_3595,plain,
truth != truth,
inference(paramod,[status(thm)],[c_2,c_3594]) ).
cnf(c_3556,plain,
$false,
inference(copy,[status(thm)],[c_3595]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL109-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 21:55:13 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2354094 was started by sandbox2 on n015,
% 0.08/0.36 % Fri Sep 25 21:55:13 2026
% 0.08/0.36 % 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).
% 38.00/5.18
% 38.00/5.18 % Assigning unary symbol not kb_weight 0 and highest precedence (9).
% 38.00/5.18
% 38.00/5.18 % SZS status Unsatisfiable for theBenchmark
% 38.00/5.18
% 38.00/5.18 % Proof 1 at 4.01 (+ 0.77) seconds.
% 38.00/5.18 % Length of proof is 33.
% 38.00/5.18 % Level of proof is 7.
% 38.00/5.18 % Maximum clause weight is 88.000.
% 38.00/5.18 % Given clauses 170.
% 38.00/5.18
% 38.00/5.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------