%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL164-1 : 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 : 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 0.07s 0.36s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 37 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 15 ( 15 ~; 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 : 30 ( 0 sgn 12 !; 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_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(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(not(x),not(y)),implies(y,x)) != truth,
file('theBenchmark.p',prove_wajsberg_axiom) ).
cnf(c_15,plain,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
inference(clausify,[status(thm)],[prove_wajsberg_axiom]) ).
cnf(c_30,plain,
implies(implies(xor(x,truth),not(y)),implies(y,x)) != truth,
inference(paramod,[status(thm)],[c_1,c_15]) ).
cnf(c_31,plain,
implies(implies(xor(truth,x),not(y)),implies(y,x)) != truth,
inference(paramod,[status(thm)],[c_10,c_30]) ).
cnf(c_32,plain,
implies(implies(xor(truth,x),xor(y,truth)),implies(y,x)) != truth,
inference(paramod,[status(thm)],[c_1,c_31]) ).
cnf(c_33,plain,
implies(implies(xor(truth,x),xor(truth,y)),implies(y,x)) != truth,
inference(paramod,[status(thm)],[c_10,c_32]) ).
cnf(c_34,plain,
implies(xor(truth,and_star(xor(truth,x),xor(truth,xor(truth,y)))),implies(y,x)) != truth,
inference(paramod,[status(thm)],[c_14,c_33]) ).
cnf(c_35,plain,
implies(xor(truth,and_star(xor(truth,x),xor(truth,xor(truth,y)))),xor(truth,and_star(y,xor(truth,x)))) != truth,
inference(paramod,[status(thm)],[c_14,c_34]) ).
cnf(c_36,plain,
xor(truth,and_star(xor(truth,and_star(xor(truth,x),xor(truth,xor(truth,y)))),xor(truth,xor(truth,and_star(y,xor(truth,x)))))) != truth,
inference(paramod,[status(thm)],[c_14,c_35]) ).
cnf(c_16,plain,
xor(truth,and_star(xor(truth,xor(truth,and_star(y,xor(truth,x)))),xor(truth,and_star(xor(truth,x),xor(truth,xor(truth,y)))))) != truth,
inference(paramod,[status(thm)],[c_12,c_36]) ).
cnf(c_18,plain,
and_star(A,xor(truth,A)) = falsehood,
inference(paramod,[status(thm)],[c_12,c_6]) ).
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_38,plain,
xor(truth,and_star(and_star(y,xor(truth,x)),xor(truth,and_star(xor(truth,x),xor(truth,xor(truth,y)))))) != truth,
inference(paramod,[status(thm)],[c_24,c_16]) ).
cnf(c_39,plain,
xor(truth,and_star(and_star(y,xor(truth,x)),xor(truth,and_star(xor(truth,x),y)))) != truth,
inference(paramod,[status(thm)],[c_24,c_38]) ).
cnf(c_40,plain,
xor(truth,and_star(and_star(y,xor(truth,x)),xor(truth,and_star(y,xor(truth,x))))) != truth,
inference(paramod,[status(thm)],[c_12,c_39]) ).
cnf(c_41,plain,
xor(truth,falsehood) != truth,
inference(paramod,[status(thm)],[c_18,c_40]) ).
cnf(c_42,plain,
truth != truth,
inference(paramod,[status(thm)],[c_2,c_41]) ).
cnf(c_29,plain,
$false,
inference(copy,[status(thm)],[c_42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n009.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 21:56:44 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2646442 was started by sandbox on n009,
% 0.07/0.35 % Fri Sep 25 21:56:44 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.07/0.36
% 0.07/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.36
% 0.07/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/0.36 % Length of proof is 15.
% 0.07/0.36 % Level of proof is 4.
% 0.07/0.36 % Maximum clause weight is 25.000.
% 0.07/0.36 % Given clauses 7.
% 0.07/0.36
% 0.07/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------