%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL162-1 : 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 : n008.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 125.21s 17.32s
% Output : CNFRefutation 125.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 49 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 21 ( 21 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 3 sgn 17 !; 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_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_axiom,axiom,
implies(implies(x,y),implies(implies(y,z),implies(x,z))) != truth,
file('theBenchmark.p',prove_wajsberg_axiom) ).
cnf(c_15,plain,
implies(implies(x,y),implies(implies(y,z),implies(x,z))) != truth,
inference(clausify,[status(thm)],[prove_wajsberg_axiom]) ).
cnf(c_999,plain,
implies(xor(truth,and_star(x,xor(truth,y))),implies(implies(y,z),implies(x,z))) != truth,
inference(paramod,[status(thm)],[c_14,c_15]) ).
cnf(c_1000,plain,
implies(xor(truth,and_star(x,xor(truth,y))),implies(xor(truth,and_star(y,xor(truth,z))),implies(x,z))) != truth,
inference(paramod,[status(thm)],[c_14,c_999]) ).
cnf(c_1001,plain,
implies(xor(truth,and_star(x,xor(truth,y))),implies(xor(truth,and_star(y,xor(truth,z))),xor(truth,and_star(x,xor(truth,z))))) != truth,
inference(paramod,[status(thm)],[c_14,c_1000]) ).
cnf(c_1002,plain,
implies(xor(truth,and_star(x,xor(truth,y))),xor(truth,and_star(xor(truth,and_star(y,xor(truth,z))),xor(truth,xor(truth,and_star(x,xor(truth,z))))))) != truth,
inference(paramod,[status(thm)],[c_14,c_1001]) ).
cnf(c_1003,plain,
implies(xor(truth,and_star(x,xor(truth,y))),xor(truth,and_star(xor(truth,and_star(y,xor(truth,z))),xor(xor(truth,truth),and_star(x,xor(truth,z)))))) != truth,
inference(paramod,[status(thm)],[c_8,c_1002]) ).
cnf(c_1004,plain,
implies(xor(truth,and_star(x,xor(truth,y))),xor(truth,and_star(xor(truth,and_star(y,xor(truth,z))),xor(falsehood,and_star(x,xor(truth,z)))))) != truth,
inference(paramod,[status(thm)],[c_3,c_1003]) ).
cnf(c_1005,plain,
xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,xor(truth,and_star(xor(truth,and_star(y,xor(truth,z))),xor(falsehood,and_star(x,xor(truth,z)))))))) != truth,
inference(paramod,[status(thm)],[c_14,c_1004]) ).
cnf(c_1006,plain,
xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(xor(truth,truth),and_star(xor(truth,and_star(y,xor(truth,z))),xor(falsehood,and_star(x,xor(truth,z))))))) != truth,
inference(paramod,[status(thm)],[c_8,c_1005]) ).
cnf(c_16,plain,
xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(falsehood,and_star(xor(truth,and_star(y,xor(truth,z))),xor(falsehood,and_star(x,xor(truth,z))))))) != truth,
inference(paramod,[status(thm)],[c_3,c_1006]) ).
cnf(c_25,plain,
xor(falsehood,A) = A,
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_1007,plain,
xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),xor(falsehood,and_star(xor(truth,and_star(y,xor(truth,z))),and_star(x,xor(truth,z)))))) != truth,
inference(paramod,[status(thm)],[c_25,c_16]) ).
cnf(c_1008,plain,
xor(truth,and_star(xor(truth,and_star(x,xor(truth,y))),and_star(xor(truth,and_star(y,xor(truth,z))),and_star(x,xor(truth,z))))) != truth,
inference(paramod,[status(thm)],[c_25,c_1007]) ).
cnf(c_36,plain,
xor(truth,and_star(and_star(xor(truth,and_star(x,xor(truth,y))),xor(truth,and_star(y,xor(truth,z)))),and_star(x,xor(truth,z)))) != truth,
inference(paramod,[status(thm)],[c_11,c_1008]) ).
cnf(c_1009,plain,
and_star(and_star(A,xor(truth,B)),B) = and_star(A,falsehood),
inference(paramod,[status(thm)],[c_6,c_11]) ).
cnf(c_40,plain,
and_star(and_star(A,xor(truth,B)),B) = falsehood,
inference(paramod,[status(thm)],[c_5,c_1009]) ).
cnf(c_42,plain,
and_star(and_star(xor(and_star(xor(truth,A),B),truth),B),C) = and_star(xor(and_star(xor(truth,B),A),truth),and_star(A,C)),
inference(paramod,[status(thm)],[c_9,c_11]) ).
cnf(c_53,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_60,plain,
and_star(xor(truth,A),and_star(B,A)) = falsehood,
inference(paramod,[status(thm)],[c_53,c_40]) ).
cnf(c_61,plain,
xor(truth,and_star(xor(truth,and_star(y,xor(truth,z))),and_star(xor(truth,and_star(x,xor(truth,y))),and_star(x,xor(truth,z))))) != truth,
inference(paramod,[status(thm)],[c_53,c_36]) ).
cnf(c_70,plain,
xor(truth,and_star(xor(truth,and_star(y,xor(truth,z))),and_star(xor(and_star(x,xor(truth,y)),truth),and_star(x,xor(truth,z))))) != truth,
inference(paramod,[status(thm)],[c_10,c_61]) ).
cnf(c_119,plain,
xor(truth,and_star(xor(truth,and_star(y,xor(truth,z))),and_star(xor(and_star(xor(truth,y),x),truth),and_star(x,xor(truth,z))))) != truth,
inference(paramod,[status(thm)],[c_12,c_70]) ).
cnf(c_1010,plain,
xor(truth,and_star(xor(truth,and_star(y,xor(truth,z))),and_star(and_star(xor(and_star(xor(truth,x),y),truth),y),xor(truth,z)))) != truth,
inference(paramod,[status(thm)],[c_42,c_119]) ).
cnf(c_1011,plain,
xor(truth,and_star(xor(truth,and_star(y,xor(truth,z))),and_star(xor(and_star(xor(truth,x),y),truth),and_star(y,xor(truth,z))))) != truth,
inference(paramod,[status(thm)],[c_11,c_1010]) ).
cnf(c_1012,plain,
xor(truth,falsehood) != truth,
inference(paramod,[status(thm)],[c_60,c_1011]) ).
cnf(c_1013,plain,
truth != truth,
inference(paramod,[status(thm)],[c_2,c_1012]) ).
cnf(c_998,plain,
$false,
inference(copy,[status(thm)],[c_1013]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n008.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 21:57:24 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2008359 was started by sandbox on n008,
% 0.17/0.43 % Fri Sep 25 21:57:24 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 125.21/17.32
% 125.21/17.32 % SZS status Unsatisfiable for theBenchmark
% 125.21/17.32
% 125.21/17.32 % Proof 1 at 0.63 (+ 0.14) seconds.
% 125.21/17.32 % Length of proof is 23.
% 125.21/17.32 % Level of proof is 7.
% 125.21/17.32 % Maximum clause weight is 69.000.
% 125.21/17.32 % Given clauses 116.
% 125.21/17.32
% 125.21/17.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------