%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 09:16:24 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 59 ( 57 unt; 0 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 12 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 104 ( 17 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : aux(VAR_0,VAR_1,VAR_2,btrue) = union(VAR_2,VAR_0),
file('theBenchmark.p',axiom) ).
cnf(c_1,plain,
aux(A,B,C,btrue) = union(C,A),
inference(clausify,[status(thm)],[axiom]) ).
fof(axiom_001,axiom,
! [VAR_0,VAR_1,VAR_2] : aux(VAR_0,VAR_1,VAR_2,bfalse) = cons(VAR_1,union(VAR_2,VAR_0)),
file('theBenchmark.p',axiom_001) ).
cnf(c_2,plain,
aux(A,B,C,bfalse) = cons(B,union(C,A)),
inference(clausify,[status(thm)],[axiom_001]) ).
fof(axiom_002,axiom,
! [VAR_0] : barbar(btrue,VAR_0) = btrue,
file('theBenchmark.p',axiom_002) ).
cnf(c_3,plain,
barbar(btrue,A) = btrue,
inference(clausify,[status(thm)],[axiom_002]) ).
fof(axiom_003,axiom,
! [VAR_0] : barbar(bfalse,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_003) ).
cnf(c_4,plain,
barbar(bfalse,A) = A,
inference(clausify,[status(thm)],[axiom_003]) ).
fof(axiom_005,axiom,
! [VAR_0] : eqNat(s(VAR_0),z) = bfalse,
file('theBenchmark.p',axiom_005) ).
cnf(c_6,plain,
eqNat(s(A),z) = bfalse,
inference(clausify,[status(thm)],[axiom_005]) ).
fof(axiom_007,axiom,
eqNat(z,z) = btrue,
file('theBenchmark.p',axiom_007) ).
cnf(c_8,plain,
eqNat(z,z) = btrue,
inference(clausify,[status(thm)],[axiom_007]) ).
cnf(c_9,plain,
btrue = eqNat(z,z),
inference(copy,[status(thm)],[c_8]) ).
fof(axiom_008,axiom,
! [VAR_0] : elem(VAR_0,nil) = bfalse,
file('theBenchmark.p',axiom_008) ).
cnf(c_10,plain,
elem(A,nil) = bfalse,
inference(clausify,[status(thm)],[axiom_008]) ).
fof(axiom_009,axiom,
! [VAR_0,VAR_1,VAR_2] : elem(VAR_0,cons(VAR_1,VAR_2)) = barbar(eqNat(VAR_0,VAR_1),elem(VAR_0,VAR_2)),
file('theBenchmark.p',axiom_009) ).
cnf(c_11,plain,
elem(A,cons(B,C)) = barbar(eqNat(A,B),elem(A,C)),
inference(clausify,[status(thm)],[axiom_009]) ).
cnf(c_12,plain,
barbar(eqNat(A,B),elem(A,C)) = elem(A,cons(B,C)),
inference(copy,[status(thm)],[c_11]) ).
fof(axiom_010,axiom,
! [VAR_0] : union(nil,VAR_0) = VAR_0,
file('theBenchmark.p',axiom_010) ).
cnf(c_13,plain,
union(nil,A) = A,
inference(clausify,[status(thm)],[axiom_010]) ).
fof(axiom_011,axiom,
! [VAR_0,VAR_1,VAR_2] : union(cons(VAR_0,VAR_1),VAR_2) = aux(VAR_2,VAR_0,VAR_1,elem(VAR_0,VAR_2)),
file('theBenchmark.p',axiom_011) ).
cnf(c_14,plain,
union(cons(A,B),C) = aux(C,A,B,elem(A,C)),
inference(clausify,[status(thm)],[axiom_011]) ).
cnf(c_15,plain,
aux(A,B,C,elem(B,A)) = union(cons(B,C),A),
inference(copy,[status(thm)],[c_14]) ).
fof(axiom_012,axiom,
! [VAR_0,VAR_1] : prop_union_comm(VAR_0,VAR_1) = eq(union(VAR_0,VAR_1),union(VAR_1,VAR_0)),
file('theBenchmark.p',axiom_012) ).
cnf(c_16,plain,
prop_union_comm(A,B) = eq(union(A,B),union(B,A)),
inference(clausify,[status(thm)],[axiom_012]) ).
fof(axiom_016,axiom,
! [VAR_0] : eq2(s(VAR_0),z) = bfalse,
file('theBenchmark.p',axiom_016) ).
cnf(c_22,plain,
eq2(s(A),z) = bfalse,
inference(clausify,[status(thm)],[axiom_016]) ).
fof(axiom_020,axiom,
! [VAR_0] : eq3(VAR_0,VAR_0) = btrue,
file('theBenchmark.p',axiom_020) ).
cnf(c_28,plain,
eq3(A,A) = btrue,
inference(clausify,[status(thm)],[axiom_020]) ).
cnf(c_29,plain,
eq3(A,A) = eqNat(z,z),
inference(paramod,[status(thm)],[c_9,c_28]) ).
fof(axiom_021,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( eq(cons(VAR_0,VAR_2),cons(VAR_1,VAR_3)) = bfalse
| eq2(VAR_0,VAR_1) != bfalse ),
file('theBenchmark.p',axiom_021) ).
cnf(c_30,plain,
( eq(cons(A,C),cons(B,D)) = bfalse
| eq2(A,B) != bfalse ),
inference(clausify,[status(thm)],[axiom_021]) ).
fof(goal,axiom,
! [VAR_0,VAR_1] : eq3(prop_union_comm(VAR_0,VAR_1),bfalse) != btrue,
file('theBenchmark.p',goal) ).
cnf(c_35,plain,
eq3(prop_union_comm(A,B),bfalse) != btrue,
inference(clausify,[status(thm)],[goal]) ).
cnf(c_152,plain,
eq3(eq(union(A,B),union(B,A)),bfalse) != btrue,
inference(paramod,[status(thm)],[c_16,c_35]) ).
cnf(c_36,plain,
eq3(eq(union(A,B),union(B,A)),bfalse) != eqNat(z,z),
inference(paramod,[status(thm)],[c_9,c_152]) ).
cnf(c_153,plain,
barbar(eqNat(z,z),A) = btrue,
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_37,plain,
barbar(eqNat(z,z),A) = eqNat(z,z),
inference(paramod,[status(thm)],[c_9,c_153]) ).
cnf(c_38,plain,
aux(A,B,C,eqNat(z,z)) = union(C,A),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_154,plain,
barbar(bfalse,elem(s(A),B)) = elem(s(A),cons(z,B)),
inference(paramod,[status(thm)],[c_6,c_12]) ).
cnf(c_155,plain,
elem(s(A),B) = elem(s(A),cons(z,B)),
inference(paramod,[status(thm)],[c_4,c_154]) ).
cnf(c_40,plain,
elem(s(A),cons(z,B)) = elem(s(A),B),
inference(copy,[status(thm)],[c_155]) ).
cnf(c_54,plain,
eq(cons(s(A),B),cons(z,C)) = bfalse,
inference(resolve,[status(thm)],[c_30,c_22]) ).
cnf(c_156,plain,
eqNat(z,z) = elem(z,cons(z,A)),
inference(paramod,[status(thm)],[c_37,c_12]) ).
cnf(c_67,plain,
elem(z,cons(z,A)) = eqNat(z,z),
inference(copy,[status(thm)],[c_156]) ).
cnf(c_81,plain,
aux(cons(z,A),s(B),C,elem(s(B),A)) = union(cons(s(B),C),cons(z,A)),
inference(paramod,[status(thm)],[c_40,c_15]) ).
cnf(c_157,plain,
aux(cons(z,A),z,B,eqNat(z,z)) = union(cons(z,B),cons(z,A)),
inference(paramod,[status(thm)],[c_67,c_15]) ).
cnf(c_158,plain,
union(B,cons(z,A)) = union(cons(z,B),cons(z,A)),
inference(paramod,[status(thm)],[c_38,c_157]) ).
cnf(c_91,plain,
union(cons(z,A),cons(z,B)) = union(A,cons(z,B)),
inference(copy,[status(thm)],[c_158]) ).
cnf(c_159,plain,
eq3(eq(union(A,cons(z,B)),union(cons(z,B),cons(z,A))),bfalse) != eqNat(z,z),
inference(paramod,[status(thm)],[c_91,c_36]) ).
cnf(c_95,plain,
eq3(eq(union(A,cons(z,B)),union(B,cons(z,A))),bfalse) != eqNat(z,z),
inference(paramod,[status(thm)],[c_91,c_159]) ).
cnf(c_160,plain,
aux(cons(z,nil),s(A),B,bfalse) = union(cons(s(A),B),cons(z,nil)),
inference(paramod,[status(thm)],[c_10,c_81]) ).
cnf(c_161,plain,
cons(s(A),union(B,cons(z,nil))) = union(cons(s(A),B),cons(z,nil)),
inference(paramod,[status(thm)],[c_2,c_160]) ).
cnf(c_137,plain,
union(cons(s(A),B),cons(z,nil)) = cons(s(A),union(B,cons(z,nil))),
inference(copy,[status(thm)],[c_161]) ).
cnf(c_162,plain,
eq3(eq(cons(s(A),union(B,cons(z,nil))),union(nil,cons(z,cons(s(A),B)))),bfalse) != eqNat(z,z),
inference(paramod,[status(thm)],[c_137,c_95]) ).
cnf(c_163,plain,
eq3(eq(cons(s(A),union(B,cons(z,nil))),cons(z,cons(s(A),B))),bfalse) != eqNat(z,z),
inference(paramod,[status(thm)],[c_13,c_162]) ).
cnf(c_164,plain,
eq3(bfalse,bfalse) != eqNat(z,z),
inference(paramod,[status(thm)],[c_54,c_163]) ).
cnf(c_165,plain,
eqNat(z,z) != eqNat(z,z),
inference(paramod,[status(thm)],[c_29,c_164]) ).
cnf(c_151,plain,
$false,
inference(copy,[status(thm)],[c_165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 17:05:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2267053 was started by sandbox on n001,
% 0.09/0.36 % Sat Sep 26 17:05:13 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.09/0.40 % Length of proof is 30.
% 0.09/0.40 % Level of proof is 6.
% 0.09/0.40 % Maximum clause weight is 42.000.
% 0.09/0.40 % Given clauses 75.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------