%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWX200-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : Tue Sep 29 01:45:33 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.28s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of clauses : 99 ( 99 unt; 0 nHn; 28 RR)
% Number of literals : 99 ( 98 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 127 ( 45 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
eq2(prop_merge_ord_not3(X,Y),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
eq2(bfalse,btrue) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
bfalse = eq2(bfalse,btrue),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
eq2(prop_merge_ord_not3(nil,cons(s(X3),cons(z,X2))),bfalse) = eq2(prop_merge_ord_not3(nil,cons(s(X3),cons(z,X2))),eq2(bfalse,btrue)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
eq2(btrue,bfalse) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
bfalse = eq2(bfalse,btrue),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c7,plain,
eq2(btrue,bfalse) = eq2(bfalse,btrue),
inference(transitivity,[status(thm)],[c5,c6]) ).
cnf(c8,plain,
eq2(bfalse,btrue) = eq2(btrue,bfalse),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
eq2(prop_merge_ord_not3(nil,cons(s(X3),cons(z,X2))),eq2(bfalse,btrue)) = eq2(prop_merge_ord_not3(nil,cons(s(X3),cons(z,X2))),eq2(btrue,bfalse)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
merge(nil,Y3) = Y3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
cnf(c11,plain,
merge(nil,X2) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
X2 = merge(nil,X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
ord(X2) = ord(merge(nil,X2)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
eq2(ord(X2),ord(nil)) = eq2(ord(merge(nil,X2)),ord(nil)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(X2),ord(nil))) = impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(nil,X2)),ord(nil))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
ord(nil) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c17,plain,
impl(ord(nil),X2) = impl(btrue,X2),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,axiom,
impl(btrue,Q) = Q,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
cnf(c19,plain,
impl(btrue,X2) = X2,
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
impl(ord(nil),X2) = X2,
inference(transitivity,[status(thm)],[c17,c19]) ).
cnf(c21,plain,
impl(ord(nil),impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(nil,X2)),ord(nil)))) = impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(nil,X2)),ord(nil))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(nil,X2)),ord(nil))) = impl(ord(nil),impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(nil,X2)),ord(nil)))),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,axiom,
eq2(X2,X2) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c24,plain,
btrue = ord(nil),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c25,plain,
eq2(X2,X2) = ord(nil),
inference(transitivity,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
eq2(ord(nil),ord(nil)) = ord(nil),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
ord(nil) = eq2(ord(nil),ord(nil)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
impl(ord(nil),impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(nil,X2)),ord(nil)))) = impl(eq2(ord(nil),ord(nil)),impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(nil,X2)),ord(nil)))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
eq2(ord(X2),eq2(btrue,bfalse)) = eq2(ord(X2),eq2(bfalse,btrue)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c30,plain,
impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(X3,X2)),ord(nil))) = impl(eq2(ord(X2),eq2(bfalse,btrue)),eq2(ord(merge(X3,X2)),ord(nil))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
impl(eq2(ord(X3),ord(nil)),impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(X3,X2)),ord(nil)))) = impl(eq2(ord(X3),ord(nil)),impl(eq2(ord(X2),eq2(bfalse,btrue)),eq2(ord(merge(X3,X2)),ord(nil)))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
eq2(ord(X2),eq2(bfalse,btrue)) = eq2(ord(X2),bfalse),
inference(congruence,[status(thm)],[c2]) ).
cnf(c33,plain,
impl(eq2(ord(X2),eq2(bfalse,btrue)),eq2(ord(merge(X3,X2)),ord(nil))) = impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),ord(nil))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
impl(eq2(ord(X3),ord(nil)),impl(eq2(ord(X2),eq2(bfalse,btrue)),eq2(ord(merge(X3,X2)),ord(nil)))) = impl(eq2(ord(X3),ord(nil)),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),ord(nil)))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
eq2(ord(X2),ord(nil)) = eq2(ord(X2),btrue),
inference(congruence,[status(thm)],[c16]) ).
cnf(c36,plain,
impl(eq2(ord(X3),ord(nil)),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),ord(nil)))) = impl(eq2(ord(X3),btrue),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),ord(nil)))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
eq2(ord(merge(X3,X2)),ord(nil)) = eq2(ord(merge(X3,X2)),btrue),
inference(congruence,[status(thm)],[c16]) ).
cnf(c38,plain,
impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),ord(nil))) = impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),btrue)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
impl(eq2(ord(X3),btrue),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),ord(nil)))) = impl(eq2(ord(X3),btrue),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),btrue))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,axiom,
prop_merge_ord_not3(X2,Y3) = impl(eq2(ord(X2),btrue),impl(eq2(ord(Y3),bfalse),eq2(ord(merge(X2,Y3)),btrue))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
cnf(c41,plain,
prop_merge_ord_not3(X3,X2) = impl(eq2(ord(X3),btrue),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),btrue))),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
impl(eq2(ord(X3),btrue),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),btrue))) = prop_merge_ord_not3(X3,X2),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
impl(eq2(ord(X3),btrue),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),ord(nil)))) = prop_merge_ord_not3(X3,X2),
inference(transitivity,[status(thm)],[c39,c42]) ).
cnf(c44,plain,
impl(eq2(ord(X3),ord(nil)),impl(eq2(ord(X2),bfalse),eq2(ord(merge(X3,X2)),ord(nil)))) = prop_merge_ord_not3(X3,X2),
inference(transitivity,[status(thm)],[c36,c43]) ).
cnf(c45,plain,
impl(eq2(ord(X3),ord(nil)),impl(eq2(ord(X2),eq2(bfalse,btrue)),eq2(ord(merge(X3,X2)),ord(nil)))) = prop_merge_ord_not3(X3,X2),
inference(transitivity,[status(thm)],[c34,c44]) ).
cnf(c46,plain,
impl(eq2(ord(X3),ord(nil)),impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(X3,X2)),ord(nil)))) = prop_merge_ord_not3(X3,X2),
inference(transitivity,[status(thm)],[c31,c45]) ).
cnf(c47,plain,
impl(eq2(ord(nil),ord(nil)),impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(nil,X2)),ord(nil)))) = prop_merge_ord_not3(nil,X2),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
impl(ord(nil),impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(nil,X2)),ord(nil)))) = prop_merge_ord_not3(nil,X2),
inference(transitivity,[status(thm)],[c28,c47]) ).
cnf(c49,plain,
impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(merge(nil,X2)),ord(nil))) = prop_merge_ord_not3(nil,X2),
inference(transitivity,[status(thm)],[c22,c48]) ).
cnf(c50,plain,
impl(eq2(ord(X2),eq2(btrue,bfalse)),eq2(ord(X2),ord(nil))) = prop_merge_ord_not3(nil,X2),
inference(transitivity,[status(thm)],[c15,c49]) ).
cnf(c51,plain,
impl(eq2(ord(cons(s(X3),cons(z,X2))),eq2(btrue,bfalse)),eq2(ord(cons(s(X3),cons(z,X2))),ord(nil))) = prop_merge_ord_not3(nil,cons(s(X3),cons(z,X2))),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
prop_merge_ord_not3(nil,cons(s(X3),cons(z,X2))) = impl(eq2(ord(cons(s(X3),cons(z,X2))),eq2(btrue,bfalse)),eq2(ord(cons(s(X3),cons(z,X2))),ord(nil))),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,axiom,
ord(cons(Y3,cons(Y2,Xs))) = aux2(Y3,Y2,Xs,leqNat(Y3,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
cnf(c54,plain,
ord(cons(s(X3),cons(z,X2))) = aux2(s(X3),z,X2,leqNat(s(X3),z)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,axiom,
leqNat(s(Z),z) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
cnf(c56,plain,
leqNat(s(X2),z) = bfalse,
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
bfalse = eq2(bfalse,btrue),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c58,plain,
eq2(bfalse,btrue) = eq2(btrue,bfalse),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c59,plain,
bfalse = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
leqNat(s(X2),z) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c56,c59]) ).
cnf(c61,plain,
aux2(s(X3),z,X2,leqNat(s(X3),z)) = aux2(s(X3),z,X2,eq2(btrue,bfalse)),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
aux2(X3,X2,X4,eq2(btrue,bfalse)) = aux2(X3,X2,X4,eq2(bfalse,btrue)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c63,plain,
aux2(X4,X3,X2,eq2(bfalse,btrue)) = aux2(X4,X3,X2,bfalse),
inference(congruence,[status(thm)],[c2]) ).
cnf(c64,axiom,
aux2(Y3,Y2_2,Xs2,bfalse) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
cnf(c65,plain,
aux2(X4,X3,X2,bfalse) = bfalse,
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
bfalse = eq2(bfalse,btrue),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c67,plain,
eq2(bfalse,btrue) = eq2(btrue,bfalse),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c68,plain,
bfalse = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c66,c67]) ).
cnf(c69,plain,
aux2(X4,X3,X2,bfalse) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c65,c68]) ).
cnf(c70,plain,
aux2(X4,X3,X2,eq2(bfalse,btrue)) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c63,c69]) ).
cnf(c71,plain,
aux2(X4,X3,X2,eq2(btrue,bfalse)) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c62,c70]) ).
cnf(c72,plain,
aux2(s(X3),z,X2,eq2(btrue,bfalse)) = eq2(btrue,bfalse),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
aux2(s(X3),z,X2,leqNat(s(X3),z)) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c61,c72]) ).
cnf(c74,plain,
ord(cons(s(X3),cons(z,X2))) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c54,c73]) ).
cnf(c75,plain,
eq2(ord(cons(s(X3),cons(z,X2))),eq2(btrue,bfalse)) = eq2(eq2(btrue,bfalse),eq2(btrue,bfalse)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
impl(eq2(ord(cons(s(X3),cons(z,X2))),eq2(btrue,bfalse)),eq2(ord(cons(s(X3),cons(z,X2))),ord(nil))) = impl(eq2(eq2(btrue,bfalse),eq2(btrue,bfalse)),eq2(ord(cons(s(X3),cons(z,X2))),ord(nil))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
eq2(eq2(btrue,bfalse),eq2(btrue,bfalse)) = ord(nil),
inference(substitution,[status(thm)],[c25]) ).
cnf(c78,plain,
impl(eq2(eq2(btrue,bfalse),eq2(btrue,bfalse)),eq2(ord(cons(s(X3),cons(z,X2))),ord(nil))) = impl(ord(nil),eq2(ord(cons(s(X3),cons(z,X2))),ord(nil))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
impl(ord(nil),eq2(ord(cons(s(X3),cons(z,X2))),ord(nil))) = eq2(ord(cons(s(X3),cons(z,X2))),ord(nil)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c80,plain,
eq2(ord(cons(s(X3),cons(z,X2))),ord(nil)) = eq2(eq2(btrue,bfalse),ord(nil)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c81,plain,
eq2(eq2(btrue,bfalse),ord(nil)) = eq2(eq2(bfalse,btrue),ord(nil)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c82,plain,
eq2(eq2(bfalse,btrue),ord(nil)) = eq2(bfalse,ord(nil)),
inference(congruence,[status(thm)],[c2]) ).
cnf(c83,plain,
eq2(bfalse,ord(nil)) = eq2(bfalse,btrue),
inference(congruence,[status(thm)],[c16]) ).
cnf(c84,plain,
eq2(bfalse,btrue) = eq2(btrue,bfalse),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c85,plain,
eq2(bfalse,ord(nil)) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
eq2(eq2(bfalse,btrue),ord(nil)) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c82,c85]) ).
cnf(c87,plain,
eq2(eq2(btrue,bfalse),ord(nil)) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c81,c86]) ).
cnf(c88,plain,
eq2(ord(cons(s(X3),cons(z,X2))),ord(nil)) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c80,c87]) ).
cnf(c89,plain,
impl(ord(nil),eq2(ord(cons(s(X3),cons(z,X2))),ord(nil))) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c79,c88]) ).
cnf(c90,plain,
impl(eq2(eq2(btrue,bfalse),eq2(btrue,bfalse)),eq2(ord(cons(s(X3),cons(z,X2))),ord(nil))) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c78,c89]) ).
cnf(c91,plain,
impl(eq2(ord(cons(s(X3),cons(z,X2))),eq2(btrue,bfalse)),eq2(ord(cons(s(X3),cons(z,X2))),ord(nil))) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c76,c90]) ).
cnf(c92,plain,
prop_merge_ord_not3(nil,cons(s(X3),cons(z,X2))) = eq2(btrue,bfalse),
inference(transitivity,[status(thm)],[c52,c91]) ).
cnf(c93,plain,
eq2(prop_merge_ord_not3(nil,cons(s(X3),cons(z,X2))),eq2(btrue,bfalse)) = eq2(eq2(btrue,bfalse),eq2(btrue,bfalse)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
eq2(eq2(btrue,bfalse),eq2(btrue,bfalse)) = ord(nil),
inference(substitution,[status(thm)],[c25]) ).
cnf(c95,plain,
eq2(eq2(btrue,bfalse),eq2(btrue,bfalse)) = btrue,
inference(transitivity,[status(thm)],[c94,c16]) ).
cnf(c96,plain,
eq2(prop_merge_ord_not3(nil,cons(s(X3),cons(z,X2))),eq2(btrue,bfalse)) = btrue,
inference(transitivity,[status(thm)],[c93,c95]) ).
cnf(c97,plain,
eq2(prop_merge_ord_not3(nil,cons(s(X3),cons(z,X2))),eq2(bfalse,btrue)) = btrue,
inference(transitivity,[status(thm)],[c9,c96]) ).
cnf(c98,plain,
eq2(prop_merge_ord_not3(nil,cons(s(X3),cons(z,X2))),bfalse) = btrue,
inference(transitivity,[status(thm)],[c4,c97]) ).
cnf(c99,plain,
$false,
inference(resolution,[status(thm)],[c1,c98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX200-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n005.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Mon Sep 28 15:10:02 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 Command-line arguments: --flatten --complete-subsets
% 0.21/0.28
% 0.21/0.28 % SZS status Unsatisfiable
% 0.21/0.28
% 0.21/0.28 % SZS output start CNFRefutation
% See solution above
% 0.21/0.31
% 0.21/0.31 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------