%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 01:45:37 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.29s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n016.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 15:18:18 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.29 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.29
% 0.19/0.29 % SZS status Unsatisfiable
% 0.19/0.29
% 0.19/0.30 % SZS output start Proof
% 0.19/0.30 Axiom 1 (axiom_017): eq2(z, s(X)) = bfalse.
% 0.19/0.30 Axiom 2 (axiom_010): union(nil, X) = X.
% 0.19/0.30 Axiom 3 (axiom_007): eqNat(z, z) = btrue.
% 0.19/0.30 Axiom 4 (axiom_005): eqNat(s(X), z) = bfalse.
% 0.19/0.30 Axiom 5 (axiom_008): elem(X, nil) = bfalse.
% 0.19/0.30 Axiom 6 (axiom_020): eq3(X, X) = btrue.
% 0.19/0.30 Axiom 7 (axiom_003): barbar(bfalse, X) = X.
% 0.19/0.30 Axiom 8 (axiom_002): barbar(btrue, X) = btrue.
% 0.19/0.30 Axiom 9 (axiom_001): aux(X, Y, Z, bfalse) = cons(Y, union(Z, X)).
% 0.19/0.30 Axiom 10 (axiom): aux(X, Y, Z, btrue) = union(Z, X).
% 0.19/0.30 Axiom 11 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.30 Axiom 12 (axiom_012): prop_union_comm(X, Y) = eq(union(X, Y), union(Y, X)).
% 0.19/0.30 Axiom 13 (axiom_011): union(cons(X, Y), Z) = aux(Z, X, Y, elem(X, Z)).
% 0.19/0.30 Axiom 14 (axiom_009): elem(X, cons(Y, Z)) = barbar(eqNat(X, Y), elem(X, Z)).
% 0.19/0.30 Axiom 15 (axiom_021): ifeq(eq2(X, Y), bfalse, eq(cons(X, Z), cons(Y, W)), bfalse) = bfalse.
% 0.19/0.30
% 0.19/0.30 Lemma 16: union(cons(z, X), cons(z, Y)) = union(X, cons(z, Y)).
% 0.19/0.30 Proof:
% 0.19/0.30 union(cons(z, X), cons(z, Y))
% 0.19/0.30 = { by axiom 13 (axiom_011) }
% 0.19/0.30 aux(cons(z, Y), z, X, elem(z, cons(z, Y)))
% 0.19/0.30 = { by axiom 14 (axiom_009) }
% 0.19/0.30 aux(cons(z, Y), z, X, barbar(eqNat(z, z), elem(z, Y)))
% 0.19/0.30 = { by axiom 3 (axiom_007) }
% 0.19/0.30 aux(cons(z, Y), z, X, barbar(btrue, elem(z, Y)))
% 0.19/0.30 = { by axiom 8 (axiom_002) }
% 0.19/0.30 aux(cons(z, Y), z, X, btrue)
% 0.19/0.30 = { by axiom 10 (axiom) }
% 0.19/0.30 union(X, cons(z, Y))
% 0.19/0.30
% 0.19/0.30 Goal 1 (goal): eq3(prop_union_comm(X, Y), bfalse) = btrue.
% 0.19/0.30 The goal is true when:
% 0.19/0.30 X = cons(z, nil)
% 0.19/0.30 Y = cons(z, cons(s(X), Y))
% 0.19/0.30
% 0.19/0.30 Proof:
% 0.19/0.30 eq3(prop_union_comm(cons(z, nil), cons(z, cons(s(X), Y))), bfalse)
% 0.19/0.30 = { by axiom 12 (axiom_012) }
% 0.19/0.30 eq3(eq(union(cons(z, nil), cons(z, cons(s(X), Y))), union(cons(z, cons(s(X), Y)), cons(z, nil))), bfalse)
% 0.19/0.30 = { by lemma 16 }
% 0.19/0.30 eq3(eq(union(nil, cons(z, cons(s(X), Y))), union(cons(z, cons(s(X), Y)), cons(z, nil))), bfalse)
% 0.19/0.30 = { by lemma 16 }
% 0.19/0.30 eq3(eq(union(nil, cons(z, cons(s(X), Y))), union(cons(s(X), Y), cons(z, nil))), bfalse)
% 0.19/0.30 = { by axiom 13 (axiom_011) }
% 0.19/0.30 eq3(eq(union(nil, cons(z, cons(s(X), Y))), aux(cons(z, nil), s(X), Y, elem(s(X), cons(z, nil)))), bfalse)
% 0.19/0.30 = { by axiom 14 (axiom_009) }
% 0.19/0.30 eq3(eq(union(nil, cons(z, cons(s(X), Y))), aux(cons(z, nil), s(X), Y, barbar(eqNat(s(X), z), elem(s(X), nil)))), bfalse)
% 0.19/0.30 = { by axiom 4 (axiom_005) }
% 0.19/0.30 eq3(eq(union(nil, cons(z, cons(s(X), Y))), aux(cons(z, nil), s(X), Y, barbar(bfalse, elem(s(X), nil)))), bfalse)
% 0.19/0.30 = { by axiom 7 (axiom_003) }
% 0.19/0.30 eq3(eq(union(nil, cons(z, cons(s(X), Y))), aux(cons(z, nil), s(X), Y, elem(s(X), nil))), bfalse)
% 0.19/0.30 = { by axiom 5 (axiom_008) }
% 0.19/0.30 eq3(eq(union(nil, cons(z, cons(s(X), Y))), aux(cons(z, nil), s(X), Y, bfalse)), bfalse)
% 0.19/0.30 = { by axiom 9 (axiom_001) }
% 0.19/0.30 eq3(eq(union(nil, cons(z, cons(s(X), Y))), cons(s(X), union(Y, cons(z, nil)))), bfalse)
% 0.19/0.30 = { by axiom 2 (axiom_010) }
% 0.19/0.30 eq3(eq(cons(z, cons(s(X), Y)), cons(s(X), union(Y, cons(z, nil)))), bfalse)
% 0.19/0.30 = { by axiom 11 (ifeq_axiom) R->L }
% 0.19/0.30 eq3(ifeq(bfalse, bfalse, eq(cons(z, cons(s(X), Y)), cons(s(X), union(Y, cons(z, nil)))), bfalse), bfalse)
% 0.19/0.30 = { by axiom 1 (axiom_017) R->L }
% 0.19/0.30 eq3(ifeq(eq2(z, s(X)), bfalse, eq(cons(z, cons(s(X), Y)), cons(s(X), union(Y, cons(z, nil)))), bfalse), bfalse)
% 0.19/0.30 = { by axiom 15 (axiom_021) }
% 0.19/0.30 eq3(bfalse, bfalse)
% 0.19/0.30 = { by axiom 6 (axiom_020) }
% 0.19/0.30 btrue
% 0.19/0.30 % SZS output end Proof
% 0.19/0.30
% 0.19/0.30 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------