TSTP Solution File: SYO038-1.003.003 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYO038-1.003.003 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 04:56:59 EDT 2023
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO038-1.003.003 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 07:43:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.37 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.18/0.37
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 Take the following subset of the input axioms:
% 0.18/0.40 fof(ax1, axiom, ![N]: f(N, one)=s(one)).
% 0.18/0.40 fof(ax2, axiom, ![X]: f(one, s(X))=s(s(f(one, X)))).
% 0.18/0.40 fof(ax3, axiom, ![X2, N2]: f(s(N2), s(X2))=f(N2, f(s(N2), X2))).
% 0.18/0.40 fof(ax4, axiom, d(one)).
% 0.18/0.40 fof(ax5, axiom, ![X2]: (~d(X2) | d(s(X2)))).
% 0.18/0.40 fof(conj, negated_conjecture, ~d(f(s(s(one)), s(s(one))))).
% 0.18/0.40
% 0.18/0.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.40 fresh(y, y, x1...xn) = u
% 0.18/0.40 C => fresh(s, t, x1...xn) = v
% 0.18/0.40 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.40 variables of u and v.
% 0.18/0.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.40 input problem has no model of domain size 1).
% 0.18/0.40
% 0.18/0.40 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.40
% 0.18/0.40 Axiom 1 (ax4): d(one) = true.
% 0.18/0.40 Axiom 2 (ax1): f(X, one) = s(one).
% 0.18/0.40 Axiom 3 (ax5): fresh(X, X, Y) = true.
% 0.18/0.40 Axiom 4 (ax5): fresh(d(X), true, X) = d(s(X)).
% 0.18/0.40 Axiom 5 (ax2): f(one, s(X)) = s(s(f(one, X))).
% 0.18/0.40 Axiom 6 (ax3): f(s(X), s(Y)) = f(X, f(s(X), Y)).
% 0.18/0.40
% 0.18/0.40 Lemma 7: s(s(s(one))) = f(one, s(one)).
% 0.18/0.40 Proof:
% 0.18/0.40 s(s(s(one)))
% 0.18/0.40 = { by axiom 2 (ax1) R->L }
% 0.18/0.40 s(s(f(one, one)))
% 0.18/0.40 = { by axiom 5 (ax2) R->L }
% 0.18/0.40 f(one, s(one))
% 0.18/0.40
% 0.18/0.40 Lemma 8: f(s(X), s(one)) = f(X, s(one)).
% 0.18/0.40 Proof:
% 0.18/0.40 f(s(X), s(one))
% 0.18/0.40 = { by axiom 6 (ax3) }
% 0.18/0.40 f(X, f(s(X), one))
% 0.18/0.40 = { by axiom 2 (ax1) }
% 0.18/0.40 f(X, s(one))
% 0.18/0.40
% 0.18/0.40 Lemma 9: f(s(X), s(s(one))) = f(X, f(X, s(one))).
% 0.18/0.40 Proof:
% 0.18/0.40 f(s(X), s(s(one)))
% 0.18/0.40 = { by axiom 6 (ax3) }
% 0.18/0.40 f(X, f(s(X), s(one)))
% 0.18/0.40 = { by lemma 8 }
% 0.18/0.41 f(X, f(X, s(one)))
% 0.18/0.41
% 0.18/0.41 Goal 1 (conj): d(f(s(s(one)), s(s(one)))) = true.
% 0.18/0.41 Proof:
% 0.18/0.41 d(f(s(s(one)), s(s(one))))
% 0.18/0.41 = { by lemma 9 }
% 0.18/0.41 d(f(s(one), f(s(one), s(one))))
% 0.18/0.41 = { by lemma 8 }
% 0.18/0.41 d(f(s(one), f(one, s(one))))
% 0.18/0.41 = { by lemma 7 R->L }
% 0.18/0.41 d(f(s(one), s(s(s(one)))))
% 0.18/0.41 = { by axiom 6 (ax3) }
% 0.18/0.41 d(f(one, f(s(one), s(s(one)))))
% 0.18/0.41 = { by lemma 9 }
% 0.18/0.41 d(f(one, f(one, f(one, s(one)))))
% 0.18/0.41 = { by lemma 7 R->L }
% 0.18/0.41 d(f(one, f(one, s(s(s(one))))))
% 0.18/0.41 = { by axiom 5 (ax2) }
% 0.18/0.41 d(f(one, s(s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 5 (ax2) }
% 0.18/0.41 d(s(s(f(one, s(f(one, s(s(one))))))))
% 0.18/0.41 = { by axiom 4 (ax5) R->L }
% 0.18/0.41 fresh(d(s(f(one, s(f(one, s(s(one))))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 4 (ax5) R->L }
% 0.18/0.41 fresh(fresh(d(f(one, s(f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 5 (ax2) }
% 0.18/0.41 fresh(fresh(d(s(s(f(one, f(one, s(s(one))))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 4 (ax5) R->L }
% 0.18/0.41 fresh(fresh(fresh(d(s(f(one, f(one, s(s(one)))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 4 (ax5) R->L }
% 0.18/0.41 fresh(fresh(fresh(fresh(d(f(one, f(one, s(s(one))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 5 (ax2) }
% 0.18/0.41 fresh(fresh(fresh(fresh(d(f(one, s(s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 5 (ax2) }
% 0.18/0.41 fresh(fresh(fresh(fresh(d(s(s(f(one, s(f(one, s(one))))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 4 (ax5) R->L }
% 0.18/0.41 fresh(fresh(fresh(fresh(fresh(d(s(f(one, s(f(one, s(one)))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 4 (ax5) R->L }
% 0.18/0.41 fresh(fresh(fresh(fresh(fresh(fresh(d(f(one, s(f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 5 (ax2) }
% 0.18/0.41 fresh(fresh(fresh(fresh(fresh(fresh(d(s(s(f(one, f(one, s(one)))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 4 (ax5) R->L }
% 0.18/0.41 fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(s(f(one, f(one, s(one))))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 4 (ax5) R->L }
% 0.18/0.41 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(f(one, f(one, s(one)))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by lemma 7 R->L }
% 0.18/0.41 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(f(one, s(s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 5 (ax2) }
% 0.18/0.41 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(s(s(f(one, s(s(one)))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 4 (ax5) R->L }
% 0.18/0.41 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(s(f(one, s(s(one))))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 4 (ax5) R->L }
% 0.18/0.41 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(f(one, s(s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 5 (ax2) }
% 0.18/0.41 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(s(s(f(one, s(one))))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.41 = { by axiom 4 (ax5) R->L }
% 0.18/0.41 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(s(f(one, s(one)))), true, s(f(one, s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 4 (ax5) R->L }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(f(one, s(one))), true, f(one, s(one))), true, s(f(one, s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by lemma 7 R->L }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(s(s(s(one)))), true, f(one, s(one))), true, s(f(one, s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 4 (ax5) R->L }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(s(s(one))), true, s(s(one))), true, f(one, s(one))), true, s(f(one, s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 4 (ax5) R->L }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(s(one)), true, s(one)), true, s(s(one))), true, f(one, s(one))), true, s(f(one, s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 4 (ax5) R->L }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(d(one), true, one), true, s(one)), true, s(s(one))), true, f(one, s(one))), true, s(f(one, s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 1 (ax4) }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, one), true, s(one)), true, s(s(one))), true, f(one, s(one))), true, s(f(one, s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 3 (ax5) }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, s(one)), true, s(s(one))), true, f(one, s(one))), true, s(f(one, s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 3 (ax5) }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, s(s(one))), true, f(one, s(one))), true, s(f(one, s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 3 (ax5) }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, f(one, s(one))), true, s(f(one, s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 3 (ax5) }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, s(f(one, s(one)))), true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 3 (ax5) }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, f(one, s(s(one)))), true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 3 (ax5) }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, s(f(one, s(s(one))))), true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 3 (ax5) }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, f(one, f(one, s(one)))), true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 3 (ax5) }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(fresh(true, true, s(f(one, f(one, s(one))))), true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 3 (ax5) }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(fresh(true, true, f(one, s(f(one, s(one))))), true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 3 (ax5) }
% 0.18/0.42 fresh(fresh(fresh(fresh(fresh(true, true, s(f(one, s(f(one, s(one)))))), true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.42 = { by axiom 3 (ax5) }
% 0.18/0.42 fresh(fresh(fresh(fresh(true, true, f(one, f(one, s(s(one))))), true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.43 = { by axiom 3 (ax5) }
% 0.18/0.43 fresh(fresh(fresh(true, true, s(f(one, f(one, s(s(one)))))), true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.43 = { by axiom 3 (ax5) }
% 0.18/0.43 fresh(fresh(true, true, f(one, s(f(one, s(s(one)))))), true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.43 = { by axiom 3 (ax5) }
% 0.18/0.43 fresh(true, true, s(f(one, s(f(one, s(s(one)))))))
% 0.18/0.43 = { by axiom 3 (ax5) }
% 0.18/0.43 true
% 0.18/0.43 % SZS output end Proof
% 0.18/0.43
% 0.18/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------