%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYO038-1.003.003 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 02:23:17 PM UTC 2026
% Result : Unsatisfiable 0.63s 0.31s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO038-1.003.003 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n004.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 17:21:51 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.63/0.31 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.63/0.31
% 0.63/0.31 % SZS status Unsatisfiable
% 0.63/0.31
% 0.63/0.37 % SZS output start Proof
% 0.63/0.37 Axiom 1 (ax4): d(one) = true.
% 0.63/0.37 Axiom 2 (ax1): f(X, one) = s(one).
% 0.63/0.37 Axiom 3 (ax2): f(one, s(X)) = s(s(f(one, X))).
% 0.63/0.37 Axiom 4 (ax3): f(s(X), s(Y)) = f(X, f(s(X), Y)).
% 0.63/0.37 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.63/0.37 Axiom 6 (ax5): ifeq(d(X), true, d(s(X)), true) = true.
% 0.63/0.37
% 0.63/0.37 Lemma 7: f(one, s(one)) = s(s(s(one))).
% 0.63/0.37 Proof:
% 0.63/0.38 f(one, s(one))
% 0.63/0.38 = { by axiom 3 (ax2) }
% 0.63/0.38 s(s(f(one, one)))
% 0.63/0.38 = { by axiom 2 (ax1) }
% 0.63/0.38 s(s(s(one)))
% 0.63/0.38
% 0.63/0.38 Lemma 8: f(one, s(s(one))) = s(s(s(s(s(one))))).
% 0.63/0.38 Proof:
% 0.63/0.38 f(one, s(s(one)))
% 0.63/0.38 = { by axiom 3 (ax2) }
% 0.63/0.38 s(s(f(one, s(one))))
% 0.63/0.38 = { by lemma 7 }
% 0.63/0.38 s(s(s(s(s(one)))))
% 0.63/0.38
% 0.63/0.38 Lemma 9: f(s(X), s(one)) = f(X, s(one)).
% 0.63/0.38 Proof:
% 0.63/0.38 f(s(X), s(one))
% 0.63/0.38 = { by axiom 4 (ax3) }
% 0.63/0.38 f(X, f(s(X), one))
% 0.63/0.38 = { by axiom 2 (ax1) }
% 0.63/0.38 f(X, s(one))
% 0.63/0.38
% 0.63/0.38 Lemma 10: f(s(one), s(one)) = s(s(s(one))).
% 0.63/0.38 Proof:
% 0.63/0.38 f(s(one), s(one))
% 0.63/0.38 = { by lemma 9 }
% 0.63/0.38 f(one, s(one))
% 0.63/0.38 = { by lemma 7 }
% 0.63/0.38 s(s(s(one)))
% 0.63/0.38
% 0.63/0.38 Lemma 11: f(one, s(s(s(one)))) = s(s(s(s(s(s(s(one))))))).
% 0.63/0.38 Proof:
% 0.63/0.38 f(one, s(s(s(one))))
% 0.63/0.38 = { by axiom 3 (ax2) }
% 0.63/0.38 s(s(f(one, s(s(one)))))
% 0.63/0.38 = { by lemma 8 }
% 0.63/0.38 s(s(s(s(s(s(s(one)))))))
% 0.63/0.38
% 0.63/0.38 Lemma 12: f(one, s(s(s(s(one))))) = s(s(s(s(s(s(s(s(s(one))))))))).
% 0.63/0.38 Proof:
% 0.63/0.38 f(one, s(s(s(s(one)))))
% 0.63/0.38 = { by axiom 3 (ax2) }
% 0.63/0.38 s(s(f(one, s(s(s(one))))))
% 0.63/0.38 = { by lemma 11 }
% 0.63/0.38 s(s(s(s(s(s(s(s(s(one)))))))))
% 0.63/0.38
% 0.63/0.38 Lemma 13: f(one, s(s(s(s(s(s(one))))))) = s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))).
% 0.63/0.38 Proof:
% 0.63/0.38 f(one, s(s(s(s(s(s(one)))))))
% 0.63/0.38 = { by axiom 3 (ax2) }
% 0.63/0.38 s(s(f(one, s(s(s(s(s(one))))))))
% 0.63/0.38 = { by axiom 3 (ax2) }
% 0.63/0.38 s(s(s(s(f(one, s(s(s(s(one)))))))))
% 0.63/0.38 = { by lemma 12 }
% 0.63/0.38 s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))
% 0.63/0.38
% 0.63/0.38 Goal 1 (conj): d(f(s(s(one)), s(s(one)))) = true.
% 0.63/0.38 Proof:
% 0.63/0.38 d(f(s(s(one)), s(s(one))))
% 0.63/0.38 = { by axiom 4 (ax3) }
% 0.63/0.38 d(f(s(one), f(s(s(one)), s(one))))
% 0.63/0.38 = { by lemma 9 }
% 0.63/0.38 d(f(s(one), f(s(one), s(one))))
% 0.63/0.38 = { by lemma 10 }
% 0.63/0.38 d(f(s(one), s(s(s(one)))))
% 0.63/0.38 = { by axiom 4 (ax3) }
% 0.63/0.38 d(f(one, f(s(one), s(s(one)))))
% 0.63/0.38 = { by axiom 4 (ax3) }
% 0.63/0.38 d(f(one, f(one, f(s(one), s(one)))))
% 0.63/0.38 = { by lemma 10 }
% 0.63/0.38 d(f(one, f(one, s(s(s(one))))))
% 0.63/0.38 = { by lemma 11 }
% 0.63/0.38 d(f(one, s(s(s(s(s(s(s(one)))))))))
% 0.63/0.38 = { by axiom 3 (ax2) }
% 0.63/0.38 d(s(s(f(one, s(s(s(s(s(s(one))))))))))
% 0.63/0.38 = { by lemma 13 }
% 0.63/0.38 d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))))
% 0.63/0.38 = { by axiom 5 (ifeq_axiom) R->L }
% 0.63/0.38 ifeq(true, true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.38 = { by axiom 6 (ax5) R->L }
% 0.63/0.38 ifeq(ifeq(d(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.38 = { by lemma 13 R->L }
% 0.63/0.38 ifeq(ifeq(d(f(one, s(s(s(s(s(s(one)))))))), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.38 = { by axiom 5 (ifeq_axiom) R->L }
% 0.63/0.38 ifeq(ifeq(ifeq(true, true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.38 = { by axiom 6 (ax5) R->L }
% 0.63/0.38 ifeq(ifeq(ifeq(ifeq(d(f(one, s(s(s(s(s(one))))))), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.38 = { by axiom 5 (ifeq_axiom) R->L }
% 0.63/0.38 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.38 = { by axiom 6 (ax5) R->L }
% 0.63/0.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(s(s(s(s(s(s(s(s(s(one)))))))))), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.38 = { by axiom 5 (ifeq_axiom) R->L }
% 0.63/0.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.38 = { by axiom 6 (ax5) R->L }
% 0.63/0.38 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(s(s(s(s(s(s(s(one)))))))), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 5 (ifeq_axiom) R->L }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 6 (ax5) R->L }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(s(s(s(s(s(one)))))), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by lemma 8 R->L }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(f(one, s(s(one)))), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 5 (ifeq_axiom) R->L }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, d(f(one, s(s(one)))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 6 (ax5) R->L }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(s(s(s(one)))), true, d(s(s(s(s(one))))), true), true, d(f(one, s(s(one)))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 5 (ifeq_axiom) R->L }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, d(s(s(s(one)))), true), true, d(s(s(s(s(one))))), true), true, d(f(one, s(s(one)))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 6 (ax5) R->L }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(s(one)), true, d(s(s(one))), true), true, d(s(s(s(one)))), true), true, d(s(s(s(s(one))))), true), true, d(f(one, s(s(one)))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 5 (ifeq_axiom) R->L }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, d(s(one)), true), true, d(s(s(one))), true), true, d(s(s(s(one)))), true), true, d(s(s(s(s(one))))), true), true, d(f(one, s(s(one)))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 1 (ax4) R->L }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(one), true, d(s(one)), true), true, d(s(s(one))), true), true, d(s(s(s(one)))), true), true, d(s(s(s(s(one))))), true), true, d(f(one, s(s(one)))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 6 (ax5) }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, d(s(s(one))), true), true, d(s(s(s(one)))), true), true, d(s(s(s(s(one))))), true), true, d(f(one, s(s(one)))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 5 (ifeq_axiom) }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(s(s(one))), true, d(s(s(s(one)))), true), true, d(s(s(s(s(one))))), true), true, d(f(one, s(s(one)))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 6 (ax5) }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, d(s(s(s(s(one))))), true), true, d(f(one, s(s(one)))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.39 = { by axiom 5 (ifeq_axiom) }
% 0.63/0.39 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(s(s(s(s(one))))), true, d(f(one, s(s(one)))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by lemma 7 R->L }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(s(f(one, s(one)))), true, d(f(one, s(s(one)))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 3 (ax2) }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(s(f(one, s(one)))), true, d(s(s(f(one, s(one))))), true), true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 6 (ax5) }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, d(s(s(s(s(s(s(one))))))), true), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 5 (ifeq_axiom) }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(s(s(s(s(s(s(one))))))), true, d(s(s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 6 (ax5) }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, d(s(s(s(s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 5 (ifeq_axiom) }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(d(s(s(s(s(s(s(s(s(one))))))))), true, d(s(s(s(s(s(s(s(s(s(one)))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 6 (ax5) }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 5 (ifeq_axiom) }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true, d(f(one, s(s(s(s(s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by lemma 8 R->L }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(d(s(s(s(s(s(s(s(s(s(s(one))))))))))), true, d(f(one, f(one, s(s(one))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by lemma 12 R->L }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(d(s(f(one, s(s(s(s(one))))))), true, d(f(one, f(one, s(s(one))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by lemma 7 R->L }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(d(s(f(one, s(f(one, s(one)))))), true, d(f(one, f(one, s(s(one))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 3 (ax2) }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(d(s(f(one, s(f(one, s(one)))))), true, d(f(one, s(s(f(one, s(one)))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 3 (ax2) }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(ifeq(d(s(f(one, s(f(one, s(one)))))), true, d(s(s(f(one, s(f(one, s(one))))))), true), true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 6 (ax5) }
% 0.63/0.40 ifeq(ifeq(ifeq(ifeq(true, true, d(s(f(one, s(s(s(s(s(one)))))))), true), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 5 (ifeq_axiom) }
% 0.63/0.40 ifeq(ifeq(ifeq(d(s(f(one, s(s(s(s(s(one)))))))), true, d(f(one, s(s(s(s(s(s(one)))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 3 (ax2) }
% 0.63/0.40 ifeq(ifeq(ifeq(d(s(f(one, s(s(s(s(s(one)))))))), true, d(s(s(f(one, s(s(s(s(s(one))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 6 (ax5) }
% 0.63/0.40 ifeq(ifeq(true, true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 5 (ifeq_axiom) }
% 0.63/0.40 ifeq(d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one))))))))))))))), true, d(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(one)))))))))))))))), true)
% 0.63/0.40 = { by axiom 6 (ax5) }
% 0.63/0.40 true
% 0.63/0.40 % SZS output end Proof
% 0.63/0.40
% 0.63/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------