TSTP Solution File: GRP655-14 by Twee---2.5.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : GRP655-14 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n001.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 : Mon Jun 24 07:13:14 EDT 2024
% Result : Unsatisfiable 2.83s 0.74s
% Output : Proof 2.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP655-14 : TPTP v8.2.0. Released v8.1.0.
% 0.11/0.13 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 20 09:09:08 EDT 2024
% 0.12/0.34 % CPUTime :
% 2.83/0.74 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.83/0.74
% 2.83/0.74 % SZS status Unsatisfiable
% 2.83/0.74
% 2.83/0.77 % SZS output start Proof
% 2.83/0.77 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 2.83/0.77 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 2.83/0.77 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 2.83/0.77 Axiom 4 (f04): rd(mult(X, Y), Y) = X.
% 2.83/0.77 Axiom 5 (f05): mult(X, mult(Y, mult(Z, Y))) = mult(mult(mult(X, Y), Z), Y).
% 2.83/0.77
% 2.83/0.77 Lemma 6: rd(mult(X, mult(Y, Z)), Y) = mult(mult(X, Y), rd(Z, Y)).
% 2.83/0.77 Proof:
% 2.83/0.77 rd(mult(X, mult(Y, Z)), Y)
% 2.83/0.77 = { by axiom 2 (f03) R->L }
% 2.83/0.77 rd(mult(X, mult(Y, mult(rd(Z, Y), Y))), Y)
% 2.83/0.77 = { by axiom 5 (f05) }
% 2.83/0.77 rd(mult(mult(mult(X, Y), rd(Z, Y)), Y), Y)
% 2.83/0.77 = { by axiom 4 (f04) }
% 2.83/0.77 mult(mult(X, Y), rd(Z, Y))
% 2.83/0.77
% 2.83/0.77 Lemma 7: mult(mult(X, Y), rd(ld(Y, Z), Y)) = rd(mult(X, Z), Y).
% 2.83/0.77 Proof:
% 2.83/0.77 mult(mult(X, Y), rd(ld(Y, Z), Y))
% 2.83/0.77 = { by lemma 6 R->L }
% 2.83/0.77 rd(mult(X, mult(Y, ld(Y, Z))), Y)
% 2.83/0.77 = { by axiom 1 (f01) }
% 2.83/0.77 rd(mult(X, Z), Y)
% 2.83/0.77
% 2.83/0.77 Lemma 8: ld(rd(X, Y), X) = Y.
% 2.83/0.77 Proof:
% 2.83/0.77 ld(rd(X, Y), X)
% 2.83/0.77 = { by axiom 2 (f03) R->L }
% 2.83/0.77 ld(rd(X, Y), mult(rd(X, Y), Y))
% 2.83/0.77 = { by axiom 3 (f02) }
% 2.83/0.77 Y
% 2.83/0.77
% 2.83/0.77 Lemma 9: mult(rd(X, Y), mult(Y, mult(Z, Y))) = mult(mult(X, Z), Y).
% 2.83/0.77 Proof:
% 2.83/0.77 mult(rd(X, Y), mult(Y, mult(Z, Y)))
% 2.83/0.77 = { by axiom 5 (f05) }
% 2.83/0.77 mult(mult(mult(rd(X, Y), Y), Z), Y)
% 2.83/0.77 = { by axiom 2 (f03) }
% 2.83/0.77 mult(mult(X, Z), Y)
% 2.83/0.77
% 2.83/0.77 Lemma 10: mult(ld(X, rd(X, Y)), Y) = ld(Y, Y).
% 2.83/0.77 Proof:
% 2.83/0.77 mult(ld(X, rd(X, Y)), Y)
% 2.83/0.77 = { by axiom 3 (f02) R->L }
% 2.83/0.77 ld(Y, mult(Y, mult(ld(X, rd(X, Y)), Y)))
% 2.83/0.77 = { by axiom 3 (f02) R->L }
% 2.83/0.77 ld(Y, ld(rd(X, Y), mult(rd(X, Y), mult(Y, mult(ld(X, rd(X, Y)), Y)))))
% 2.83/0.77 = { by lemma 9 }
% 2.83/0.77 ld(Y, ld(rd(X, Y), mult(mult(X, ld(X, rd(X, Y))), Y)))
% 2.83/0.77 = { by axiom 1 (f01) }
% 2.83/0.77 ld(Y, ld(rd(X, Y), mult(rd(X, Y), Y)))
% 2.83/0.77 = { by axiom 3 (f02) }
% 2.83/0.77 ld(Y, Y)
% 2.83/0.77
% 2.83/0.77 Lemma 11: ld(Z, rd(Z, Y)) = ld(X, rd(X, Y)).
% 2.83/0.77 Proof:
% 2.83/0.77 ld(Z, rd(Z, Y))
% 2.83/0.77 = { by axiom 4 (f04) R->L }
% 2.83/0.77 rd(mult(ld(Z, rd(Z, Y)), Y), Y)
% 2.83/0.77 = { by lemma 10 }
% 2.83/0.77 rd(ld(Y, Y), Y)
% 2.83/0.77 = { by lemma 10 R->L }
% 2.83/0.77 rd(mult(ld(X, rd(X, Y)), Y), Y)
% 2.83/0.77 = { by axiom 4 (f04) }
% 2.83/0.77 ld(X, rd(X, Y))
% 2.83/0.77
% 2.83/0.77 Lemma 12: mult(X, ld(Y, rd(Y, Z))) = rd(X, Z).
% 2.83/0.77 Proof:
% 2.83/0.77 mult(X, ld(Y, rd(Y, Z)))
% 2.83/0.77 = { by lemma 11 }
% 2.83/0.77 mult(X, ld(X, rd(X, Z)))
% 2.83/0.77 = { by axiom 1 (f01) }
% 2.83/0.77 rd(X, Z)
% 2.83/0.77
% 2.83/0.77 Lemma 13: rd(X, ld(Y, X)) = Y.
% 2.83/0.77 Proof:
% 2.83/0.77 rd(X, ld(Y, X))
% 2.83/0.77 = { by axiom 1 (f01) R->L }
% 2.83/0.77 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 2.83/0.77 = { by axiom 4 (f04) }
% 2.83/0.77 Y
% 2.83/0.77
% 2.83/0.77 Lemma 14: ld(X, rd(X, ld(Y, Z))) = ld(Z, Y).
% 2.83/0.77 Proof:
% 2.83/0.77 ld(X, rd(X, ld(Y, Z)))
% 2.83/0.77 = { by lemma 11 }
% 2.83/0.77 ld(Z, rd(Z, ld(Y, Z)))
% 2.83/0.77 = { by lemma 13 }
% 2.83/0.77 ld(Z, Y)
% 2.83/0.77
% 2.83/0.77 Lemma 15: rd(X, ld(Y, Z)) = mult(X, ld(Z, Y)).
% 2.83/0.77 Proof:
% 2.83/0.77 rd(X, ld(Y, Z))
% 2.83/0.77 = { by lemma 12 R->L }
% 2.83/0.77 mult(X, ld(W, rd(W, ld(Y, Z))))
% 2.83/0.77 = { by lemma 14 }
% 2.83/0.77 mult(X, ld(Z, Y))
% 2.83/0.77
% 2.83/0.77 Lemma 16: rd(ld(X, X), X) = ld(Y, rd(Y, X)).
% 2.83/0.77 Proof:
% 2.83/0.77 rd(ld(X, X), X)
% 2.83/0.77 = { by lemma 10 R->L }
% 2.83/0.77 rd(mult(ld(Y, rd(Y, X)), X), X)
% 2.83/0.77 = { by axiom 4 (f04) }
% 2.83/0.77 ld(Y, rd(Y, X))
% 2.83/0.77
% 2.83/0.77 Lemma 17: mult(X, rd(Y, Y)) = mult(X, ld(Y, Y)).
% 2.83/0.77 Proof:
% 2.83/0.77 mult(X, rd(Y, Y))
% 2.83/0.77 = { by axiom 3 (f02) R->L }
% 2.83/0.77 mult(X, rd(ld(Y, mult(Y, Y)), Y))
% 2.83/0.77 = { by axiom 2 (f03) R->L }
% 2.83/0.77 mult(mult(rd(X, Y), Y), rd(ld(Y, mult(Y, Y)), Y))
% 2.83/0.77 = { by lemma 7 }
% 2.83/0.77 rd(mult(rd(X, Y), mult(Y, Y)), Y)
% 2.83/0.77 = { by lemma 8 R->L }
% 2.83/0.77 rd(mult(rd(X, Y), mult(Y, ld(rd(Z, Y), Z))), Y)
% 2.83/0.77 = { by lemma 15 R->L }
% 2.83/0.77 rd(mult(rd(X, Y), rd(Y, ld(Z, rd(Z, Y)))), Y)
% 2.83/0.77 = { by lemma 16 R->L }
% 2.83/0.77 rd(mult(rd(X, Y), rd(Y, rd(ld(Y, Y), Y))), Y)
% 2.83/0.77 = { by lemma 12 R->L }
% 2.83/0.77 rd(mult(mult(X, ld(W, rd(W, Y))), rd(Y, rd(ld(Y, Y), Y))), Y)
% 2.83/0.77 = { by lemma 16 R->L }
% 2.83/0.77 rd(mult(mult(X, rd(ld(Y, Y), Y)), rd(Y, rd(ld(Y, Y), Y))), Y)
% 2.83/0.77 = { by lemma 6 R->L }
% 2.83/0.77 rd(rd(mult(X, mult(rd(ld(Y, Y), Y), Y)), rd(ld(Y, Y), Y)), Y)
% 2.83/0.77 = { by axiom 2 (f03) }
% 2.83/0.77 rd(rd(mult(X, ld(Y, Y)), rd(ld(Y, Y), Y)), Y)
% 2.83/0.77 = { by lemma 16 }
% 2.83/0.77 rd(rd(mult(X, ld(Y, Y)), ld(V, rd(V, Y))), Y)
% 2.83/0.77 = { by lemma 15 }
% 2.83/0.77 rd(mult(mult(X, ld(Y, Y)), ld(rd(V, Y), V)), Y)
% 2.83/0.77 = { by lemma 8 }
% 2.83/0.77 rd(mult(mult(X, ld(Y, Y)), Y), Y)
% 2.83/0.77 = { by axiom 4 (f04) }
% 2.83/0.77 mult(X, ld(Y, Y))
% 2.83/0.77
% 2.83/0.77 Lemma 18: rd(X, X) = ld(X, X).
% 2.83/0.77 Proof:
% 2.83/0.77 rd(X, X)
% 2.83/0.77 = { by axiom 3 (f02) R->L }
% 2.83/0.77 ld(Y, mult(Y, rd(X, X)))
% 2.83/0.77 = { by lemma 17 }
% 2.83/0.77 ld(Y, mult(Y, ld(X, X)))
% 2.83/0.77 = { by axiom 3 (f02) }
% 2.83/0.77 ld(X, X)
% 2.83/0.77
% 2.83/0.77 Lemma 19: ld(X, rd(X, Y)) = ld(Y, ld(Y, Y)).
% 2.83/0.77 Proof:
% 2.83/0.77 ld(X, rd(X, Y))
% 2.83/0.77 = { by lemma 11 }
% 2.83/0.77 ld(Y, rd(Y, Y))
% 2.83/0.77 = { by lemma 18 }
% 2.83/0.77 ld(Y, ld(Y, Y))
% 2.83/0.77
% 2.83/0.77 Lemma 20: ld(mult(X, Y), X) = ld(Z, rd(Z, Y)).
% 2.83/0.77 Proof:
% 2.83/0.77 ld(mult(X, Y), X)
% 2.83/0.77 = { by axiom 4 (f04) R->L }
% 2.83/0.77 ld(mult(X, Y), rd(mult(X, Y), Y))
% 2.83/0.77 = { by lemma 11 R->L }
% 2.83/0.77 ld(Z, rd(Z, Y))
% 2.83/0.77
% 2.83/0.77 Lemma 21: mult(X, mult(ld(X, Y), mult(Z, ld(X, Y)))) = mult(mult(Y, Z), ld(X, Y)).
% 2.83/0.77 Proof:
% 2.83/0.77 mult(X, mult(ld(X, Y), mult(Z, ld(X, Y))))
% 2.83/0.77 = { by axiom 5 (f05) }
% 2.83/0.77 mult(mult(mult(X, ld(X, Y)), Z), ld(X, Y))
% 2.83/0.77 = { by axiom 1 (f01) }
% 2.83/0.77 mult(mult(Y, Z), ld(X, Y))
% 2.83/0.77
% 2.83/0.77 Lemma 22: ld(X, mult(mult(Y, Z), ld(X, Y))) = mult(ld(X, Y), mult(Z, ld(X, Y))).
% 2.83/0.77 Proof:
% 2.83/0.77 ld(X, mult(mult(Y, Z), ld(X, Y)))
% 2.83/0.77 = { by lemma 21 R->L }
% 2.83/0.77 ld(X, mult(X, mult(ld(X, Y), mult(Z, ld(X, Y)))))
% 2.83/0.77 = { by axiom 3 (f02) }
% 2.83/0.77 mult(ld(X, Y), mult(Z, ld(X, Y)))
% 2.83/0.77
% 2.83/0.77 Lemma 23: mult(ld(X, rd(X, Y)), rd(Y, Y)) = ld(Z, rd(Z, Y)).
% 2.83/0.77 Proof:
% 2.83/0.77 mult(ld(X, rd(X, Y)), rd(Y, Y))
% 2.83/0.77 = { by lemma 12 R->L }
% 2.83/0.77 mult(ld(X, rd(X, Y)), mult(Y, ld(W, rd(W, Y))))
% 2.83/0.77 = { by lemma 20 R->L }
% 2.83/0.77 mult(ld(mult(V, Y), V), mult(Y, ld(W, rd(W, Y))))
% 2.83/0.77 = { by lemma 20 R->L }
% 2.83/0.77 mult(ld(mult(V, Y), V), mult(Y, ld(mult(V, Y), V)))
% 2.83/0.77 = { by lemma 22 R->L }
% 2.83/0.77 ld(mult(V, Y), mult(mult(V, Y), ld(mult(V, Y), V)))
% 2.83/0.77 = { by axiom 1 (f01) }
% 2.83/0.77 ld(mult(V, Y), V)
% 2.83/0.77 = { by lemma 20 }
% 2.83/0.77 ld(Z, rd(Z, Y))
% 2.83/0.77
% 2.83/0.77 Lemma 24: rd(X, rd(Y, Y)) = mult(X, rd(Y, Y)).
% 2.83/0.77 Proof:
% 2.83/0.77 rd(X, rd(Y, Y))
% 2.83/0.77 = { by lemma 12 R->L }
% 2.83/0.77 mult(X, ld(Z, rd(Z, rd(Y, Y))))
% 2.83/0.77 = { by lemma 20 R->L }
% 2.83/0.77 mult(X, ld(mult(ld(W, rd(W, Y)), rd(Y, Y)), ld(W, rd(W, Y))))
% 2.83/0.77 = { by lemma 23 }
% 2.83/0.77 mult(X, ld(ld(W, rd(W, Y)), ld(W, rd(W, Y))))
% 2.83/0.77 = { by lemma 10 R->L }
% 2.83/0.77 mult(X, mult(ld(rd(W, Y), rd(rd(W, Y), ld(W, rd(W, Y)))), ld(W, rd(W, Y))))
% 2.83/0.77 = { by lemma 13 }
% 2.83/0.77 mult(X, mult(ld(rd(W, Y), W), ld(W, rd(W, Y))))
% 2.83/0.77 = { by lemma 12 }
% 2.83/0.77 mult(X, rd(ld(rd(W, Y), W), Y))
% 2.83/0.77 = { by lemma 8 }
% 2.83/0.77 mult(X, rd(Y, Y))
% 2.83/0.77
% 2.83/0.77 Lemma 25: mult(ld(X, X), ld(X, X)) = ld(X, X).
% 2.83/0.77 Proof:
% 2.83/0.77 mult(ld(X, X), ld(X, X))
% 2.83/0.77 = { by lemma 18 R->L }
% 2.83/0.77 mult(rd(X, X), ld(X, X))
% 2.83/0.77 = { by lemma 12 R->L }
% 2.83/0.77 mult(mult(X, ld(Y, rd(Y, X))), ld(X, X))
% 2.83/0.77 = { by lemma 21 R->L }
% 2.83/0.78 mult(X, mult(ld(X, X), mult(ld(Y, rd(Y, X)), ld(X, X))))
% 2.83/0.78 = { by lemma 19 }
% 2.83/0.78 mult(X, mult(ld(X, X), mult(ld(X, ld(X, X)), ld(X, X))))
% 2.83/0.78 = { by lemma 17 R->L }
% 2.83/0.78 mult(X, mult(ld(X, X), mult(ld(X, ld(X, X)), rd(X, X))))
% 2.83/0.78 = { by lemma 19 R->L }
% 2.83/0.78 mult(X, mult(ld(X, X), mult(ld(Z, rd(Z, X)), rd(X, X))))
% 2.83/0.78 = { by lemma 23 }
% 2.83/0.78 mult(X, mult(ld(X, X), ld(W, rd(W, X))))
% 2.83/0.78 = { by lemma 12 }
% 2.83/0.78 mult(X, rd(ld(X, X), X))
% 2.83/0.78 = { by lemma 16 }
% 2.83/0.78 mult(X, ld(V, rd(V, X)))
% 2.83/0.78 = { by lemma 12 }
% 2.83/0.78 rd(X, X)
% 2.83/0.78 = { by lemma 18 }
% 2.83/0.78 ld(X, X)
% 2.83/0.78
% 2.83/0.78 Lemma 26: mult(ld(ld(X, Y), Z), ld(Y, X)) = mult(ld(Y, X), mult(Z, ld(Y, X))).
% 2.83/0.78 Proof:
% 2.83/0.78 mult(ld(ld(X, Y), Z), ld(Y, X))
% 2.83/0.78 = { by lemma 15 R->L }
% 2.83/0.78 rd(ld(ld(X, Y), Z), ld(X, Y))
% 2.83/0.78 = { by axiom 3 (f02) R->L }
% 2.83/0.78 ld(Y, mult(Y, rd(ld(ld(X, Y), Z), ld(X, Y))))
% 2.83/0.78 = { by axiom 4 (f04) R->L }
% 2.83/0.78 ld(Y, rd(mult(mult(Y, rd(ld(ld(X, Y), Z), ld(X, Y))), ld(X, Y)), ld(X, Y)))
% 2.83/0.78 = { by lemma 21 R->L }
% 2.83/0.78 ld(Y, rd(mult(X, mult(ld(X, Y), mult(rd(ld(ld(X, Y), Z), ld(X, Y)), ld(X, Y)))), ld(X, Y)))
% 2.83/0.78 = { by axiom 2 (f03) }
% 2.83/0.78 ld(Y, rd(mult(X, mult(ld(X, Y), ld(ld(X, Y), Z))), ld(X, Y)))
% 2.83/0.78 = { by axiom 1 (f01) }
% 2.83/0.78 ld(Y, rd(mult(X, Z), ld(X, Y)))
% 2.83/0.78 = { by lemma 15 }
% 2.83/0.78 ld(Y, mult(mult(X, Z), ld(Y, X)))
% 2.83/0.78 = { by lemma 22 }
% 2.83/0.78 mult(ld(Y, X), mult(Z, ld(Y, X)))
% 2.83/0.78
% 2.83/0.78 Lemma 27: mult(ld(X, Y), mult(ld(Y, X), ld(X, Y))) = ld(X, Y).
% 2.83/0.78 Proof:
% 2.83/0.78 mult(ld(X, Y), mult(ld(Y, X), ld(X, Y)))
% 2.83/0.78 = { by lemma 22 R->L }
% 2.83/0.78 ld(X, mult(mult(Y, ld(Y, X)), ld(X, Y)))
% 2.83/0.78 = { by axiom 1 (f01) }
% 2.83/0.78 ld(X, mult(X, ld(X, Y)))
% 2.83/0.78 = { by axiom 3 (f02) }
% 2.83/0.78 ld(X, Y)
% 2.83/0.78
% 2.83/0.78 Lemma 28: mult(mult(X, ld(Y, Z)), ld(Z, Y)) = X.
% 2.83/0.78 Proof:
% 2.83/0.78 mult(mult(X, ld(Y, Z)), ld(Z, Y))
% 2.83/0.78 = { by lemma 9 R->L }
% 2.83/0.78 mult(rd(X, ld(Z, Y)), mult(ld(Z, Y), mult(ld(Y, Z), ld(Z, Y))))
% 2.83/0.78 = { by lemma 27 }
% 2.83/0.78 mult(rd(X, ld(Z, Y)), ld(Z, Y))
% 2.83/0.78 = { by axiom 2 (f03) }
% 2.83/0.78 X
% 2.83/0.78
% 2.83/0.78 Lemma 29: mult(mult(ld(X, Y), ld(X, Y)), mult(ld(Y, X), Z)) = ld(ld(Y, X), Z).
% 2.83/0.78 Proof:
% 2.83/0.78 mult(mult(ld(X, Y), ld(X, Y)), mult(ld(Y, X), Z))
% 2.83/0.78 = { by lemma 15 R->L }
% 2.83/0.78 mult(rd(ld(X, Y), ld(Y, X)), mult(ld(Y, X), Z))
% 2.83/0.78 = { by lemma 28 R->L }
% 2.83/0.78 mult(rd(ld(X, Y), ld(Y, X)), mult(ld(Y, X), mult(mult(Z, ld(X, Y)), ld(Y, X))))
% 2.83/0.78 = { by lemma 9 }
% 2.83/0.78 mult(mult(ld(X, Y), mult(Z, ld(X, Y))), ld(Y, X))
% 2.83/0.78 = { by lemma 26 R->L }
% 2.83/0.78 mult(mult(ld(ld(Y, X), Z), ld(X, Y)), ld(Y, X))
% 2.83/0.78 = { by lemma 28 }
% 2.83/0.78 ld(ld(Y, X), Z)
% 2.83/0.78
% 2.83/0.78 Goal 1 (goal): mult(ld(x1, x1), x0) = x0.
% 2.83/0.78 Proof:
% 2.83/0.78 mult(ld(x1, x1), x0)
% 2.83/0.78 = { by axiom 4 (f04) R->L }
% 2.83/0.78 mult(rd(mult(ld(x1, x1), ld(x0, x0)), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 25 R->L }
% 2.83/0.78 mult(rd(mult(mult(ld(x1, x1), ld(x1, x1)), ld(x0, x0)), ld(x0, x0)), x0)
% 2.83/0.78 = { by axiom 1 (f01) R->L }
% 2.83/0.78 mult(rd(mult(mult(ld(x1, x1), ld(x1, x1)), mult(ld(x1, x1), ld(ld(x1, x1), ld(x0, x0)))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 29 }
% 2.83/0.78 mult(rd(ld(ld(x1, x1), ld(ld(x1, x1), ld(x0, x0))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 14 R->L }
% 2.83/0.78 mult(rd(ld(X, rd(X, ld(ld(ld(x1, x1), ld(x0, x0)), ld(x1, x1)))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 25 R->L }
% 2.83/0.78 mult(rd(ld(X, rd(X, ld(ld(ld(x1, x1), ld(x0, x0)), mult(ld(x1, x1), ld(x1, x1))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 29 R->L }
% 2.83/0.78 mult(rd(ld(X, rd(X, ld(mult(mult(ld(x1, x1), ld(x1, x1)), mult(ld(x1, x1), ld(x0, x0))), mult(ld(x1, x1), ld(x1, x1))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 20 }
% 2.83/0.78 mult(rd(ld(X, rd(X, ld(Y, rd(Y, mult(ld(x1, x1), ld(x0, x0)))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 16 R->L }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(ld(mult(ld(x1, x1), ld(x0, x0)), mult(ld(x1, x1), ld(x0, x0))), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 17 R->L }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(ld(mult(ld(x1, x1), rd(x0, x0)), mult(ld(x1, x1), ld(x0, x0))), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 17 R->L }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(ld(mult(ld(x1, x1), rd(x0, x0)), mult(ld(x1, x1), rd(x0, x0))), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 24 R->L }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(ld(mult(ld(x1, x1), rd(x0, x0)), rd(ld(x1, x1), rd(x0, x0))), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 27 R->L }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(ld(mult(ld(x1, x1), rd(x0, x0)), rd(mult(ld(x1, x1), mult(ld(x1, x1), ld(x1, x1))), rd(x0, x0))), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 7 R->L }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(ld(mult(ld(x1, x1), rd(x0, x0)), mult(mult(ld(x1, x1), rd(x0, x0)), rd(ld(rd(x0, x0), mult(ld(x1, x1), ld(x1, x1))), rd(x0, x0)))), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by axiom 3 (f02) }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(rd(ld(rd(x0, x0), mult(ld(x1, x1), ld(x1, x1))), rd(x0, x0)), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 25 }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(rd(ld(rd(x0, x0), ld(x1, x1)), rd(x0, x0)), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 24 }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(mult(ld(rd(x0, x0), ld(x1, x1)), rd(x0, x0)), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 17 }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(mult(ld(rd(x0, x0), ld(x1, x1)), ld(x0, x0)), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 18 }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(mult(ld(ld(x0, x0), ld(x1, x1)), ld(x0, x0)), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 26 }
% 2.83/0.78 mult(rd(ld(X, rd(X, rd(mult(ld(x0, x0), mult(ld(x1, x1), ld(x0, x0))), mult(ld(x1, x1), ld(x0, x0))))), ld(x0, x0)), x0)
% 2.83/0.78 = { by axiom 4 (f04) }
% 2.83/0.78 mult(rd(ld(X, rd(X, ld(x0, x0))), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 14 }
% 2.83/0.78 mult(rd(ld(x0, x0), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 15 }
% 2.83/0.78 mult(mult(ld(x0, x0), ld(x0, x0)), x0)
% 2.83/0.78 = { by lemma 25 }
% 2.83/0.78 mult(ld(x0, x0), x0)
% 2.83/0.78 = { by lemma 18 R->L }
% 2.83/0.78 mult(rd(x0, x0), x0)
% 2.83/0.78 = { by axiom 2 (f03) }
% 2.83/0.78 x0
% 2.83/0.78 % SZS output end Proof
% 2.83/0.78
% 2.83/0.78 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------