TSTP Solution File: SYN090-1.008 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN090-1.008 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : 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 : Fri Sep 1 03:33:07 EDT 2023
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN090-1.008 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.35 % Computer : n001.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sat Aug 26 18:30:01 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.19/0.46 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.46
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 Take the following subset of the input axioms:
% 0.19/0.48 fof(s3_goal_1, negated_conjecture, ~p_0 | ~q_0).
% 0.19/0.48 fof(s3_type11_11, axiom, p_5 | (~p_6 | ~p_7)).
% 0.19/0.48 fof(s3_type11_13, axiom, p_6 | (~p_7 | ~p_8)).
% 0.19/0.48 fof(s3_type11_15, axiom, p_7 | (~p_8 | ~p_9)).
% 0.19/0.48 fof(s3_type11_17, axiom, p_8 | (~p_9 | ~p_10)).
% 0.19/0.48 fof(s3_type11_19, axiom, p_9 | (~p_10 | ~p_11)).
% 0.19/0.48 fof(s3_type11_2, axiom, p_0 | (~q_1 | ~q_2)).
% 0.19/0.48 fof(s3_type11_22, axiom, p_10 | (~q_11 | ~q_12)).
% 0.19/0.48 fof(s3_type11_23, axiom, p_11 | (~p_12 | ~p_13)).
% 0.19/0.48 fof(s3_type11_25, axiom, p_12 | (~p_13 | ~p_14)).
% 0.19/0.48 fof(s3_type11_27, axiom, p_13 | (~p_14 | ~p_15)).
% 0.19/0.48 fof(s3_type11_3, axiom, p_1 | (~p_2 | ~p_3)).
% 0.19/0.48 fof(s3_type11_5, axiom, p_2 | (~p_3 | ~p_4)).
% 0.19/0.48 fof(s3_type11_7, axiom, p_3 | (~p_4 | ~p_5)).
% 0.19/0.48 fof(s3_type11_9, axiom, p_4 | (~p_5 | ~p_6)).
% 0.19/0.48 fof(s3_type12_1, axiom, q_0 | (~p_1 | ~q_2)).
% 0.19/0.48 fof(s3_type12_11, axiom, q_5 | (~p_6 | ~q_7)).
% 0.19/0.48 fof(s3_type12_13, axiom, q_6 | (~p_7 | ~q_8)).
% 0.19/0.48 fof(s3_type12_15, axiom, q_7 | (~p_8 | ~q_9)).
% 0.19/0.48 fof(s3_type12_17, axiom, q_8 | (~p_9 | ~q_10)).
% 0.19/0.48 fof(s3_type12_19, axiom, q_9 | (~p_10 | ~q_11)).
% 0.19/0.48 fof(s3_type12_22, axiom, q_10 | (~q_11 | ~p_12)).
% 0.19/0.48 fof(s3_type12_24, axiom, q_11 | (~q_12 | ~p_13)).
% 0.19/0.48 fof(s3_type12_25, axiom, q_12 | (~p_13 | ~q_14)).
% 0.19/0.48 fof(s3_type12_3, axiom, q_1 | (~p_2 | ~q_3)).
% 0.19/0.48 fof(s3_type12_5, axiom, q_2 | (~p_3 | ~q_4)).
% 0.19/0.48 fof(s3_type12_7, axiom, q_3 | (~p_4 | ~q_5)).
% 0.19/0.48 fof(s3_type12_9, axiom, q_4 | (~p_5 | ~q_6)).
% 0.19/0.48 fof(t3_1, axiom, p_14).
% 0.19/0.48 fof(t3_2, axiom, p_15).
% 0.19/0.48 fof(t3_3, axiom, q_14).
% 0.19/0.48
% 0.19/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.48 fresh(y, y, x1...xn) = u
% 0.19/0.48 C => fresh(s, t, x1...xn) = v
% 0.19/0.48 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.48 variables of u and v.
% 0.19/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.48 input problem has no model of domain size 1).
% 0.19/0.48
% 0.19/0.48 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.48
% 0.19/0.48 Axiom 1 (t3_1): p_14 = true.
% 0.19/0.48 Axiom 2 (t3_3): q_14 = true.
% 0.19/0.48 Axiom 3 (t3_2): p_15 = true.
% 0.19/0.48 Axiom 4 (s3_type11_11): fresh112(X, X) = p_5.
% 0.19/0.48 Axiom 5 (s3_type11_11): fresh111(X, X) = true.
% 0.19/0.48 Axiom 6 (s3_type11_11): fresh112(p_7, true) = fresh111(p_6, true).
% 0.19/0.48 Axiom 7 (s3_type11_13): fresh108(X, X) = p_6.
% 0.19/0.48 Axiom 8 (s3_type11_13): fresh107(X, X) = true.
% 0.19/0.48 Axiom 9 (s3_type11_13): fresh108(p_8, true) = fresh107(p_7, true).
% 0.19/0.48 Axiom 10 (s3_type11_15): fresh104(X, X) = p_7.
% 0.19/0.48 Axiom 11 (s3_type11_15): fresh103(X, X) = true.
% 0.19/0.48 Axiom 12 (s3_type11_15): fresh104(p_9, true) = fresh103(p_8, true).
% 0.19/0.48 Axiom 13 (s3_type11_17): fresh100(X, X) = p_8.
% 0.19/0.48 Axiom 14 (s3_type11_17): fresh99(X, X) = true.
% 0.19/0.48 Axiom 15 (s3_type11_17): fresh100(p_10, true) = fresh99(p_9, true).
% 0.19/0.48 Axiom 16 (s3_type11_19): fresh96(X, X) = p_9.
% 0.19/0.48 Axiom 17 (s3_type11_19): fresh95(X, X) = true.
% 0.19/0.48 Axiom 18 (s3_type11_19): fresh96(p_11, true) = fresh95(p_10, true).
% 0.19/0.48 Axiom 19 (s3_type11_2): fresh94(X, X) = p_0.
% 0.19/0.48 Axiom 20 (s3_type11_2): fresh93(X, X) = true.
% 0.19/0.48 Axiom 21 (s3_type11_2): fresh94(q_2, true) = fresh93(q_1, true).
% 0.19/0.48 Axiom 22 (s3_type11_22): fresh88(X, X) = p_10.
% 0.19/0.48 Axiom 23 (s3_type11_22): fresh87(X, X) = true.
% 0.19/0.48 Axiom 24 (s3_type11_22): fresh88(q_12, true) = fresh87(q_11, true).
% 0.19/0.48 Axiom 25 (s3_type11_23): fresh86(X, X) = p_11.
% 0.19/0.48 Axiom 26 (s3_type11_23): fresh85(X, X) = true.
% 0.19/0.48 Axiom 27 (s3_type11_23): fresh86(p_13, true) = fresh85(p_12, true).
% 0.19/0.48 Axiom 28 (s3_type11_25): fresh82(X, X) = p_12.
% 0.19/0.48 Axiom 29 (s3_type11_25): fresh81(X, X) = true.
% 0.19/0.48 Axiom 30 (s3_type11_25): fresh82(p_14, true) = fresh81(p_13, true).
% 0.19/0.48 Axiom 31 (s3_type11_27): fresh78(X, X) = p_13.
% 0.19/0.48 Axiom 32 (s3_type11_27): fresh77(X, X) = true.
% 0.19/0.48 Axiom 33 (s3_type11_27): fresh78(p_15, true) = fresh77(p_14, true).
% 0.19/0.48 Axiom 34 (s3_type11_3): fresh74(X, X) = p_1.
% 0.19/0.48 Axiom 35 (s3_type11_3): fresh73(X, X) = true.
% 0.19/0.48 Axiom 36 (s3_type11_3): fresh74(p_3, true) = fresh73(p_2, true).
% 0.19/0.48 Axiom 37 (s3_type11_5): fresh70(X, X) = p_2.
% 0.19/0.48 Axiom 38 (s3_type11_5): fresh69(X, X) = true.
% 0.19/0.48 Axiom 39 (s3_type11_5): fresh70(p_4, true) = fresh69(p_3, true).
% 0.19/0.48 Axiom 40 (s3_type11_7): fresh66(X, X) = p_3.
% 0.19/0.48 Axiom 41 (s3_type11_7): fresh65(X, X) = true.
% 0.19/0.48 Axiom 42 (s3_type11_7): fresh66(p_5, true) = fresh65(p_4, true).
% 0.19/0.48 Axiom 43 (s3_type11_9): fresh62(X, X) = p_4.
% 0.19/0.48 Axiom 44 (s3_type11_9): fresh61(X, X) = true.
% 0.19/0.48 Axiom 45 (s3_type11_9): fresh62(p_6, true) = fresh61(p_5, true).
% 0.19/0.48 Axiom 46 (s3_type12_1): fresh60(X, X) = q_0.
% 0.19/0.48 Axiom 47 (s3_type12_1): fresh59(X, X) = true.
% 0.19/0.48 Axiom 48 (s3_type12_1): fresh60(q_2, true) = fresh59(p_1, true).
% 0.19/0.48 Axiom 49 (s3_type12_11): fresh56(X, X) = q_5.
% 0.19/0.48 Axiom 50 (s3_type12_11): fresh55(X, X) = true.
% 0.19/0.48 Axiom 51 (s3_type12_11): fresh56(q_7, true) = fresh55(p_6, true).
% 0.19/0.48 Axiom 52 (s3_type12_13): fresh52(X, X) = q_6.
% 0.19/0.48 Axiom 53 (s3_type12_13): fresh51(X, X) = true.
% 0.19/0.48 Axiom 54 (s3_type12_13): fresh52(q_8, true) = fresh51(p_7, true).
% 0.19/0.48 Axiom 55 (s3_type12_15): fresh48(X, X) = q_7.
% 0.19/0.48 Axiom 56 (s3_type12_15): fresh47(X, X) = true.
% 0.19/0.48 Axiom 57 (s3_type12_15): fresh48(q_9, true) = fresh47(p_8, true).
% 0.19/0.48 Axiom 58 (s3_type12_17): fresh44(X, X) = q_8.
% 0.19/0.48 Axiom 59 (s3_type12_17): fresh43(X, X) = true.
% 0.19/0.48 Axiom 60 (s3_type12_17): fresh44(q_10, true) = fresh43(p_9, true).
% 0.19/0.48 Axiom 61 (s3_type12_19): fresh40(X, X) = q_9.
% 0.19/0.48 Axiom 62 (s3_type12_19): fresh39(X, X) = true.
% 0.19/0.48 Axiom 63 (s3_type12_19): fresh40(q_11, true) = fresh39(p_10, true).
% 0.19/0.48 Axiom 64 (s3_type12_22): fresh32(X, X) = q_10.
% 0.19/0.48 Axiom 65 (s3_type12_22): fresh31(X, X) = true.
% 0.19/0.48 Axiom 66 (s3_type12_22): fresh32(p_12, true) = fresh31(q_11, true).
% 0.19/0.48 Axiom 67 (s3_type12_24): fresh28(X, X) = q_11.
% 0.19/0.48 Axiom 68 (s3_type12_24): fresh27(X, X) = true.
% 0.19/0.48 Axiom 69 (s3_type12_24): fresh28(p_13, true) = fresh27(q_12, true).
% 0.19/0.48 Axiom 70 (s3_type12_25): fresh26(X, X) = q_12.
% 0.19/0.48 Axiom 71 (s3_type12_25): fresh25(X, X) = true.
% 0.19/0.48 Axiom 72 (s3_type12_25): fresh26(q_14, true) = fresh25(p_13, true).
% 0.19/0.48 Axiom 73 (s3_type12_3): fresh18(X, X) = q_1.
% 0.19/0.48 Axiom 74 (s3_type12_3): fresh17(X, X) = true.
% 0.19/0.48 Axiom 75 (s3_type12_3): fresh18(q_3, true) = fresh17(p_2, true).
% 0.19/0.48 Axiom 76 (s3_type12_5): fresh14(X, X) = q_2.
% 0.19/0.48 Axiom 77 (s3_type12_5): fresh13(X, X) = true.
% 0.19/0.48 Axiom 78 (s3_type12_5): fresh14(q_4, true) = fresh13(p_3, true).
% 0.19/0.48 Axiom 79 (s3_type12_7): fresh10(X, X) = q_3.
% 0.19/0.48 Axiom 80 (s3_type12_7): fresh9(X, X) = true.
% 0.19/0.48 Axiom 81 (s3_type12_7): fresh10(q_5, true) = fresh9(p_4, true).
% 0.19/0.48 Axiom 82 (s3_type12_9): fresh6(X, X) = q_4.
% 0.19/0.48 Axiom 83 (s3_type12_9): fresh5(X, X) = true.
% 0.19/0.48 Axiom 84 (s3_type12_9): fresh6(q_6, true) = fresh5(p_5, true).
% 0.19/0.48
% 0.19/0.48 Lemma 85: p_13 = true.
% 0.19/0.48 Proof:
% 0.19/0.48 p_13
% 0.19/0.48 = { by axiom 31 (s3_type11_27) R->L }
% 0.19/0.48 fresh78(true, true)
% 0.19/0.48 = { by axiom 3 (t3_2) R->L }
% 0.19/0.48 fresh78(p_15, true)
% 0.19/0.48 = { by axiom 33 (s3_type11_27) }
% 0.19/0.48 fresh77(p_14, true)
% 0.19/0.48 = { by axiom 1 (t3_1) }
% 0.19/0.48 fresh77(true, true)
% 0.19/0.48 = { by axiom 32 (s3_type11_27) }
% 0.19/0.48 true
% 0.19/0.48
% 0.19/0.48 Lemma 86: q_12 = true.
% 0.19/0.48 Proof:
% 0.19/0.48 q_12
% 0.19/0.48 = { by axiom 70 (s3_type12_25) R->L }
% 0.19/0.48 fresh26(true, true)
% 0.19/0.48 = { by axiom 2 (t3_3) R->L }
% 0.19/0.48 fresh26(q_14, true)
% 0.19/0.48 = { by axiom 72 (s3_type12_25) }
% 0.19/0.48 fresh25(p_13, true)
% 0.19/0.48 = { by lemma 85 }
% 0.19/0.48 fresh25(true, true)
% 0.19/0.48 = { by axiom 71 (s3_type12_25) }
% 0.19/0.48 true
% 0.19/0.48
% 0.19/0.48 Lemma 87: q_11 = true.
% 0.19/0.48 Proof:
% 0.19/0.48 q_11
% 0.19/0.48 = { by axiom 67 (s3_type12_24) R->L }
% 0.19/0.48 fresh28(true, true)
% 0.19/0.48 = { by lemma 85 R->L }
% 0.19/0.48 fresh28(p_13, true)
% 0.19/0.48 = { by axiom 69 (s3_type12_24) }
% 0.19/0.48 fresh27(q_12, true)
% 0.19/0.48 = { by lemma 86 }
% 0.19/0.48 fresh27(true, true)
% 0.19/0.48 = { by axiom 68 (s3_type12_24) }
% 0.19/0.48 true
% 0.19/0.48
% 0.19/0.48 Lemma 88: p_10 = true.
% 0.19/0.48 Proof:
% 0.19/0.48 p_10
% 0.19/0.48 = { by axiom 22 (s3_type11_22) R->L }
% 0.19/0.48 fresh88(true, true)
% 0.19/0.48 = { by lemma 86 R->L }
% 0.19/0.48 fresh88(q_12, true)
% 0.19/0.48 = { by axiom 24 (s3_type11_22) }
% 0.19/0.48 fresh87(q_11, true)
% 0.19/0.48 = { by lemma 87 }
% 0.19/0.48 fresh87(true, true)
% 0.19/0.48 = { by axiom 23 (s3_type11_22) }
% 0.19/0.48 true
% 0.19/0.48
% 0.19/0.48 Lemma 89: p_12 = true.
% 0.19/0.48 Proof:
% 0.19/0.48 p_12
% 0.19/0.48 = { by axiom 28 (s3_type11_25) R->L }
% 0.19/0.48 fresh82(true, true)
% 0.19/0.48 = { by axiom 1 (t3_1) R->L }
% 0.19/0.48 fresh82(p_14, true)
% 0.19/0.48 = { by axiom 30 (s3_type11_25) }
% 0.19/0.48 fresh81(p_13, true)
% 0.19/0.48 = { by lemma 85 }
% 0.19/0.48 fresh81(true, true)
% 0.19/0.48 = { by axiom 29 (s3_type11_25) }
% 0.19/0.48 true
% 0.19/0.48
% 0.19/0.48 Lemma 90: p_9 = true.
% 0.19/0.48 Proof:
% 0.19/0.48 p_9
% 0.19/0.48 = { by axiom 16 (s3_type11_19) R->L }
% 0.19/0.48 fresh96(true, true)
% 0.19/0.48 = { by axiom 26 (s3_type11_23) R->L }
% 0.19/0.48 fresh96(fresh85(true, true), true)
% 0.19/0.48 = { by lemma 89 R->L }
% 0.19/0.48 fresh96(fresh85(p_12, true), true)
% 0.19/0.48 = { by axiom 27 (s3_type11_23) R->L }
% 0.19/0.48 fresh96(fresh86(p_13, true), true)
% 0.19/0.48 = { by lemma 85 }
% 0.19/0.48 fresh96(fresh86(true, true), true)
% 0.19/0.48 = { by axiom 25 (s3_type11_23) }
% 0.19/0.48 fresh96(p_11, true)
% 0.19/0.48 = { by axiom 18 (s3_type11_19) }
% 0.19/0.48 fresh95(p_10, true)
% 0.19/0.48 = { by lemma 88 }
% 0.19/0.48 fresh95(true, true)
% 0.19/0.48 = { by axiom 17 (s3_type11_19) }
% 0.19/0.48 true
% 0.19/0.48
% 0.19/0.49 Lemma 91: p_8 = true.
% 0.19/0.49 Proof:
% 0.19/0.49 p_8
% 0.19/0.49 = { by axiom 13 (s3_type11_17) R->L }
% 0.19/0.49 fresh100(true, true)
% 0.19/0.49 = { by lemma 88 R->L }
% 0.19/0.49 fresh100(p_10, true)
% 0.19/0.49 = { by axiom 15 (s3_type11_17) }
% 0.19/0.49 fresh99(p_9, true)
% 0.19/0.49 = { by lemma 90 }
% 0.19/0.49 fresh99(true, true)
% 0.19/0.49 = { by axiom 14 (s3_type11_17) }
% 0.19/0.49 true
% 0.19/0.49
% 0.19/0.49 Lemma 92: p_7 = true.
% 0.19/0.49 Proof:
% 0.19/0.49 p_7
% 0.19/0.49 = { by axiom 10 (s3_type11_15) R->L }
% 0.19/0.49 fresh104(true, true)
% 0.19/0.49 = { by lemma 90 R->L }
% 0.19/0.49 fresh104(p_9, true)
% 0.19/0.49 = { by axiom 12 (s3_type11_15) }
% 0.19/0.49 fresh103(p_8, true)
% 0.19/0.49 = { by lemma 91 }
% 0.19/0.49 fresh103(true, true)
% 0.19/0.49 = { by axiom 11 (s3_type11_15) }
% 0.19/0.49 true
% 0.19/0.49
% 0.19/0.49 Lemma 93: p_6 = true.
% 0.19/0.49 Proof:
% 0.19/0.49 p_6
% 0.19/0.49 = { by axiom 7 (s3_type11_13) R->L }
% 0.19/0.49 fresh108(true, true)
% 0.19/0.49 = { by lemma 91 R->L }
% 0.19/0.49 fresh108(p_8, true)
% 0.19/0.49 = { by axiom 9 (s3_type11_13) }
% 0.19/0.49 fresh107(p_7, true)
% 0.19/0.49 = { by lemma 92 }
% 0.19/0.49 fresh107(true, true)
% 0.19/0.49 = { by axiom 8 (s3_type11_13) }
% 0.19/0.49 true
% 0.19/0.49
% 0.19/0.49 Lemma 94: p_5 = true.
% 0.19/0.49 Proof:
% 0.19/0.49 p_5
% 0.19/0.49 = { by axiom 4 (s3_type11_11) R->L }
% 0.19/0.49 fresh112(true, true)
% 0.19/0.49 = { by lemma 92 R->L }
% 0.19/0.49 fresh112(p_7, true)
% 0.19/0.49 = { by axiom 6 (s3_type11_11) }
% 0.19/0.49 fresh111(p_6, true)
% 0.19/0.49 = { by lemma 93 }
% 0.19/0.49 fresh111(true, true)
% 0.19/0.49 = { by axiom 5 (s3_type11_11) }
% 0.19/0.49 true
% 0.19/0.49
% 0.19/0.49 Lemma 95: p_4 = true.
% 0.19/0.49 Proof:
% 0.19/0.49 p_4
% 0.19/0.49 = { by axiom 43 (s3_type11_9) R->L }
% 0.19/0.49 fresh62(true, true)
% 0.19/0.49 = { by lemma 93 R->L }
% 0.19/0.49 fresh62(p_6, true)
% 0.19/0.49 = { by axiom 45 (s3_type11_9) }
% 0.19/0.49 fresh61(p_5, true)
% 0.19/0.49 = { by lemma 94 }
% 0.19/0.49 fresh61(true, true)
% 0.19/0.49 = { by axiom 44 (s3_type11_9) }
% 0.19/0.49 true
% 0.19/0.49
% 0.19/0.49 Lemma 96: p_3 = true.
% 0.19/0.49 Proof:
% 0.19/0.49 p_3
% 0.19/0.49 = { by axiom 40 (s3_type11_7) R->L }
% 0.19/0.49 fresh66(true, true)
% 0.19/0.49 = { by lemma 94 R->L }
% 0.19/0.49 fresh66(p_5, true)
% 0.19/0.49 = { by axiom 42 (s3_type11_7) }
% 0.19/0.49 fresh65(p_4, true)
% 0.19/0.49 = { by lemma 95 }
% 0.19/0.49 fresh65(true, true)
% 0.19/0.49 = { by axiom 41 (s3_type11_7) }
% 0.19/0.49 true
% 0.19/0.49
% 0.19/0.49 Lemma 97: p_2 = true.
% 0.19/0.49 Proof:
% 0.19/0.49 p_2
% 0.19/0.49 = { by axiom 37 (s3_type11_5) R->L }
% 0.19/0.49 fresh70(true, true)
% 0.19/0.49 = { by lemma 95 R->L }
% 0.19/0.49 fresh70(p_4, true)
% 0.19/0.49 = { by axiom 39 (s3_type11_5) }
% 0.19/0.49 fresh69(p_3, true)
% 0.19/0.49 = { by lemma 96 }
% 0.19/0.49 fresh69(true, true)
% 0.19/0.49 = { by axiom 38 (s3_type11_5) }
% 0.19/0.49 true
% 0.19/0.49
% 0.19/0.49 Lemma 98: q_2 = true.
% 0.19/0.49 Proof:
% 0.19/0.49 q_2
% 0.19/0.49 = { by axiom 76 (s3_type12_5) R->L }
% 0.19/0.49 fresh14(true, true)
% 0.19/0.49 = { by axiom 83 (s3_type12_9) R->L }
% 0.19/0.49 fresh14(fresh5(true, true), true)
% 0.19/0.49 = { by lemma 94 R->L }
% 0.19/0.49 fresh14(fresh5(p_5, true), true)
% 0.19/0.49 = { by axiom 84 (s3_type12_9) R->L }
% 0.19/0.49 fresh14(fresh6(q_6, true), true)
% 0.19/0.49 = { by axiom 52 (s3_type12_13) R->L }
% 0.19/0.49 fresh14(fresh6(fresh52(true, true), true), true)
% 0.19/0.49 = { by axiom 59 (s3_type12_17) R->L }
% 0.19/0.49 fresh14(fresh6(fresh52(fresh43(true, true), true), true), true)
% 0.19/0.49 = { by lemma 90 R->L }
% 0.19/0.49 fresh14(fresh6(fresh52(fresh43(p_9, true), true), true), true)
% 0.19/0.49 = { by axiom 60 (s3_type12_17) R->L }
% 0.19/0.49 fresh14(fresh6(fresh52(fresh44(q_10, true), true), true), true)
% 0.19/0.49 = { by axiom 64 (s3_type12_22) R->L }
% 0.19/0.49 fresh14(fresh6(fresh52(fresh44(fresh32(true, true), true), true), true), true)
% 0.19/0.49 = { by lemma 89 R->L }
% 0.19/0.49 fresh14(fresh6(fresh52(fresh44(fresh32(p_12, true), true), true), true), true)
% 0.19/0.49 = { by axiom 66 (s3_type12_22) }
% 0.19/0.49 fresh14(fresh6(fresh52(fresh44(fresh31(q_11, true), true), true), true), true)
% 0.19/0.49 = { by lemma 87 }
% 0.19/0.49 fresh14(fresh6(fresh52(fresh44(fresh31(true, true), true), true), true), true)
% 0.19/0.49 = { by axiom 65 (s3_type12_22) }
% 0.19/0.49 fresh14(fresh6(fresh52(fresh44(true, true), true), true), true)
% 0.19/0.49 = { by axiom 58 (s3_type12_17) }
% 0.19/0.49 fresh14(fresh6(fresh52(q_8, true), true), true)
% 0.19/0.49 = { by axiom 54 (s3_type12_13) }
% 0.19/0.49 fresh14(fresh6(fresh51(p_7, true), true), true)
% 0.19/0.49 = { by lemma 92 }
% 0.19/0.49 fresh14(fresh6(fresh51(true, true), true), true)
% 0.19/0.49 = { by axiom 53 (s3_type12_13) }
% 0.19/0.49 fresh14(fresh6(true, true), true)
% 0.19/0.49 = { by axiom 82 (s3_type12_9) }
% 0.19/0.49 fresh14(q_4, true)
% 0.19/0.49 = { by axiom 78 (s3_type12_5) }
% 0.19/0.49 fresh13(p_3, true)
% 0.19/0.49 = { by lemma 96 }
% 0.19/0.49 fresh13(true, true)
% 0.19/0.49 = { by axiom 77 (s3_type12_5) }
% 0.19/0.49 true
% 0.19/0.49
% 0.19/0.49 Goal 1 (s3_goal_1): tuple(p_0, q_0) = tuple(true, true).
% 0.19/0.49 Proof:
% 0.19/0.49 tuple(p_0, q_0)
% 0.19/0.49 = { by axiom 19 (s3_type11_2) R->L }
% 0.19/0.49 tuple(fresh94(true, true), q_0)
% 0.19/0.49 = { by lemma 98 R->L }
% 0.19/0.49 tuple(fresh94(q_2, true), q_0)
% 0.19/0.49 = { by axiom 21 (s3_type11_2) }
% 0.19/0.49 tuple(fresh93(q_1, true), q_0)
% 0.19/0.49 = { by axiom 73 (s3_type12_3) R->L }
% 0.19/0.49 tuple(fresh93(fresh18(true, true), true), q_0)
% 0.19/0.49 = { by axiom 80 (s3_type12_7) R->L }
% 0.19/0.49 tuple(fresh93(fresh18(fresh9(true, true), true), true), q_0)
% 0.19/0.49 = { by lemma 95 R->L }
% 0.19/0.49 tuple(fresh93(fresh18(fresh9(p_4, true), true), true), q_0)
% 0.19/0.49 = { by axiom 81 (s3_type12_7) R->L }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(q_5, true), true), true), q_0)
% 0.19/0.49 = { by axiom 49 (s3_type12_11) R->L }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh56(true, true), true), true), true), q_0)
% 0.19/0.49 = { by axiom 56 (s3_type12_15) R->L }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh56(fresh47(true, true), true), true), true), true), q_0)
% 0.19/0.49 = { by lemma 91 R->L }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh56(fresh47(p_8, true), true), true), true), true), q_0)
% 0.19/0.49 = { by axiom 57 (s3_type12_15) R->L }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh56(fresh48(q_9, true), true), true), true), true), q_0)
% 0.19/0.49 = { by axiom 61 (s3_type12_19) R->L }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh56(fresh48(fresh40(true, true), true), true), true), true), true), q_0)
% 0.19/0.49 = { by lemma 87 R->L }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh56(fresh48(fresh40(q_11, true), true), true), true), true), true), q_0)
% 0.19/0.49 = { by axiom 63 (s3_type12_19) }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh56(fresh48(fresh39(p_10, true), true), true), true), true), true), q_0)
% 0.19/0.49 = { by lemma 88 }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh56(fresh48(fresh39(true, true), true), true), true), true), true), q_0)
% 0.19/0.49 = { by axiom 62 (s3_type12_19) }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh56(fresh48(true, true), true), true), true), true), q_0)
% 0.19/0.49 = { by axiom 55 (s3_type12_15) }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh56(q_7, true), true), true), true), q_0)
% 0.19/0.49 = { by axiom 51 (s3_type12_11) }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh55(p_6, true), true), true), true), q_0)
% 0.19/0.49 = { by lemma 93 }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(fresh55(true, true), true), true), true), q_0)
% 0.19/0.49 = { by axiom 50 (s3_type12_11) }
% 0.19/0.49 tuple(fresh93(fresh18(fresh10(true, true), true), true), q_0)
% 0.19/0.49 = { by axiom 79 (s3_type12_7) }
% 0.19/0.49 tuple(fresh93(fresh18(q_3, true), true), q_0)
% 0.19/0.49 = { by axiom 75 (s3_type12_3) }
% 0.19/0.49 tuple(fresh93(fresh17(p_2, true), true), q_0)
% 0.19/0.49 = { by lemma 97 }
% 0.19/0.49 tuple(fresh93(fresh17(true, true), true), q_0)
% 0.19/0.49 = { by axiom 74 (s3_type12_3) }
% 0.19/0.49 tuple(fresh93(true, true), q_0)
% 0.19/0.49 = { by axiom 20 (s3_type11_2) }
% 0.19/0.49 tuple(true, q_0)
% 0.19/0.49 = { by axiom 46 (s3_type12_1) R->L }
% 0.19/0.49 tuple(true, fresh60(true, true))
% 0.19/0.49 = { by lemma 98 R->L }
% 0.19/0.49 tuple(true, fresh60(q_2, true))
% 0.19/0.49 = { by axiom 48 (s3_type12_1) }
% 0.19/0.49 tuple(true, fresh59(p_1, true))
% 0.19/0.49 = { by axiom 34 (s3_type11_3) R->L }
% 0.19/0.49 tuple(true, fresh59(fresh74(true, true), true))
% 0.19/0.49 = { by lemma 96 R->L }
% 0.19/0.49 tuple(true, fresh59(fresh74(p_3, true), true))
% 0.19/0.49 = { by axiom 36 (s3_type11_3) }
% 0.19/0.49 tuple(true, fresh59(fresh73(p_2, true), true))
% 0.19/0.49 = { by lemma 97 }
% 0.19/0.49 tuple(true, fresh59(fresh73(true, true), true))
% 0.19/0.49 = { by axiom 35 (s3_type11_3) }
% 0.19/0.49 tuple(true, fresh59(true, true))
% 0.19/0.49 = { by axiom 47 (s3_type12_1) }
% 0.19/0.49 tuple(true, true)
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49
% 0.19/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------