TSTP Solution File: LCL096-10 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : LCL096-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n006.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 : Thu Aug 31 08:13:45 EDT 2023
% Result : Unsatisfiable 191.29s 191.83s
% Output : CNFRefutation 191.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL096-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.16/0.34 % Computer : n006.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Fri Aug 25 04:32:37 EDT 2023
% 0.16/0.34 % CPUTime :
% 191.29/191.83 % SZS status Unsatisfiable
% 191.29/191.83 % SZS output start Proof
% 191.29/191.83 original problem:
% 191.29/191.83 axioms:
% 191.29/191.83 ifeq(A, A, B, C) = B
% 191.29/191.83 ifeq(is_a_theorem(equivalent(X, Y)), true(), ifeq(is_a_theorem(X), true(), is_a_theorem(Y), true()), true()) = true()
% 191.29/191.83 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), equivalent(Y, Z)), U), U)) = true()
% 191.29/191.83 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X, Y), equivalent(X, Z)), U), equivalent(equivalent(Y, Z), U)), V), V)) = true()
% 191.29/191.83 is_a_theorem(equivalent(equivalent(equivalent(equivalent(X, Y), Z), U), equivalent(equivalent(equivalent(X, V), Z), equivalent(equivalent(Y, V), U)))) = true()
% 191.29/191.83 goal:
% 191.29/191.83 is_a_theorem(equivalent(equivalent(equivalent(a(), equivalent(equivalent(b(), b()), a())), c()), c())) != true()
% 191.29/191.83 To show the unsatisfiability of the original goal,
% 191.29/191.83 it suffices to show that is_a_theorem(equivalent(equivalent(equivalent(a(), equivalent(equivalent(b(), b()), a())), c()), c())) = true() (skolemized goal) is valid under the axioms.
% 191.29/191.83 Here is an equational proof:
% 191.29/191.83 0: ifeq(X0, X0, X1, X2) = X1.
% 191.29/191.83 Proof: Axiom.
% 191.29/191.83
% 191.29/191.83 1: ifeq(is_a_theorem(equivalent(X3, X4)), true(), ifeq(is_a_theorem(X3), true(), is_a_theorem(X4), true()), true()) = true().
% 191.29/191.83 Proof: Axiom.
% 191.29/191.83
% 191.29/191.83 2: is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), equivalent(X4, X5)), X6), X6)) = true().
% 191.29/191.83 Proof: Axiom.
% 191.29/191.83
% 191.29/191.83 3: is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X3, X4), equivalent(X3, X5)), X6), equivalent(equivalent(X4, X5), X6)), X7), X7)) = true().
% 191.29/191.83 Proof: Axiom.
% 191.29/191.83
% 191.29/191.83 4: is_a_theorem(equivalent(equivalent(equivalent(equivalent(X3, X4), X5), X6), equivalent(equivalent(equivalent(X3, X7), X5), equivalent(equivalent(X4, X7), X6)))) = true().
% 191.29/191.83 Proof: Axiom.
% 191.29/191.83
% 191.29/191.83 5: true() = ifeq(true(), true(), ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7, X8), equivalent(X7, X9)), equivalent(X8, X9)), X10)), true(), is_a_theorem(X10), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 2.
% 191.29/191.83
% 191.29/191.83 8: true() = ifeq(true(), true(), ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X8, X9), equivalent(X8, X10)), X11), equivalent(equivalent(X9, X10), X11)), X12)), true(), is_a_theorem(X12), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 3.
% 191.29/191.83
% 191.29/191.83 9: true() = ifeq(true(), true(), ifeq(is_a_theorem(equivalent(equivalent(equivalent(X8, X9), X10), X11)), true(), is_a_theorem(equivalent(equivalent(equivalent(X8, X12), X10), equivalent(equivalent(X9, X12), X11))), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 4.
% 191.29/191.83
% 191.29/191.83 11: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X8, X9), equivalent(X8, X10)), X11), equivalent(equivalent(X9, X10), X11)), X12), X12), X4)), true(), ifeq(true(), true(), is_a_theorem(X4), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 3.
% 191.29/191.83
% 191.29/191.83 13: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X8, X9), X10), X11), equivalent(equivalent(equivalent(X8, X12), X10), equivalent(equivalent(X9, X12), X11))), X4)), true(), ifeq(true(), true(), is_a_theorem(X4), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 4.
% 191.29/191.83
% 191.29/191.83 14: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X8, X9), X10), X11), equivalent(equivalent(equivalent(X8, X12), X10), equivalent(equivalent(X9, X12), X11))), X4)), true(), is_a_theorem(X4), true()).
% 191.29/191.83 Proof: Rewrite equation 13,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 15: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X8, X9), equivalent(X8, X10)), X11), equivalent(equivalent(X9, X10), X11)), X12), X12), X4)), true(), is_a_theorem(X4), true()).
% 191.29/191.83 Proof: Rewrite equation 11,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 16: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X8, X9), X10), X11)), true(), is_a_theorem(equivalent(equivalent(equivalent(X8, X12), X10), equivalent(equivalent(X9, X12), X11))), true()).
% 191.29/191.83 Proof: Rewrite equation 9,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 17: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X8, X9), equivalent(X8, X10)), X11), equivalent(equivalent(X9, X10), X11)), X12)), true(), is_a_theorem(X12), true()).
% 191.29/191.83 Proof: Rewrite equation 8,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 19: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X7, X8), equivalent(X7, X9)), equivalent(X8, X9)), X10)), true(), is_a_theorem(X10), true()).
% 191.29/191.83 Proof: Rewrite equation 5,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 20: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(X14, X15), equivalent(X14, X15))), true()).
% 191.29/191.83 Proof: A critical pair between equations 17 and 2.
% 191.29/191.83
% 191.29/191.83 22: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(X8, X10), X15), equivalent(equivalent(X9, X10), equivalent(equivalent(X8, X9), X15)))), true()).
% 191.29/191.83 Proof: A critical pair between equations 15 and 3.
% 191.29/191.83
% 191.29/191.83 26: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X13, X14), equivalent(X13, X15)), X12), X16), equivalent(equivalent(equivalent(X14, X15), X12), X16))), true()).
% 191.29/191.83 Proof: A critical pair between equations 16 and 2.
% 191.29/191.83
% 191.29/191.83 34: true() = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X13, X14), equivalent(X13, X15)), X12), X16), equivalent(equivalent(equivalent(X14, X15), X12), X16))).
% 191.29/191.83 Proof: Rewrite equation 26,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 35: true() = is_a_theorem(equivalent(equivalent(equivalent(X8, X10), X15), equivalent(equivalent(X9, X10), equivalent(equivalent(X8, X9), X15)))).
% 191.29/191.83 Proof: Rewrite equation 22,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 37: true() = is_a_theorem(equivalent(equivalent(X14, X15), equivalent(X14, X15))).
% 191.29/191.83 Proof: Rewrite equation 20,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 40: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(X7, X8), equivalent(X7, X9)), equivalent(X8, X9))), true()).
% 191.29/191.83 Proof: A critical pair between equations 19 and 37.
% 191.29/191.83
% 191.29/191.83 45: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X16, X17), equivalent(X16, X17)), X4)), true(), ifeq(true(), true(), is_a_theorem(X4), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 37.
% 191.29/191.83
% 191.29/191.83 46: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(X18, X19), equivalent(equivalent(X17, X18), X9)), equivalent(equivalent(X17, X19), X9))), true()).
% 191.29/191.83 Proof: A critical pair between equations 19 and 34.
% 191.29/191.83
% 191.29/191.83 47: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(X19, equivalent(X7, X9)), equivalent(equivalent(equivalent(X7, X8), X19), equivalent(X8, X9)))), true()).
% 191.29/191.83 Proof: A critical pair between equations 19 and 35.
% 191.29/191.83
% 191.29/191.83 48: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(equivalent(X8, X9), equivalent(X8, X10)), X11), equivalent(equivalent(X9, X10), X11))), true()).
% 191.29/191.83 Proof: A critical pair between equations 17 and 37.
% 191.29/191.83
% 191.29/191.83 51: true() = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X8, X9), equivalent(X8, X10)), X11), equivalent(equivalent(X9, X10), X11))).
% 191.29/191.83 Proof: Rewrite equation 48,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 52: true() = is_a_theorem(equivalent(equivalent(X19, equivalent(X7, X9)), equivalent(equivalent(equivalent(X7, X8), X19), equivalent(X8, X9)))).
% 191.29/191.83 Proof: Rewrite equation 47,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 53: true() = is_a_theorem(equivalent(equivalent(equivalent(X18, X19), equivalent(equivalent(X17, X18), X9)), equivalent(equivalent(X17, X19), X9))).
% 191.29/191.83 Proof: Rewrite equation 46,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 54: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X16, X17), equivalent(X16, X17)), X4)), true(), is_a_theorem(X4), true()).
% 191.29/191.83 Proof: Rewrite equation 45,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 57: true() = is_a_theorem(equivalent(equivalent(equivalent(X7, X8), equivalent(X7, X9)), equivalent(X8, X9))).
% 191.29/191.83 Proof: Rewrite equation 40,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 60: true() = ifeq(true(), true(), is_a_theorem(equivalent(X14, equivalent(equivalent(X9, X9), X14))), true()).
% 191.29/191.83 Proof: A critical pair between equations 14 and 57.
% 191.29/191.83
% 191.29/191.83 61: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(X19, X20), equivalent(equivalent(X18, X19), equivalent(X18, X20)))), true()).
% 191.29/191.83 Proof: A critical pair between equations 54 and 51.
% 191.29/191.83
% 191.29/191.83 66: true() = ifeq(true(), true(), ifeq(is_a_theorem(equivalent(equivalent(X10, X11), equivalent(X10, X12))), true(), is_a_theorem(equivalent(X11, X12)), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 57.
% 191.29/191.83
% 191.29/191.83 73: true() = ifeq(is_a_theorem(equivalent(equivalent(X10, X11), equivalent(X10, X12))), true(), is_a_theorem(equivalent(X11, X12)), true()).
% 191.29/191.83 Proof: Rewrite equation 66,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 75: true() = is_a_theorem(equivalent(equivalent(X19, X20), equivalent(equivalent(X18, X19), equivalent(X18, X20)))).
% 191.29/191.83 Proof: Rewrite equation 61,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 76: true() = is_a_theorem(equivalent(X14, equivalent(equivalent(X9, X9), X14))).
% 191.29/191.83 Proof: Rewrite equation 60,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 79: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(X22, X22), X23), X23)), true()).
% 191.29/191.83 Proof: A critical pair between equations 73 and 53.
% 191.29/191.83
% 191.29/191.83 87: true() = ifeq(true(), true(), ifeq(is_a_theorem(equivalent(X21, X22)), true(), is_a_theorem(equivalent(equivalent(X23, X21), equivalent(X23, X22))), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 75.
% 191.29/191.83
% 191.29/191.83 89: true() = ifeq(is_a_theorem(equivalent(equivalent(X15, equivalent(equivalent(X16, X16), X15)), X4)), true(), ifeq(true(), true(), is_a_theorem(X4), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 76.
% 191.29/191.83
% 191.29/191.83 90: true() = ifeq(is_a_theorem(equivalent(equivalent(X15, equivalent(equivalent(X16, X16), X15)), X4)), true(), is_a_theorem(X4), true()).
% 191.29/191.83 Proof: Rewrite equation 89,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 91: true() = ifeq(is_a_theorem(equivalent(X21, X22)), true(), is_a_theorem(equivalent(equivalent(X23, X21), equivalent(X23, X22))), true()).
% 191.29/191.83 Proof: Rewrite equation 87,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 96: true() = is_a_theorem(equivalent(equivalent(equivalent(X22, X22), X23), X23)).
% 191.29/191.83 Proof: Rewrite equation 79,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 100: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(equivalent(X16, X16), X23), X22), equivalent(X23, X22))), true()).
% 191.29/191.83 Proof: A critical pair between equations 90 and 52.
% 191.29/191.83
% 191.29/191.83 104: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(X23, equivalent(equivalent(X24, X24), X25)), equivalent(X23, X25))), true()).
% 191.29/191.83 Proof: A critical pair between equations 91 and 96.
% 191.29/191.83
% 191.29/191.83 111: true() = is_a_theorem(equivalent(equivalent(X23, equivalent(equivalent(X24, X24), X25)), equivalent(X23, X25))).
% 191.29/191.83 Proof: Rewrite equation 104,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 113: true() = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X16, X16), X23), X22), equivalent(X23, X22))).
% 191.29/191.83 Proof: Rewrite equation 100,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 124: true() = ifeq(true(), true(), ifeq(is_a_theorem(equivalent(X26, equivalent(equivalent(X27, X27), X28))), true(), is_a_theorem(equivalent(X26, X28)), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 111.
% 191.29/191.83
% 191.29/191.83 125: true() = ifeq(true(), true(), ifeq(is_a_theorem(equivalent(equivalent(equivalent(X24, X24), X25), X26)), true(), is_a_theorem(equivalent(X25, X26)), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 113.
% 191.29/191.83
% 191.29/191.83 127: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X24, X24), X25), X26)), true(), is_a_theorem(equivalent(X25, X26)), true()).
% 191.29/191.83 Proof: Rewrite equation 125,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 128: true() = ifeq(is_a_theorem(equivalent(X26, equivalent(equivalent(X27, X27), X28))), true(), is_a_theorem(equivalent(X26, X28)), true()).
% 191.29/191.83 Proof: Rewrite equation 124,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 134: true() = ifeq(true(), true(), is_a_theorem(equivalent(X28, equivalent(equivalent(X29, equivalent(X24, X24)), equivalent(X29, X28)))), true()).
% 191.29/191.83 Proof: A critical pair between equations 127 and 75.
% 191.29/191.83
% 191.29/191.83 137: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(X29, X30), equivalent(equivalent(X30, X29), X32)), X32)), true()).
% 191.29/191.83 Proof: A critical pair between equations 128 and 53.
% 191.29/191.83
% 191.29/191.83 151: true() = is_a_theorem(equivalent(equivalent(equivalent(X29, X30), equivalent(equivalent(X30, X29), X32)), X32)).
% 191.29/191.83 Proof: Rewrite equation 137,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 154: true() = is_a_theorem(equivalent(X28, equivalent(equivalent(X29, equivalent(X24, X24)), equivalent(X29, X28)))).
% 191.29/191.83 Proof: Rewrite equation 134,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 159: true() = ifeq(true(), true(), is_a_theorem(equivalent(X11, equivalent(X31, equivalent(equivalent(X31, equivalent(X32, X32)), X11)))), true()).
% 191.29/191.83 Proof: A critical pair between equations 73 and 154.
% 191.29/191.83
% 191.29/191.83 173: true() = is_a_theorem(equivalent(X11, equivalent(X31, equivalent(equivalent(X31, equivalent(X32, X32)), X11)))).
% 191.29/191.83 Proof: Rewrite equation 159,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 580: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(X23, equivalent(equivalent(X24, X25), equivalent(X24, X26))), equivalent(X23, equivalent(X25, X26)))), true()).
% 191.29/191.83 Proof: A critical pair between equations 91 and 57.
% 191.29/191.83
% 191.29/191.83 581: true() = is_a_theorem(equivalent(equivalent(X23, equivalent(equivalent(X24, X25), equivalent(X24, X26))), equivalent(X23, equivalent(X25, X26)))).
% 191.29/191.83 Proof: Rewrite equation 580,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 613: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(X23, equivalent(equivalent(equivalent(X24, X24), X25), X26)), equivalent(X23, equivalent(X25, X26)))), true()).
% 191.29/191.83 Proof: A critical pair between equations 91 and 113.
% 191.29/191.83
% 191.29/191.83 618: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(X23, equivalent(equivalent(X33, X34), equivalent(equivalent(X34, X33), X35))), equivalent(X23, X35))), true()).
% 191.29/191.83 Proof: A critical pair between equations 91 and 151.
% 191.29/191.83
% 191.29/191.83 627: true() = is_a_theorem(equivalent(equivalent(X23, equivalent(equivalent(X33, X34), equivalent(equivalent(X34, X33), X35))), equivalent(X23, X35))).
% 191.29/191.83 Proof: Rewrite equation 618,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 632: true() = is_a_theorem(equivalent(equivalent(X23, equivalent(equivalent(equivalent(X24, X24), X25), X26)), equivalent(X23, equivalent(X25, X26)))).
% 191.29/191.83 Proof: Rewrite equation 613,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 659: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(equivalent(X28, X9), X29), X11), equivalent(X29, equivalent(equivalent(X9, X28), X11)))), true()).
% 191.29/191.83 Proof: A critical pair between equations 14 and 632.
% 191.29/191.83
% 191.29/191.83 668: true() = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X28, X9), X29), X11), equivalent(X29, equivalent(equivalent(X9, X28), X11)))).
% 191.29/191.83 Proof: Rewrite equation 659,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 677: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(X7, equivalent(X37, X38)), equivalent(X7, equivalent(equivalent(X38, X37), X39))), X39)), true()).
% 191.29/191.83 Proof: A critical pair between equations 19 and 627.
% 191.29/191.83
% 191.29/191.83 690: true() = is_a_theorem(equivalent(equivalent(equivalent(X7, equivalent(X37, X38)), equivalent(X7, equivalent(equivalent(X38, X37), X39))), X39)).
% 191.29/191.83 Proof: Rewrite equation 677,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 764: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(equivalent(X8, X28), equivalent(X8, X29)), equivalent(X28, X30)), equivalent(X29, X30))), true()).
% 191.29/191.83 Proof: A critical pair between equations 17 and 581.
% 191.29/191.83
% 191.29/191.83 767: true() = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X8, X28), equivalent(X8, X29)), equivalent(X28, X30)), equivalent(X29, X30))).
% 191.29/191.83 Proof: Rewrite equation 764,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 821: true() = ifeq(true(), true(), ifeq(is_a_theorem(equivalent(equivalent(equivalent(X31, X32), equivalent(X31, X33)), equivalent(X32, X34))), true(), is_a_theorem(equivalent(X33, X34)), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 767.
% 191.29/191.83
% 191.29/191.83 828: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X31, X32), equivalent(X31, X33)), equivalent(X32, X34))), true(), is_a_theorem(equivalent(X33, X34)), true()).
% 191.29/191.83 Proof: Rewrite equation 821,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 842: true() = ifeq(true(), true(), is_a_theorem(equivalent(X33, equivalent(equivalent(X36, equivalent(X37, X37)), equivalent(equivalent(X31, X36), equivalent(X31, X33))))), true()).
% 191.29/191.83 Proof: A critical pair between equations 828 and 173.
% 191.29/191.83
% 191.29/191.83 852: true() = is_a_theorem(equivalent(X33, equivalent(equivalent(X36, equivalent(X37, X37)), equivalent(equivalent(X31, X36), equivalent(X31, X33))))).
% 191.29/191.83 Proof: Rewrite equation 842,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 880: true() = ifeq(true(), true(), is_a_theorem(equivalent(X11, equivalent(equivalent(X41, X39), equivalent(X41, equivalent(equivalent(X39, equivalent(X40, X40)), X11))))), true()).
% 191.29/191.83 Proof: A critical pair between equations 73 and 852.
% 191.29/191.83
% 191.29/191.83 885: true() = is_a_theorem(equivalent(X11, equivalent(equivalent(X41, X39), equivalent(X41, equivalent(equivalent(X39, equivalent(X40, X40)), X11))))).
% 191.29/191.83 Proof: Rewrite equation 880,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 1152: true() = ifeq(true(), true(), ifeq(is_a_theorem(equivalent(equivalent(equivalent(X30, X31), X32), X33)), true(), is_a_theorem(equivalent(X32, equivalent(equivalent(X31, X30), X33))), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 668.
% 191.29/191.83
% 191.29/191.83 1155: true() = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X30, X31), X32), X33)), true(), is_a_theorem(equivalent(X32, equivalent(equivalent(X31, X30), X33))), true()).
% 191.29/191.83 Proof: Rewrite equation 1152,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 1175: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(X40, equivalent(equivalent(X42, X41), X43)), equivalent(equivalent(equivalent(X41, X42), X40), X43))), true()).
% 191.29/191.83 Proof: A critical pair between equations 1155 and 690.
% 191.29/191.83
% 191.29/191.83 1180: true() = is_a_theorem(equivalent(equivalent(X40, equivalent(equivalent(X42, X41), X43)), equivalent(equivalent(equivalent(X41, X42), X40), X43))).
% 191.29/191.83 Proof: Rewrite equation 1175,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 1240: true() = ifeq(true(), true(), ifeq(is_a_theorem(equivalent(X44, equivalent(equivalent(X45, X46), X47))), true(), is_a_theorem(equivalent(equivalent(equivalent(X46, X45), X44), X47)), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 1180.
% 191.29/191.83
% 191.29/191.83 1251: true() = ifeq(is_a_theorem(equivalent(X44, equivalent(equivalent(X45, X46), X47))), true(), is_a_theorem(equivalent(equivalent(equivalent(X46, X45), X44), X47)), true()).
% 191.29/191.83 Proof: Rewrite equation 1240,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 1258: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(X50, X49), X48), equivalent(X49, equivalent(equivalent(X50, equivalent(X51, X51)), X48)))), true()).
% 191.29/191.83 Proof: A critical pair between equations 1251 and 885.
% 191.29/191.83
% 191.29/191.83 1279: true() = is_a_theorem(equivalent(equivalent(equivalent(X50, X49), X48), equivalent(X49, equivalent(equivalent(X50, equivalent(X51, X51)), X48)))).
% 191.29/191.83 Proof: Rewrite equation 1258,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 1331: true() = ifeq(true(), true(), ifeq(is_a_theorem(equivalent(X36, equivalent(equivalent(X37, X38), equivalent(equivalent(X38, X37), X39)))), true(), is_a_theorem(equivalent(X36, X39)), true()), true()).
% 191.29/191.83 Proof: A critical pair between equations 1 and 627.
% 191.29/191.83
% 191.29/191.83 1338: true() = ifeq(is_a_theorem(equivalent(X36, equivalent(equivalent(X37, X38), equivalent(equivalent(X38, X37), X39)))), true(), is_a_theorem(equivalent(X36, X39)), true()).
% 191.29/191.83 Proof: Rewrite equation 1331,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 1346: true() = ifeq(true(), true(), is_a_theorem(equivalent(equivalent(equivalent(X52, equivalent(equivalent(X55, X55), X52)), X54), X54)), true()).
% 191.29/191.83 Proof: A critical pair between equations 1338 and 1279.
% 191.29/191.83
% 191.29/191.83 1364: true() = is_a_theorem(equivalent(equivalent(equivalent(X52, equivalent(equivalent(X55, X55), X52)), X54), X54)).
% 191.29/191.83 Proof: Rewrite equation 1346,
% 191.29/191.83 lhs with equations []
% 191.29/191.83 rhs with equations [0].
% 191.29/191.83
% 191.29/191.83 1366: is_a_theorem(equivalent(equivalent(equivalent(a(), equivalent(equivalent(b(), b()), a())), c()), c())) = true().
% 191.29/191.83 Proof: Rewrite lhs with equations [1364]
% 191.29/191.83 rhs with equations [].
% 191.29/191.83
% 191.29/191.83 % SZS output end Proof
%------------------------------------------------------------------------------