TSTP Solution File: ALG030-10 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : ALG030-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n026.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 : Wed Aug 30 16:40:47 EDT 2023
% Result : Unsatisfiable 1.63s 2.00s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG030-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 05:28:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 1.63/2.00 % SZS status Unsatisfiable
% 1.63/2.00 % SZS output start Proof
% 1.63/2.00 original problem:
% 1.63/2.00 axioms:
% 1.63/2.00 ifeq2(A, A, B, C) = B
% 1.63/2.00 ifeq(A, A, B, C) = B
% 1.63/2.00 ifeq(sorti1(V), true(), ifeq(sorti1(U), true(), sorti1(op1(U, V)), true()), true()) = true()
% 1.63/2.00 ifeq(sorti2(V), true(), ifeq(sorti2(U), true(), sorti2(op2(U, V)), true()), true()) = true()
% 1.63/2.00 sorti1(sK1_ax3_V()) = true()
% 1.63/2.00 sorti1(sK2_ax3_U()) = true()
% 1.63/2.00 ifeq2(sorti2(V), true(), ifeq2(sorti2(U), true(), op2(U, V), op2(V, U)), op2(V, U)) = op2(V, U)
% 1.63/2.00 ifeq(sorti1(U), true(), sorti2(h(U)), true()) = true()
% 1.63/2.00 ifeq2(sorti1(X), true(), ifeq2(sorti1(W), true(), op2(h(W), h(X)), h(op1(W, X))), h(op1(W, X))) = h(op1(W, X))
% 1.63/2.00 ifeq2(sorti1(X2), true(), j(h(X2)), X2) = X2
% 1.63/2.00 ifeq(sorti2(V), true(), sorti1(j(V)), true()) = true()
% 1.63/2.00 ifeq2(sorti2(Z), true(), ifeq2(sorti2(Y), true(), op1(j(Y), j(Z)), j(op2(Y, Z))), j(op2(Y, Z))) = j(op2(Y, Z))
% 1.63/2.00 ifeq2(sorti2(X1), true(), h(j(X1)), X1) = X1
% 1.63/2.00 goal:
% 1.63/2.00 op1(sK2_ax3_U(), sK1_ax3_V()) != op1(sK1_ax3_V(), sK2_ax3_U())
% 1.63/2.00 To show the unsatisfiability of the original goal,
% 1.63/2.00 it suffices to show that op1(sK2_ax3_U(), sK1_ax3_V()) = op1(sK1_ax3_V(), sK2_ax3_U()) (skolemized goal) is valid under the axioms.
% 1.63/2.00 Here is an equational proof:
% 1.63/2.00 0: ifeq2(X0, X0, X1, X2) = X1.
% 1.63/2.00 Proof: Axiom.
% 1.63/2.00
% 1.63/2.00 1: ifeq(X0, X0, X1, X2) = X1.
% 1.63/2.00 Proof: Axiom.
% 1.63/2.00
% 1.63/2.00 2: ifeq(sorti1(X3), true(), ifeq(sorti1(X4), true(), sorti1(op1(X4, X3)), true()), true()) = true().
% 1.63/2.00 Proof: Axiom.
% 1.63/2.00
% 1.63/2.00 4: sorti1(sK1_ax3_V()) = true().
% 1.63/2.00 Proof: Axiom.
% 1.63/2.00
% 1.63/2.00 5: sorti1(sK2_ax3_U()) = true().
% 1.63/2.00 Proof: Axiom.
% 1.63/2.00
% 1.63/2.00 6: ifeq2(sorti2(X3), true(), ifeq2(sorti2(X4), true(), op2(X4, X3), op2(X3, X4)), op2(X3, X4)) = op2(X3, X4).
% 1.63/2.00 Proof: Axiom.
% 1.63/2.00
% 1.63/2.00 7: ifeq(sorti1(X4), true(), sorti2(h(X4)), true()) = true().
% 1.63/2.00 Proof: Axiom.
% 1.63/2.00
% 1.63/2.00 8: ifeq2(sorti1(X5), true(), ifeq2(sorti1(X6), true(), op2(h(X6), h(X5)), h(op1(X6, X5))), h(op1(X6, X5))) = h(op1(X6, X5)).
% 1.63/2.00 Proof: Axiom.
% 1.63/2.00
% 1.63/2.00 9: ifeq2(sorti1(X7), true(), j(h(X7)), X7) = X7.
% 1.63/2.00 Proof: Axiom.
% 1.63/2.00
% 1.63/2.00 13: ifeq(sorti1(X3), sorti1(sK1_ax3_V()), ifeq(sorti1(X4), sorti1(sK1_ax3_V()), sorti1(op1(X4, X3)), sorti1(sK1_ax3_V())), sorti1(sK1_ax3_V())) = sorti1(sK1_ax3_V()).
% 1.63/2.00 Proof: Rewrite equation 2,
% 1.63/2.00 lhs with equations [4,4,4,4]
% 1.63/2.00 rhs with equations [4].
% 1.63/2.00
% 1.63/2.00 15: sorti1(sK2_ax3_U()) = sorti1(sK1_ax3_V()).
% 1.63/2.00 Proof: Rewrite equation 5,
% 1.63/2.00 lhs with equations []
% 1.63/2.00 rhs with equations [4].
% 1.63/2.00
% 1.63/2.00 16: ifeq2(sorti2(X3), sorti1(sK1_ax3_V()), ifeq2(sorti2(X4), sorti1(sK1_ax3_V()), op2(X4, X3), op2(X3, X4)), op2(X3, X4)) = op2(X3, X4).
% 1.63/2.00 Proof: Rewrite equation 6,
% 1.63/2.00 lhs with equations [4,4]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 17: ifeq(sorti1(X4), sorti1(sK1_ax3_V()), sorti2(h(X4)), sorti1(sK1_ax3_V())) = sorti1(sK1_ax3_V()).
% 1.63/2.00 Proof: Rewrite equation 7,
% 1.63/2.00 lhs with equations [4,4]
% 1.63/2.00 rhs with equations [4].
% 1.63/2.00
% 1.63/2.00 18: ifeq2(sorti1(X5), sorti1(sK1_ax3_V()), ifeq2(sorti1(X6), sorti1(sK1_ax3_V()), op2(h(X6), h(X5)), h(op1(X6, X5))), h(op1(X6, X5))) = h(op1(X6, X5)).
% 1.63/2.00 Proof: Rewrite equation 8,
% 1.63/2.00 lhs with equations [4,4]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 19: ifeq2(sorti1(X7), sorti1(sK1_ax3_V()), j(h(X7)), X7) = X7.
% 1.63/2.00 Proof: Rewrite equation 9,
% 1.63/2.00 lhs with equations [4]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 24: sorti2(h(sK1_ax3_V())) = sorti1(sK1_ax3_V()).
% 1.63/2.00 Proof: A critical pair between equations 1 and 17.
% 1.63/2.00
% 1.63/2.00 26: sorti1(sK1_ax3_V()) = ifeq(sorti1(sK1_ax3_V()), sorti1(sK1_ax3_V()), sorti2(h(sK2_ax3_U())), sorti1(sK1_ax3_V())).
% 1.63/2.00 Proof: A critical pair between equations 17 and 15.
% 1.63/2.00
% 1.63/2.00 31: sorti1(sK1_ax3_V()) = ifeq(sorti1(X3), sorti1(sK1_ax3_V()), ifeq(sorti1(sK1_ax3_V()), sorti1(sK1_ax3_V()), sorti1(op1(sK2_ax3_U(), X3)), sorti1(sK1_ax3_V())), sorti1(sK1_ax3_V())).
% 1.63/2.00 Proof: A critical pair between equations 13 and 15.
% 1.63/2.00
% 1.63/2.00 32: sorti1(sK1_ax3_V()) = ifeq(sorti1(sK1_ax3_V()), sorti1(sK1_ax3_V()), ifeq(sorti1(X4), sorti1(sK1_ax3_V()), sorti1(op1(X4, sK2_ax3_U())), sorti1(sK1_ax3_V())), sorti1(sK1_ax3_V())).
% 1.63/2.00 Proof: A critical pair between equations 13 and 15.
% 1.63/2.00
% 1.63/2.00 33: h(op1(sK2_ax3_U(), X5)) = ifeq2(sorti1(X5), sorti1(sK1_ax3_V()), ifeq2(sorti1(sK1_ax3_V()), sorti1(sK1_ax3_V()), op2(h(sK2_ax3_U()), h(X5)), h(op1(sK2_ax3_U(), X5))), h(op1(sK2_ax3_U(), X5))).
% 1.63/2.00 Proof: A critical pair between equations 18 and 15.
% 1.63/2.00
% 1.63/2.00 34: h(op1(X6, sK2_ax3_U())) = ifeq2(sorti1(sK1_ax3_V()), sorti1(sK1_ax3_V()), ifeq2(sorti1(X6), sorti1(sK1_ax3_V()), op2(h(X6), h(sK2_ax3_U())), h(op1(X6, sK2_ax3_U()))), h(op1(X6, sK2_ax3_U()))).
% 1.63/2.00 Proof: A critical pair between equations 18 and 15.
% 1.63/2.00
% 1.63/2.00 35: h(op1(X6, sK2_ax3_U())) = ifeq2(sorti1(X6), sorti2(h(sK1_ax3_V())), op2(h(X6), h(sK2_ax3_U())), h(op1(X6, sK2_ax3_U()))).
% 1.63/2.00 Proof: Rewrite equation 34,
% 1.63/2.00 lhs with equations []
% 1.63/2.00 rhs with equations [24,24,24,0].
% 1.63/2.00
% 1.63/2.00 36: h(op1(sK2_ax3_U(), X5)) = ifeq2(sorti1(X5), sorti2(h(sK1_ax3_V())), op2(h(sK2_ax3_U()), h(X5)), h(op1(sK2_ax3_U(), X5))).
% 1.63/2.00 Proof: Rewrite equation 33,
% 1.63/2.00 lhs with equations []
% 1.63/2.00 rhs with equations [24,24,24,0].
% 1.63/2.00
% 1.63/2.00 37: sorti2(h(sK1_ax3_V())) = ifeq(sorti1(X4), sorti2(h(sK1_ax3_V())), sorti1(op1(X4, sK2_ax3_U())), sorti2(h(sK1_ax3_V()))).
% 1.63/2.00 Proof: Rewrite equation 32,
% 1.63/2.00 lhs with equations [24]
% 1.63/2.00 rhs with equations [24,24,24,24,24,1].
% 1.63/2.00
% 1.63/2.00 38: sorti2(h(sK1_ax3_V())) = ifeq(sorti1(X3), sorti2(h(sK1_ax3_V())), sorti1(op1(sK2_ax3_U(), X3)), sorti2(h(sK1_ax3_V()))).
% 1.63/2.00 Proof: Rewrite equation 31,
% 1.63/2.00 lhs with equations [24]
% 1.63/2.00 rhs with equations [24,24,24,24,1,24].
% 1.63/2.00
% 1.63/2.00 43: sorti2(h(sK1_ax3_V())) = sorti2(h(sK2_ax3_U())).
% 1.63/2.00 Proof: Rewrite equation 26,
% 1.63/2.00 lhs with equations [24]
% 1.63/2.00 rhs with equations [24,24,24,1].
% 1.63/2.00
% 1.63/2.00 48: ifeq2(sorti1(X7), sorti2(h(sK1_ax3_V())), j(h(X7)), X7) = X7.
% 1.63/2.00 Proof: Rewrite equation 19,
% 1.63/2.00 lhs with equations [24]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 51: ifeq2(sorti2(X3), sorti2(h(sK1_ax3_V())), ifeq2(sorti2(X4), sorti2(h(sK1_ax3_V())), op2(X4, X3), op2(X3, X4)), op2(X3, X4)) = op2(X3, X4).
% 1.63/2.00 Proof: Rewrite equation 16,
% 1.63/2.00 lhs with equations [24,24]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 53: sorti2(h(sK1_ax3_V())) = true().
% 1.63/2.00 Proof: Rewrite equation 4,
% 1.63/2.00 lhs with equations [24]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 56: sorti2(h(sK1_ax3_V())) = ifeq(sorti2(h(sK1_ax3_V())), sorti2(h(sK1_ax3_V())), sorti1(op1(sK1_ax3_V(), sK2_ax3_U())), sorti2(h(sK1_ax3_V()))).
% 1.63/2.00 Proof: A critical pair between equations 37 and 24.
% 1.63/2.00
% 1.63/2.00 58: sorti2(h(sK1_ax3_V())) = ifeq(sorti2(h(sK1_ax3_V())), sorti2(h(sK1_ax3_V())), sorti1(op1(sK2_ax3_U(), sK1_ax3_V())), sorti2(h(sK1_ax3_V()))).
% 1.63/2.00 Proof: A critical pair between equations 38 and 24.
% 1.63/2.00
% 1.63/2.00 62: op2(X3, h(sK1_ax3_V())) = ifeq2(sorti2(X3), sorti2(h(sK1_ax3_V())), op2(h(sK1_ax3_V()), X3), op2(X3, h(sK1_ax3_V()))).
% 1.63/2.00 Proof: A critical pair between equations 51 and 0.
% 1.63/2.00
% 1.63/2.00 64: h(op1(sK1_ax3_V(), sK2_ax3_U())) = ifeq2(sorti2(h(sK1_ax3_V())), sorti2(h(sK1_ax3_V())), op2(h(sK1_ax3_V()), h(sK2_ax3_U())), h(op1(sK1_ax3_V(), sK2_ax3_U()))).
% 1.63/2.00 Proof: A critical pair between equations 35 and 24.
% 1.63/2.00
% 1.63/2.00 66: h(op1(sK2_ax3_U(), sK1_ax3_V())) = ifeq2(sorti2(h(sK1_ax3_V())), sorti2(h(sK1_ax3_V())), op2(h(sK2_ax3_U()), h(sK1_ax3_V())), h(op1(sK2_ax3_U(), sK1_ax3_V()))).
% 1.63/2.00 Proof: A critical pair between equations 36 and 24.
% 1.63/2.00
% 1.63/2.00 69: h(op1(sK2_ax3_U(), sK1_ax3_V())) = op2(h(sK2_ax3_U()), h(sK1_ax3_V())).
% 1.63/2.00 Proof: Rewrite equation 66,
% 1.63/2.00 lhs with equations []
% 1.63/2.00 rhs with equations [53,53,0].
% 1.63/2.00
% 1.63/2.00 71: h(op1(sK1_ax3_V(), sK2_ax3_U())) = op2(h(sK1_ax3_V()), h(sK2_ax3_U())).
% 1.63/2.00 Proof: Rewrite equation 64,
% 1.63/2.00 lhs with equations []
% 1.63/2.00 rhs with equations [53,53,0].
% 1.63/2.00
% 1.63/2.00 73: op2(X3, h(sK1_ax3_V())) = ifeq2(sorti2(X3), true(), op2(h(sK1_ax3_V()), X3), op2(X3, h(sK1_ax3_V()))).
% 1.63/2.00 Proof: Rewrite equation 62,
% 1.63/2.00 lhs with equations []
% 1.63/2.00 rhs with equations [53].
% 1.63/2.00
% 1.63/2.00 77: true() = sorti1(op1(sK2_ax3_U(), sK1_ax3_V())).
% 1.63/2.00 Proof: Rewrite equation 58,
% 1.63/2.00 lhs with equations [53]
% 1.63/2.00 rhs with equations [53,53,53,1].
% 1.63/2.00
% 1.63/2.00 79: true() = sorti1(op1(sK1_ax3_V(), sK2_ax3_U())).
% 1.63/2.00 Proof: Rewrite equation 56,
% 1.63/2.00 lhs with equations [53]
% 1.63/2.00 rhs with equations [53,53,53,1].
% 1.63/2.00
% 1.63/2.00 86: ifeq2(sorti1(X7), true(), j(h(X7)), X7) = X7.
% 1.63/2.00 Proof: Rewrite equation 48,
% 1.63/2.00 lhs with equations [53]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 91: true() = sorti2(h(sK2_ax3_U())).
% 1.63/2.00 Proof: Rewrite equation 43,
% 1.63/2.00 lhs with equations [53]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 133: ifeq2(sorti1(X7), sorti2(h(sK2_ax3_U())), j(h(X7)), X7) = X7.
% 1.63/2.00 Proof: Rewrite equation 86,
% 1.63/2.00 lhs with equations [91]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 138: sorti2(h(sK1_ax3_V())) = sorti2(h(sK2_ax3_U())).
% 1.63/2.00 Proof: Rewrite equation 53,
% 1.63/2.00 lhs with equations []
% 1.63/2.00 rhs with equations [91].
% 1.63/2.00
% 1.63/2.00 141: sorti2(h(sK2_ax3_U())) = sorti1(op1(sK1_ax3_V(), sK2_ax3_U())).
% 1.63/2.00 Proof: Rewrite equation 79,
% 1.63/2.00 lhs with equations [91]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 143: sorti2(h(sK2_ax3_U())) = sorti1(op1(sK2_ax3_U(), sK1_ax3_V())).
% 1.63/2.00 Proof: Rewrite equation 77,
% 1.63/2.00 lhs with equations [91]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 147: op2(X3, h(sK1_ax3_V())) = ifeq2(sorti2(X3), sorti2(h(sK2_ax3_U())), op2(h(sK1_ax3_V()), X3), op2(X3, h(sK1_ax3_V()))).
% 1.63/2.00 Proof: Rewrite equation 73,
% 1.63/2.00 lhs with equations []
% 1.63/2.00 rhs with equations [91].
% 1.63/2.00
% 1.63/2.00 149: op2(h(sK1_ax3_V()), h(sK2_ax3_U())) = op2(h(sK2_ax3_U()), h(sK1_ax3_V())).
% 1.63/2.00 Proof: A critical pair between equations 0 and 147.
% 1.63/2.00
% 1.63/2.00 152: op1(sK1_ax3_V(), sK2_ax3_U()) = ifeq2(sorti2(h(sK2_ax3_U())), sorti2(h(sK2_ax3_U())), j(h(op1(sK1_ax3_V(), sK2_ax3_U()))), op1(sK1_ax3_V(), sK2_ax3_U())).
% 1.63/2.00 Proof: A critical pair between equations 133 and 141.
% 1.63/2.00
% 1.63/2.00 154: op1(sK2_ax3_U(), sK1_ax3_V()) = ifeq2(sorti2(h(sK2_ax3_U())), sorti2(h(sK2_ax3_U())), j(h(op1(sK2_ax3_U(), sK1_ax3_V()))), op1(sK2_ax3_U(), sK1_ax3_V())).
% 1.63/2.00 Proof: A critical pair between equations 133 and 143.
% 1.63/2.00
% 1.63/2.00 167: op1(sK2_ax3_U(), sK1_ax3_V()) = j(op2(h(sK1_ax3_V()), h(sK2_ax3_U()))).
% 1.63/2.00 Proof: Rewrite equation 154,
% 1.63/2.00 lhs with equations []
% 1.63/2.00 rhs with equations [138,138,69,149,0].
% 1.63/2.00
% 1.63/2.00 169: op1(sK1_ax3_V(), sK2_ax3_U()) = op1(sK2_ax3_U(), sK1_ax3_V()).
% 1.63/2.00 Proof: Rewrite equation 152,
% 1.63/2.00 lhs with equations []
% 1.63/2.00 rhs with equations [138,138,71,167,0].
% 1.63/2.00
% 1.63/2.00 207: op1(sK2_ax3_U(), sK1_ax3_V()) = op1(sK1_ax3_V(), sK2_ax3_U()).
% 1.63/2.00 Proof: Rewrite lhs with equations [169]
% 1.63/2.00 rhs with equations [].
% 1.63/2.00
% 1.63/2.00 % SZS output end Proof
%------------------------------------------------------------------------------