TSTP Solution File: COL118-2 by Moca---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : COL118-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n017.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 : 600s
% DateTime : Fri Jul 15 00:38:01 EDT 2022
% Result : Unsatisfiable 0.96s 1.13s
% Output : Proof 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COL118-2 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % Command : moca.sh %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue May 31 08:36:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.96/1.13 % SZS status Unsatisfiable
% 0.96/1.13 % SZS output start Proof
% 0.96/1.13 The input problem is unsatisfiable because
% 0.96/1.13
% 0.96/1.13 [1] the following set of Horn clauses is unsatisfiable:
% 0.96/1.13
% 0.96/1.13 c_in(c_Pair(v_x, v_ya, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.96/1.13 c_in(c_Pair(v_z, v_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.96/1.13 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) & c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_w), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) ==> \bottom
% 0.96/1.13 c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.96/1.13 c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) & c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) ==> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.96/1.13
% 0.96/1.13 This holds because
% 0.96/1.13
% 0.96/1.13 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.96/1.13
% 0.96/1.13 E:
% 0.96/1.13 c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true__
% 0.96/1.13 c_in(c_Pair(v_x, v_ya, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true__
% 0.96/1.13 c_in(c_Pair(v_z, v_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) = true__
% 0.96/1.13 f1(true__) = false__
% 0.96/1.13 f2(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_w), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_U) = true__
% 0.96/1.13 f2(true__, V_U) = f1(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))
% 0.96/1.13 f3(true__, V_x, V_z, V_y, V_w) = c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.96/1.14 f4(c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_z, V_w, V_x, V_y) = true__
% 0.96/1.14 f4(true__, V_z, V_w, V_x, V_y) = f3(c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_x, V_z, V_y, V_w)
% 0.96/1.14 G:
% 0.96/1.14 true__ = false__
% 0.96/1.14
% 0.96/1.14 This holds because
% 0.96/1.14
% 0.96/1.14 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.96/1.14
% 0.96/1.14
% 0.96/1.14 c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__
% 0.96/1.14 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(Y1, v_x), c_Comb_Ocomb_Oop_A_D_D(Y1, v_ya), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__
% 0.96/1.14 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(Y1, v_z), c_Comb_Ocomb_Oop_A_D_D(Y1, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__
% 0.96/1.14 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, Y0), c_Comb_Ocomb_Oop_A_D_D(v_ya, Y0), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__
% 0.96/1.14 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_x), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_ya), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__
% 0.96/1.14 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__
% 0.96/1.14 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, Y0), c_Comb_Ocomb_Oop_A_D_D(v_w, Y0), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__
% 0.96/1.14 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), c_Comb_Ocomb_Oop_A_D_D(v_w, v_ya), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__
% 0.96/1.14 c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_z, v_z), c_Comb_Ocomb_Oop_A_D_D(v_w, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__
% 0.96/1.14 c_in(c_Pair(v_x, v_ya, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__
% 0.96/1.14 c_in(c_Pair(v_z, v_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) -> true__
% 0.96/1.14 f1(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) -> f2(true__, V_U)
% 0.96/1.14 f1(true__) -> false__
% 0.96/1.14 f2(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_ya, v_w), V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_U) -> true__
% 0.96/1.14 f2(true__, c_Comb_Ocomb_Oop_A_D_D(v_x, v_z)) -> false__
% 0.96/1.14 f2(true__, c_Comb_Ocomb_Oop_A_D_D(v_ya, v_w)) -> true__
% 0.96/1.14 f3(c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_x, V_z, V_y, V_w) -> f4(true__, V_z, V_w, V_x, V_y)
% 0.96/1.14 f3(true__, V_x, V_z, V_y, V_w) -> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.96/1.14 f4(c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)), V_z, V_w, V_x, V_y) -> true__
% 0.96/1.14 f4(true__, Y1, Y1, Y2, Y3) -> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(Y2, Y1), c_Comb_Ocomb_Oop_A_D_D(Y3, Y1), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.96/1.14 f4(true__, Y2, Y3, Y1, Y1) -> true__
% 0.96/1.14 f4(true__, Y2, Y3, c_Comb_Ocomb_Oop_A_D_D(v_x, v_x), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_ya)) -> true__
% 0.96/1.14 f4(true__, Y2, Y3, c_Comb_Ocomb_Oop_A_D_D(v_x, v_z), c_Comb_Ocomb_Oop_A_D_D(v_ya, v_w)) -> true__
% 0.96/1.14 f4(true__, Y2, Y3, c_Comb_Ocomb_Oop_A_D_D(v_z, v_x), c_Comb_Ocomb_Oop_A_D_D(v_w, v_ya)) -> true__
% 0.96/1.14 f4(true__, Y2, Y3, c_Comb_Ocomb_Oop_A_D_D(v_z, v_z), c_Comb_Ocomb_Oop_A_D_D(v_w, v_w)) -> true__
% 0.96/1.14 f4(true__, Y2, Y3, v_x, v_ya) -> true__
% 0.96/1.14 f4(true__, Y2, Y3, v_z, v_w) -> true__
% 0.96/1.14 f4(true__, v_x, v_ya, Y2, Y3) -> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(Y2, v_x), c_Comb_Ocomb_Oop_A_D_D(Y3, v_ya), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.96/1.14 f4(true__, v_z, v_w, Y2, Y3) -> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(Y2, v_z), c_Comb_Ocomb_Oop_A_D_D(Y3, v_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))
% 0.96/1.14 false__ -> true__
% 0.96/1.14 with the LPO induced by
% 0.96/1.14 f3 > f4 > f1 > f2 > c_Pair > c_Comb_Oparcontract > tc_Comb_Ocomb > c_Comb_Ocomb_Oop_A_D_D > v_z > v_x > v_w > tc_prod > v_ya > c_in > false__ > true__
% 0.96/1.14
% 0.96/1.14 % SZS output end Proof
% 0.96/1.14
%------------------------------------------------------------------------------