TSTP Solution File: ALG377-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : ALG377-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n032.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 16:43:07 EDT 2023
% Result : Unsatisfiable 128.59s 16.84s
% Output : Proof 128.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG377-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.31 % Computer : n032.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Mon Aug 28 03:24:45 EDT 2023
% 0.12/0.32 % CPUTime :
% 128.59/16.84 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 128.59/16.84
% 128.59/16.84 % SZS status Unsatisfiable
% 128.59/16.84
% 128.59/16.84 % SZS output start Proof
% 128.59/16.84 Take the following subset of the input axioms:
% 128.59/16.84 fof(cls_CHAINED_0, axiom, c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), tc_nat), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat)), tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 128.59/16.84 fof(cls_conjecture_0, negated_conjecture, ~c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat)), tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)).
% 128.59/16.84 fof(cls_real__add__left__mono_0, axiom, ![V_x, V_y, V_z]: (c_lessequals(c_HOL_Oplus__class_Oplus(V_z, V_x, tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(V_z, V_y, tc_RealDef_Oreal), tc_RealDef_Oreal) | ~c_lessequals(V_x, V_y, tc_RealDef_Oreal))).
% 128.59/16.84
% 128.59/16.84 Now clausify the problem and encode Horn clauses using encoding 3 of
% 128.59/16.84 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 128.59/16.84 We repeatedly replace C & s=t => u=v by the two clauses:
% 128.59/16.84 fresh(y, y, x1...xn) = u
% 128.59/16.84 C => fresh(s, t, x1...xn) = v
% 128.59/16.84 where fresh is a fresh function symbol and x1..xn are the free
% 128.59/16.84 variables of u and v.
% 128.59/16.84 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 128.59/16.84 input problem has no model of domain size 1).
% 128.59/16.84
% 128.59/16.84 The encoding turns the above axioms into the following unit equations and goals:
% 128.59/16.84
% 128.59/16.84 Axiom 1 (cls_real__add__left__mono_0): fresh114(X, X, Y, Z, W) = true2.
% 128.59/16.84 Axiom 2 (cls_real__add__left__mono_0): fresh114(c_lessequals(X, Y, tc_RealDef_Oreal), true2, Z, X, Y) = c_lessequals(c_HOL_Oplus__class_Oplus(Z, X, tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(Z, Y, tc_RealDef_Oreal), tc_RealDef_Oreal).
% 128.59/16.85 Axiom 3 (cls_CHAINED_0): c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), tc_nat), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat)), tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 128.59/16.85
% 128.59/16.85 Goal 1 (cls_conjecture_0): c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat)), tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal) = true2.
% 128.59/16.85 Proof:
% 128.59/16.85 c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat)), tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), tc_RealDef_Oreal)
% 128.59/16.85 = { by axiom 2 (cls_real__add__left__mono_0) R->L }
% 128.59/16.85 fresh114(c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), tc_nat), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat)), tc_nat), tc_RealDef_Oreal), tc_RealDef_Oreal), true2, c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), tc_nat), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat)), tc_nat), tc_RealDef_Oreal))
% 128.59/16.85 = { by axiom 3 (cls_CHAINED_0) }
% 128.59/16.85 fresh114(true2, true2, c_HOL_Ouminus__class_Ouminus(v_s____, tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(v_f____(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat))), tc_nat), tc_RealDef_Oreal), c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal), c_RealDef_Oreal(c_Suc(c_HOL_Oplus__class_Oplus(v_N1____, v_N2____, tc_nat)), tc_nat), tc_RealDef_Oreal))
% 128.59/16.85 = { by axiom 1 (cls_real__add__left__mono_0) }
% 128.59/16.85 true2
% 128.59/16.85 % SZS output end Proof
% 128.59/16.85
% 128.59/16.85 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------