%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW313+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:14:05 AM UTC 2026
% Result : Theorem 3.64s 1.14s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 11 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_asm,axiom,
! [V_G_2,V_tsa_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_G_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ),
file('theBenchmark.p',fact_asm) ).
fof(fact_cut,axiom,
! [V_G_2,V_tsa_2,V_G_Ha_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
=> c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ),
file('theBenchmark.p',fact_cut) ).
fof(conj_2,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
file('theBenchmark.p',conj_2) ).
fof(conj_2_neg,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
inference(assume_negation,[status(cth)],[conj_2]) ).
cnf(c_1547,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(A,C,B)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(A),tc_HOL_Obool)),B),C)) ),
inference(clausify,[status(thm)],[fact_asm]) ).
cnf(c_1549,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(A,D,C)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(A,D,B)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(A,B,C) ),
inference(clausify,[status(thm)],[fact_cut]) ).
fof(conj_0,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)),
file('theBenchmark.p',conj_0) ).
cnf(c_1802,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)),
inference(clausify,[status(thm)],[conj_0]) ).
fof(conj_1,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)),
file('theBenchmark.p',conj_1) ).
cnf(c_1803,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)),
inference(clausify,[status(thm)],[conj_1]) ).
cnf(c_1804,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
inference(clausify,[status(thm)],[conj_2_neg]) ).
cnf(c_2427,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts),
inference(resolve,[status(thm)],[c_1802,c_1547]) ).
cnf(c_2486,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_G),
inference(resolve,[status(thm)],[c_1803,c_1547]) ).
cnf(c_2699,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,A,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,A,v_G) ),
inference(resolve,[status(thm)],[c_1549,c_2427]) ).
cnf(c_2712,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,v_ts),
inference(resolve,[status(thm)],[c_2699,c_2486]) ).
cnf(c_2711,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1804,c_2712]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW313+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 15:43:01 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.39 % Process 1231665 was started by sandbox on n016,
% 0.11/0.39 % Sat Sep 26 15:43:01 2026
% 0.11/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 3.64/1.14
% 3.64/1.14 % SInE (scan): 455 to sos (tol 1.5x), 262 to usable (tol 2.0x), 4510 zapped, of 5227 axioms (depth 3).
% 3.64/1.14
% 3.64/1.14 % From the command line: assign(max_seconds, 300).
% 3.64/1.14
% 3.64/1.14 % SZS status Theorem for theBenchmark
% 3.64/1.14
% 3.64/1.14 % Proof 1 at 0.25 (+ 0.07) seconds.
% 3.64/1.14 % Length of proof is 12.
% 3.64/1.14 % Level of proof is 4.
% 3.64/1.14 % Maximum clause weight is 14.000.
% 3.64/1.14 % Given clauses 40.
% 3.64/1.14
% 3.64/1.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------