%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW311+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 : n026.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 09:14:04 AM UTC 2026
% Result : Theorem 5.40s 1.36s
% Output : CNFRefutation 5.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 27 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 4 |; 2 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 18 ( 0 sgn 9 !; 1 ?)
% 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_1,conjecture,
! [B_G] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),B_G))
=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,B_G,v_ts) ),
file('theBenchmark.p',conj_1) ).
fof(conj_1_neg,negated_conjecture,
~ ! [B_G] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),B_G))
=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,B_G,v_ts) ),
inference(assume_negation,[status(cth)],[conj_1]) ).
cnf(c_1554,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_1556,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,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts),
file('theBenchmark.p',conj_0) ).
cnf(c_1771,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts),
inference(clausify,[status(thm)],[conj_0]) ).
fof(nnf_665,plain,
? [B_G] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,B_G,v_ts)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),B_G)) ),
inference(fof_nnf,[status(thm)],[conj_1_neg]) ).
fof(sk_conj_1_neg,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,sK0,v_ts)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B_G,sK0)],[nnf_665]) ).
cnf(c_1772,negated_conjecture,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),sK0)),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_1773,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,sK0,v_ts),
inference(split_conjunct,[status(thm)],[sk_conj_1_neg]) ).
cnf(c_2425,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,sK0,v_G_H),
inference(resolve,[status(thm)],[c_1772,c_1554]) ).
cnf(c_2628,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,A,v_ts)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,A,v_G_H) ),
inference(resolve,[status(thm)],[c_1556,c_1771]) ).
cnf(c_2637,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,sK0,v_ts),
inference(resolve,[status(thm)],[c_2628,c_2425]) ).
cnf(c_2636,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1773,c_2637]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW311+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.40 % Computer : n026.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sat Sep 26 15:41:11 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.40 % Process 1383965 was started by sandbox on n026,
% 0.11/0.40 % Sat Sep 26 15:41:11 2026
% 0.11/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 5.40/1.36
% 5.40/1.36 % SInE (scan): 449 to sos (tol 1.5x), 252 to usable (tol 2.0x), 4521 zapped, of 5222 axioms (depth 3).
% 5.40/1.36
% 5.40/1.36 % From the command line: assign(max_seconds, 300).
% 5.40/1.36
% 5.40/1.36 % SZS status Theorem for theBenchmark
% 5.40/1.36
% 5.40/1.36 % Proof 1 at 0.46 (+ 0.14) seconds.
% 5.40/1.36 % Length of proof is 11.
% 5.40/1.36 % Level of proof is 3.
% 5.40/1.36 % Maximum clause weight is 14.000.
% 5.40/1.36 % Given clauses 40.
% 5.40/1.36
% 5.40/1.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------