%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW216+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 : n017.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 09:13:57 AM UTC 2026
% Result : Theorem 7.86s 1.94s
% Output : CNFRefutation 7.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 11 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 6 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_pos__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ),
file('theBenchmark.p',fact_pos__less__divide__eq) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
file('theBenchmark.p',conj_0) ).
fof(conj_0_neg,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(fact_m_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
file('theBenchmark.p',fact_m_I1_J) ).
cnf(c_1638,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
inference(clausify,[status(thm)],[fact_m_I1_J]) ).
fof(fact_H_I3_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
file('theBenchmark.p',fact_H_I3_J) ).
cnf(c_1639,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(clausify,[status(thm)],[fact_H_I3_J]) ).
cnf(c_1689,plain,
( c_Orderings_Oord__class_Oless(A,hAPP(c_Groups_Otimes__class_Otimes(A,C),B),D)
| ~ c_Orderings_Oord__class_Oless(A,C,c_Rings_Oinverse__class_Odivide(A,D,B))
| ~ c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)
| ~ class_Fields_Olinordered__field(A) ),
inference(clausify,[status(thm)],[fact_pos__less__divide__eq]) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
cnf(c_2587,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]) ).
cnf(c_2615,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
inference(clausify,[status(thm)],[conj_0_neg]) ).
cnf(c_8311,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____)
| ~ class_Fields_Olinordered__field(tc_RealDef_Oreal) ),
inference(resolve,[status(thm)],[c_1689,c_1639]) ).
cnf(c_8312,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
inference(resolve,[status(thm)],[c_2587,c_8311]) ).
cnf(c_8313,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
inference(resolve,[status(thm)],[c_1638,c_8312]) ).
cnf(c_8310,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2615,c_8313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW216+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n017.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Sat Sep 26 15:24:20 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.57 % Process 1064637 was started by sandbox on n017,
% 0.09/0.57 % Sat Sep 26 15:24:20 2026
% 0.09/0.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.80
% 0.13/0.80 % From the command line: assign(max_seconds, 300).
% 0.13/0.80
% 0.13/0.80 % SInE: 760 to sos, 489 to usable, of 1249 axioms (tolerance 2.00, depth 0 fixpoint).
% 7.86/1.94
% 7.86/1.94 % SZS status Theorem for theBenchmark
% 7.86/1.94
% 7.86/1.94 % Proof 1 at 0.97 (+ 0.10) seconds.
% 7.86/1.94 % Length of proof is 8.
% 7.86/1.94 % Level of proof is 2.
% 7.86/1.94 % Maximum clause weight is 337.000.
% 7.86/1.94 % Given clauses 242.
% 7.86/1.94
% 7.86/1.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------