%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV243-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 09:07:07 AM UTC 2026
% Result : Unsatisfiable 119.92s 17.15s
% Output : CNFRefutation 119.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 18 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Set_OUn__absorb_0,axiom,
! [VAR_0,VAR_1] : c_union(VAR_0,VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Set_OUn__absorb_0) ).
cnf(c_3571,plain,
c_union(A,A,B) = A,
inference(clausify,[status(thm)],[cls_Set_OUn__absorb_0]) ).
fof(cls_Set_OUn__empty__right_0,axiom,
! [VAR_0,VAR_1] : c_union(VAR_0,c_emptyset,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Set_OUn__empty__right_0) ).
cnf(c_3578,plain,
c_union(A,c_emptyset,B) = A,
inference(clausify,[status(thm)],[cls_Set_OUn__empty__right_0]) ).
fof(cls_Message_Oanalz__synth__Un_0,axiom,
! [VAR_0,VAR_1] : c_Message_Oanalz(c_union(c_Message_Osynth(VAR_0),VAR_1,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(VAR_0,VAR_1,tc_Message_Omsg)),c_Message_Osynth(VAR_0),tc_Message_Omsg),
file('theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).
cnf(c_3805,plain,
c_Message_Oanalz(c_union(c_Message_Osynth(A),B,tc_Message_Omsg)) = c_union(c_Message_Oanalz(c_union(A,B,tc_Message_Omsg)),c_Message_Osynth(A),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_Message_Oanalz__synth__Un_0]) ).
cnf(c_3806,plain,
c_union(c_Message_Oanalz(c_union(A,B,tc_Message_Omsg)),c_Message_Osynth(A),tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(A),B,tc_Message_Omsg)),
inference(copy,[status(thm)],[c_3805]) ).
fof(cls_conjecture_0,axiom,
c_Message_Oanalz(c_Message_Osynth(v_H)) != c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_3809,plain,
c_Message_Oanalz(c_Message_Osynth(v_H)) != c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_3810,plain,
c_union(c_Message_Oanalz(v_H),c_Message_Osynth(v_H),tc_Message_Omsg) != c_Message_Oanalz(c_Message_Osynth(v_H)),
inference(copy,[status(thm)],[c_3809]) ).
cnf(c_11365,plain,
c_union(c_Message_Oanalz(A),c_Message_Osynth(A),tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(A),A,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_3571,c_3806]) ).
cnf(c_11378,plain,
c_union(c_Message_Oanalz(A),c_Message_Osynth(A),tc_Message_Omsg) = c_Message_Oanalz(c_union(c_Message_Osynth(A),c_emptyset,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_3578,c_3806]) ).
cnf(c_11379,plain,
c_Message_Oanalz(c_union(c_Message_Osynth(A),A,tc_Message_Omsg)) = c_Message_Oanalz(c_union(c_Message_Osynth(A),c_emptyset,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_11365,c_11378]) ).
cnf(c_11367,plain,
c_Message_Oanalz(c_union(c_Message_Osynth(A),A,tc_Message_Omsg)) = c_Message_Oanalz(c_Message_Osynth(A)),
inference(paramod,[status(thm)],[c_3578,c_11379]) ).
cnf(c_11380,plain,
c_Message_Oanalz(c_union(c_Message_Osynth(v_H),v_H,tc_Message_Omsg)) != c_Message_Oanalz(c_Message_Osynth(v_H)),
inference(paramod,[status(thm)],[c_11365,c_3810]) ).
cnf(c_11381,plain,
c_Message_Oanalz(c_Message_Osynth(v_H)) != c_Message_Oanalz(c_Message_Osynth(v_H)),
inference(paramod,[status(thm)],[c_11367,c_11380]) ).
cnf(c_11377,plain,
$false,
inference(copy,[status(thm)],[c_11381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV243-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 13:21:34 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1415319 was started by sandbox2 on n019,
% 0.18/0.45 % Sat Sep 26 13:21:34 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.22/0.58
% 0.22/0.58 % From the command line: assign(max_seconds, 300).
% 119.92/17.15
% 119.92/17.15 % given #500 (I,wt=9): 788 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | class_OrderedGroup_Osemigroup__mult(A) # tptp_name(clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) # clausal_fof(1). [assumption].
% 119.92/17.15
% 119.92/17.15 % given #1000 (I,wt=7): 1288 class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) # tptp_name(clsarity_IntDef__Oint_30) # clausal_fof(1). [assumption].
% 119.92/17.15
% 119.92/17.15 % given #1500 (I,wt=26): 1826 -class_Ring__and__Field_Oordered__semidom(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(c_1,A),B,A) | c_less(c_uminus(B,A),c_1,A). [resolve(56,b,53,a)].
% 119.92/17.15
% 119.92/17.15 % given #2000 (I,wt=30): 2531 c_append(c_List_Orev(A,B),c_List_Orev(C,B),B) = c_List_Orev(c_append(C,A,B),B). [copy(2530),flip(a)].
% 119.92/17.15
% 119.92/17.15 % given #2500 (I,wt=28): 3220 -c_less(c_0,A,tc_nat) | c_less(c_0,c_Nat_Opower(A,c_Numeral_Onumber__of(B,tc_nat),tc_nat),tc_nat) # tptp_name(cls_Parity_Ozero__less__power__nat__eq__number__of_2) # clausal_fof(1). [assumption].
% 119.92/17.15
% 119.92/17.15 % SZS status Unsatisfiable for theBenchmark
% 119.92/17.15
% 119.92/17.15 % Proof 1 at 7.14 (+ 0.75) seconds.
% 119.92/17.16 % Length of proof is 9.
% 119.92/17.16 % Level of proof is 4.
% 119.92/17.16 % Maximum clause weight is 36.000.
% 119.92/17.16 % Given clauses 2919.
% 119.92/17.16
% 119.92/17.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------