%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV262-1 : 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 : n013.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 09:07:11 AM UTC 2026
% Result : Unsatisfiable 49.50s 7.74s
% Output : CNFRefutation 49.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 28 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 40 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Datatype_Oo2s_Osimps__2_0,axiom,
! [VAR_0,VAR_1] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(VAR_0,VAR_1),VAR_1) = c_insert(VAR_0,c_emptyset,VAR_1),
file('theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
cnf(c_1381,plain,
c_Datatype_Oo2s(c_Datatype_Ooption_OSome(A,B),B) = c_insert(A,c_emptyset,B),
inference(clausify,[status(thm)],[cls_Datatype_Oo2s_Osimps__2_0]) ).
cnf(c_1382,plain,
c_insert(A,c_emptyset,B) = c_Datatype_Oo2s(c_Datatype_Ooption_OSome(A,B),B),
inference(copy,[status(thm)],[c_1381]) ).
fof(cls_Set_OUn__empty__left_0,axiom,
! [VAR_0,VAR_1] : c_union(c_emptyset,VAR_0,VAR_1) = VAR_0,
file('theBenchmark.p',cls_Set_OUn__empty__left_0) ).
cnf(c_3765,plain,
c_union(c_emptyset,A,B) = A,
inference(clausify,[status(thm)],[cls_Set_OUn__empty__left_0]) ).
fof(cls_Set_OUn__insert__left_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_union(c_insert(VAR_0,VAR_1,VAR_2),VAR_3,VAR_2) = c_insert(VAR_0,c_union(VAR_1,VAR_3,VAR_2),VAR_2),
file('theBenchmark.p',cls_Set_OUn__insert__left_0) ).
cnf(c_3770,plain,
c_union(c_insert(A,B,C),D,C) = c_insert(A,c_union(B,D,C),C),
inference(clausify,[status(thm)],[cls_Set_OUn__insert__left_0]) ).
fof(cls_Message_Oparts__Un_0,axiom,
! [VAR_0,VAR_1] : c_Message_Oparts(c_union(VAR_0,VAR_1,tc_Message_Omsg)) = c_union(c_Message_Oparts(VAR_0),c_Message_Oparts(VAR_1),tc_Message_Omsg),
file('theBenchmark.p',cls_Message_Oparts__Un_0) ).
cnf(c_3927,plain,
c_Message_Oparts(c_union(A,B,tc_Message_Omsg)) = c_union(c_Message_Oparts(A),c_Message_Oparts(B),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_Message_Oparts__Un_0]) ).
cnf(c_3928,plain,
c_union(c_Message_Oparts(A),c_Message_Oparts(B),tc_Message_Omsg) = c_Message_Oparts(c_union(A,B,tc_Message_Omsg)),
inference(copy,[status(thm)],[c_3927]) ).
fof(cls_Message_Oparts__insert_0,axiom,
! [VAR_0,VAR_1] : c_Message_Oparts(c_insert(VAR_0,VAR_1,tc_Message_Omsg)) = c_union(c_Message_Oparts(c_insert(VAR_0,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(VAR_1),tc_Message_Omsg),
file('theBenchmark.p',cls_Message_Oparts__insert_0) ).
cnf(c_3933,plain,
c_Message_Oparts(c_insert(A,B,tc_Message_Omsg)) = c_union(c_Message_Oparts(c_insert(A,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(B),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_Message_Oparts__insert_0]) ).
cnf(c_9679,plain,
c_Message_Oparts(c_insert(A,B,tc_Message_Omsg)) = c_union(c_Message_Oparts(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(A,tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(B),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_1382,c_3933]) ).
cnf(c_9680,plain,
c_Message_Oparts(c_insert(A,B,tc_Message_Omsg)) = c_Message_Oparts(c_union(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(A,tc_Message_Omsg),tc_Message_Omsg),B,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_3928,c_9679]) ).
cnf(c_3934,plain,
c_Message_Oparts(c_union(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(A,tc_Message_Omsg),tc_Message_Omsg),B,tc_Message_Omsg)) = c_Message_Oparts(c_insert(A,B,tc_Message_Omsg)),
inference(copy,[status(thm)],[c_9680]) ).
fof(cls_conjecture_0,axiom,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_3936,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_insert(v_X,c_emptyset,tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_9681,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(v_X,tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(c_insert(v_Y,c_emptyset,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_1382,c_3936]) ).
cnf(c_9682,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_union(c_Message_Oparts(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(v_X,tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(v_Y,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_1382,c_9681]) ).
cnf(c_9683,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_Message_Oparts(c_union(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(v_X,tc_Message_Omsg),tc_Message_Omsg),c_Datatype_Oo2s(c_Datatype_Ooption_OSome(v_Y,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_3928,c_9682]) ).
cnf(c_9684,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_union(c_Message_Oparts(c_insert(v_X,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(v_Y,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(v_H),tc_Message_Omsg),
inference(paramod,[status(thm)],[c_3934,c_9683]) ).
cnf(c_9685,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_Message_Oparts(c_union(c_insert(v_X,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(v_Y,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_3928,c_9684]) ).
cnf(c_9686,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_Message_Oparts(c_insert(v_X,c_union(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(v_Y,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg),tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_3770,c_9685]) ).
cnf(c_3937,plain,
c_Message_Oparts(c_insert(v_X,c_union(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(v_Y,tc_Message_Omsg),tc_Message_Omsg),v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)),
inference(copy,[status(thm)],[c_9686]) ).
cnf(c_9687,plain,
c_union(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(A,B),B),C,B) = c_insert(A,c_union(c_emptyset,C,B),B),
inference(paramod,[status(thm)],[c_1382,c_3770]) ).
cnf(c_9674,plain,
c_union(c_Datatype_Oo2s(c_Datatype_Ooption_OSome(A,B),B),C,B) = c_insert(A,C,B),
inference(paramod,[status(thm)],[c_3765,c_9687]) ).
cnf(c_9688,plain,
c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)) != c_Message_Oparts(c_insert(v_X,c_insert(v_Y,v_H,tc_Message_Omsg),tc_Message_Omsg)),
inference(paramod,[status(thm)],[c_9674,c_3937]) ).
cnf(c_9678,plain,
$false,
inference(copy,[status(thm)],[c_9688]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV262-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 13:23:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2838657 was started by sandbox2 on n013,
% 0.10/0.37 % Sat Sep 26 13:23:36 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.44
% 0.10/0.44 % From the command line: assign(max_seconds, 300).
% 49.50/7.74
% 49.50/7.74 % given #500 (I,wt=12): 1047 c_Divides_Oop_Amod(c_Divides_Oop_Amod(A,B,tc_IntDef_Oint),B,tc_IntDef_Oint) = c_Divides_Oop_Amod(A,B,tc_IntDef_Oint) # tptp_name(cls_IntDiv_Omod__mod__trivial_0) # clausal_fof(1). [assumption].
% 49.50/7.74
% 49.50/7.74 % given #1000 (I,wt=4): 1679 -class_Ring__and__Field_Oordered__field(A) | class_Ring__and__Field_Oordered__semidom(A) # tptp_name(clsrel_Ring__and__Field_Oordered__field_60) # clausal_fof(1). [assumption].
% 49.50/7.74
% 49.50/7.74 % given #1500 (I,wt=2): 2179 class_Orderings_Oord(tc_IntDef_Oint) # tptp_name(clsarity_IntDef__Oint_5) # clausal_fof(1). [assumption].
% 49.50/7.74
% 49.50/7.74 % given #2000 (I,wt=16): 2776 -class_Ring__and__Field_Osemiring__1(A) | -class_OrderedGroup_Opordered__ab__group__add(A) | -c_less(c_uminus(B,A),c_1,A) | c_less(c_uminus(c_1,A),B,A). [resolve(54,b,52,a)].
% 49.50/7.74
% 49.50/7.74 % given #2500 (I,wt=8): 3438 c_Relation_ODomain(c_Relation_Odiag(A,B),B,B) = A # tptp_name(cls_Relation_ODomain__diag_0) # clausal_fof(1). [assumption].
% 49.50/7.74
% 49.50/7.74 % SZS status Unsatisfiable for theBenchmark
% 49.50/7.74
% 49.50/7.74 % Proof 1 at 6.77 (+ 0.39) seconds.
% 49.50/7.74 % Length of proof is 12.
% 49.50/7.74 % Level of proof is 4.
% 49.50/7.74 % Maximum clause weight is 21.000.
% 49.50/7.74 % Given clauses 2735.
% 49.50/7.74
% 49.50/7.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------