%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT277-1 : 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 : n010.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 07:49:59 AM UTC 2026
% Result : Unsatisfiable 231.68s 36.19s
% Output : CNFRefutation 231.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 16 unt; 0 def)
% Number of atoms : 28 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 13 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_1,axiom,
~ c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2240,plain,
~ c_in(c_Pair(v_x,v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_0,axiom,
c_in(v_x,v_A,t_a),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_2241,plain,
c_in(v_x,v_A,t_a),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_Tarski_Or_A_61_61_Aorder_Acl_0,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
cnf(c_2242,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(clausify,[status(thm)],[cls_Tarski_Or_A_61_61_Aorder_Acl_0]) ).
fof(cls_Tarski_Ocl_A_58_APartialOrder_0,axiom,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
cnf(c_2243,plain,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(clausify,[status(thm)],[cls_Tarski_Ocl_A_58_APartialOrder_0]) ).
fof(cls_Tarski_OPartialOrder__iff_0,axiom,
! [VAR_0,VAR_1] :
( c_Relation_Orefl(c_Tarski_Opotype_Opset(VAR_0,VAR_1,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(VAR_0,VAR_1,tc_Product__Type_Ounit),VAR_1)
| ~ c_in(VAR_0,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(VAR_1,tc_Product__Type_Ounit)) ),
file('theBenchmark.p',cls_Tarski_OPartialOrder__iff_0) ).
cnf(c_2247,plain,
( c_Relation_Orefl(c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(A,B,tc_Product__Type_Ounit),B)
| ~ c_in(A,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit)) ),
inference(clausify,[status(thm)],[cls_Tarski_OPartialOrder__iff_0]) ).
fof(cls_Tarski_OA_A_61_61_Apset_Acl_0,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
cnf(c_2248,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(clausify,[status(thm)],[cls_Tarski_OA_A_61_61_Apset_Acl_0]) ).
cnf(c_2249,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(copy,[status(thm)],[c_2248]) ).
fof(cls_Relation_OreflD_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(c_Pair(VAR_3,VAR_3,VAR_2,VAR_2),VAR_1,tc_prod(VAR_2,VAR_2))
| ~ c_in(VAR_3,VAR_0,VAR_2)
| ~ c_Relation_Orefl(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Relation_OreflD_0) ).
cnf(c_2250,plain,
( c_in(c_Pair(D,D,C,C),B,tc_prod(C,C))
| ~ c_in(D,A,C)
| ~ c_Relation_Orefl(A,B,C) ),
inference(clausify,[status(thm)],[cls_Relation_OreflD_0]) ).
cnf(c_5298,plain,
~ c_in(c_Pair(v_x,v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(paramod,[status(thm)],[c_2242,c_2240]) ).
cnf(c_13388,plain,
c_Relation_Orefl(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(resolve,[status(thm)],[c_2247,c_2243]) ).
cnf(c_5804,plain,
c_Relation_Orefl(v_A,c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(paramod,[status(thm)],[c_2249,c_13388]) ).
cnf(c_5805,plain,
( c_in(c_Pair(v_x,v_x,t_a,t_a),A,tc_prod(t_a,t_a))
| ~ c_Relation_Orefl(v_A,A,t_a) ),
inference(resolve,[status(thm)],[c_2250,c_2241]) ).
cnf(c_13389,plain,
c_in(c_Pair(v_x,v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(resolve,[status(thm)],[c_5805,c_5804]) ).
cnf(c_13387,plain,
$false,
inference(resolve,[status(thm)],[c_5298,c_13389]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT277-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.37 % Computer : n010.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Fri Sep 25 20:23:41 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.38 % Process 1584133 was started by sandbox2 on n010,
% 0.12/5.38 % Fri Sep 25 20:23:41 2026
% 0.12/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.42
% 0.14/5.42 % From the command line: assign(max_seconds, 300).
% 231.68/36.19
% 231.68/36.19 % given #500 (I,wt=32): 1347 -class_Ring__and__Field_Oordered__idom(A) | c_plus(c_NatArith_Oof__nat(B,A),c_NatArith_Oof__nat(C,A),A) = c_NatArith_Oof__nat(c_plus(B,C,tc_nat),A). [copy(1346),flip(b)].
% 231.68/36.19
% 231.68/36.19 % given #1000 (I,wt=26): 2131 -class_OrderedGroup_Oordered__cancel__ab__semigroup__add(A) | -c_in(B,c_Finite__Set_OFinites,tc_set(A)) | c_in(c_Finite__Set_OMin(B,A),B,A) | c_emptyset = B. [copy(2130),flip(d)].
% 231.68/36.19
% 231.68/36.19 % given #1500 (I,wt=9): 2701 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | class_HOL_Oplus(A) # tptp_name(clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) # clausal_fof(1). [assumption].
% 231.68/36.19
% 231.68/36.19 % given #2000 (I,wt=18): 3389 c_Relation_Orel__comp(c_Relation_OId,A,B,B,C) = A # tptp_name(cls_Relation_OId__O__R_0) # clausal_fof(1). [assumption].
% 231.68/36.19
% 231.68/36.19 % given #2500 (I,wt=27): 4278 c_0 = A | c_div(c_times(B,A,tc_IntDef_Oint),A,tc_IntDef_Oint) = B. [copy(4277),flip(a)].
% 231.68/36.19
% 231.68/36.19 % given #3000 (I,wt=20): 5193 c_HOL_Oabs(A,B) != c_0 | c_0 = A | -class_Ring__and__Field_Oordered__ring__strict(B). [copy(5192),flip(b)].
% 231.68/36.19
% 231.68/36.19 % given #3500 (A,wt=28): 5683 -c_in(c_IntDef_ONats,c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) | -c_less(c_Finite__Set_OMax(c_IntDef_ONats,tc_IntDef_Oint),A,tc_IntDef_Oint) | c_less(c_0,A,tc_IntDef_Oint) | c_emptyset = c_IntDef_ONats. [resolve(1504,a,1029,a),unit_del(e,2820)].
% 231.68/36.19
% 231.68/36.19 % given #4000 (W,wt=20): 6736 c_less(c_0,A,tc_nat) | c_times(B,A,tc_nat) = c_0. [resolve(3646,a,3636,a),flip(b)].
% 231.68/36.19
% 231.68/36.19 % SZS status Unsatisfiable for theBenchmark
% 231.68/36.19
% 231.68/36.19 % Proof 1 at 5.55 (+ 0.49) seconds.
% 231.68/36.19 % Length of proof is 12.
% 231.68/36.19 % Level of proof is 3.
% 231.68/36.19 % Maximum clause weight is 28.000.
% 231.68/36.19 % Given clauses 4289.
% 231.68/36.19
% 231.68/36.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------