%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% 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 07:49:57 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.56s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 72 unt; 0 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-4 aty)
% Number of variables : 129 ( 1 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
fof(cls_conjecture_0,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_2,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_3,plain,
true = c_lessequals(v_S,v_A,tc_set(t_a)),
inference(copy,[status(thm)],[c_2]) ).
fof(cls_conjecture_1,axiom,
c_in(v_x,v_S,t_a) = true,
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_4,plain,
c_in(v_x,v_S,t_a) = true,
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_34,plain,
c_in(v_x,v_S,t_a) = c_lessequals(v_S,v_A,tc_set(t_a)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_5,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = c_in(v_x,v_S,t_a),
inference(copy,[status(thm)],[c_34]) ).
fof(cls_conjecture_2,axiom,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != true,
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_6,plain,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != true,
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_35,plain,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != c_lessequals(v_S,v_A,tc_set(t_a)),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_7,plain,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_5,c_35]) ).
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_8,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_9,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(copy,[status(thm)],[c_8]) ).
fof(cls_Tarski_OCL_Olub__upper_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ifeq(c_lessequals(VAR_0,c_Tarski_Opotype_Opset(VAR_1,VAR_2,tc_Product__Type_Ounit),tc_set(VAR_2)),true,ifeq(c_in(VAR_1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(VAR_2,tc_Product__Type_Ounit)),true,ifeq(c_in(VAR_1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(VAR_2,tc_Product__Type_Ounit)),true,ifeq(c_in(VAR_3,VAR_0,VAR_2),true,c_in(c_Pair(VAR_3,c_Tarski_Olub(VAR_0,VAR_1,VAR_2),VAR_2,VAR_2),c_Tarski_Opotype_Oorder(VAR_1,VAR_2,tc_Product__Type_Ounit),tc_prod(VAR_2,VAR_2)),true),true),true),true) = true,
file('theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
cnf(c_10,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),true,ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ifeq(c_in(D,A,C),true,c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true) = true,
inference(clausify,[status(thm)],[cls_Tarski_OCL_Olub__upper_0]) ).
cnf(c_36,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ifeq(c_in(D,A,C),true,c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_10]) ).
cnf(c_37,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ifeq(c_in(D,A,C),true,c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_5,c_36]) ).
cnf(c_38,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ifeq(c_in(D,A,C),true,c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_37]) ).
cnf(c_39,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ifeq(c_in(D,A,C),true,c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_5,c_38]) ).
cnf(c_40,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(D,A,C),true,c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_39]) ).
cnf(c_41,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),true,c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_5,c_40]) ).
cnf(c_42,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_41]) ).
cnf(c_43,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_in(v_x,v_S,t_a),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true) = true,
inference(paramod,[status(thm)],[c_5,c_42]) ).
cnf(c_44,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_in(v_x,v_S,t_a),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_lessequals(v_S,v_A,tc_set(t_a))),true),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_43]) ).
cnf(c_45,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_in(v_x,v_S,t_a),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)),true),true),true) = true,
inference(paramod,[status(thm)],[c_5,c_44]) ).
cnf(c_46,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_in(v_x,v_S,t_a),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_45]) ).
cnf(c_47,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_in(v_x,v_S,t_a),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),true),true) = true,
inference(paramod,[status(thm)],[c_5,c_46]) ).
cnf(c_48,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_in(v_x,v_S,t_a),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),true) = true,
inference(paramod,[status(thm)],[c_3,c_47]) ).
cnf(c_49,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_in(v_x,v_S,t_a),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),true) = true,
inference(paramod,[status(thm)],[c_5,c_48]) ).
cnf(c_50,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_in(v_x,v_S,t_a),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))) = true,
inference(paramod,[status(thm)],[c_3,c_49]) ).
cnf(c_51,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_in(v_x,v_S,t_a),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)) = true,
inference(paramod,[status(thm)],[c_5,c_50]) ).
cnf(c_52,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_in(v_x,v_S,t_a),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)) = c_lessequals(v_S,v_A,tc_set(t_a)),
inference(paramod,[status(thm)],[c_3,c_51]) ).
cnf(c_11,plain,
ifeq(c_lessequals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(D,A,C),c_in(v_x,v_S,t_a),c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_5,c_52]) ).
fof(cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ifeq(c_in(c_Pair(VAR_0,VAR_1,VAR_2,VAR_2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(VAR_3,VAR_2),VAR_2,tc_Product__Type_Ounit),tc_prod(VAR_2,VAR_2)),true,c_in(c_Pair(VAR_1,VAR_0,VAR_2,VAR_2),c_Tarski_Opotype_Oorder(VAR_3,VAR_2,tc_Product__Type_Ounit),tc_prod(VAR_2,VAR_2)),true) = true,
file('theBenchmark.p',cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) ).
cnf(c_12,plain,
ifeq(c_in(c_Pair(A,B,C,C),c_Tarski_Opotype_Oorder(c_Tarski_Odual(D,C),C,tc_Product__Type_Ounit),tc_prod(C,C)),true,c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)),true) = true,
inference(clausify,[status(thm)],[cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0]) ).
cnf(c_53,plain,
ifeq(c_in(c_Pair(A,B,C,C),c_Tarski_Opotype_Oorder(c_Tarski_Odual(D,C),C,tc_Product__Type_Ounit),tc_prod(C,C)),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)),true) = true,
inference(paramod,[status(thm)],[c_3,c_12]) ).
cnf(c_54,plain,
ifeq(c_in(c_Pair(A,B,C,C),c_Tarski_Opotype_Oorder(c_Tarski_Odual(D,C),C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a),c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)),true) = true,
inference(paramod,[status(thm)],[c_5,c_53]) ).
cnf(c_55,plain,
ifeq(c_in(c_Pair(A,B,C,C),c_Tarski_Opotype_Oorder(c_Tarski_Odual(D,C),C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a),c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_lessequals(v_S,v_A,tc_set(t_a))) = true,
inference(paramod,[status(thm)],[c_3,c_54]) ).
cnf(c_56,plain,
ifeq(c_in(c_Pair(A,B,C,C),c_Tarski_Opotype_Oorder(c_Tarski_Odual(D,C),C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a),c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)) = true,
inference(paramod,[status(thm)],[c_5,c_55]) ).
cnf(c_57,plain,
ifeq(c_in(c_Pair(A,B,C,C),c_Tarski_Opotype_Oorder(c_Tarski_Odual(D,C),C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a),c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)) = c_lessequals(v_S,v_A,tc_set(t_a)),
inference(paramod,[status(thm)],[c_3,c_56]) ).
cnf(c_13,plain,
ifeq(c_in(c_Pair(A,B,C,C),c_Tarski_Opotype_Oorder(c_Tarski_Odual(D,C),C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a),c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)),c_in(v_x,v_S,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_5,c_57]) ).
fof(cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
file('theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
cnf(c_14,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
inference(clausify,[status(thm)],[cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0]) ).
cnf(c_58,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = c_lessequals(v_S,v_A,tc_set(t_a)),
inference(paramod,[status(thm)],[c_3,c_14]) ).
cnf(c_15,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_5,c_58]) ).
fof(cls_Tarski_Odual_Acl_A_58_APartialOrder_0,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
file('theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
cnf(c_16,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
inference(clausify,[status(thm)],[cls_Tarski_Odual_Acl_A_58_APartialOrder_0]) ).
cnf(c_59,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = c_lessequals(v_S,v_A,tc_set(t_a)),
inference(paramod,[status(thm)],[c_3,c_16]) ).
cnf(c_17,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_5,c_59]) ).
fof(cls_Tarski_Oglb__dual__lub_0,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Tarski_Oglb(VAR_0,VAR_1,VAR_2) = c_Tarski_Olub(VAR_0,c_Tarski_Odual(VAR_1,VAR_2),VAR_2),
file('theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
cnf(c_18,plain,
c_Tarski_Oglb(A,B,C) = c_Tarski_Olub(A,c_Tarski_Odual(B,C),C),
inference(clausify,[status(thm)],[cls_Tarski_Oglb__dual__lub_0]) ).
fof(cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0,axiom,
! [VAR_0,VAR_1] : c_Tarski_Opotype_Opset(c_Tarski_Odual(VAR_0,VAR_1),VAR_1,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(VAR_0,VAR_1,tc_Product__Type_Ounit),
file('theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
cnf(c_19,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(A,B),B,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),
inference(clausify,[status(thm)],[cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_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_20,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]) ).
cnf(c_60,plain,
c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_18,c_7]) ).
cnf(c_22,plain,
c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) != c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_20,c_60]) ).
cnf(c_23,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(A,t_a,tc_Product__Type_Ounit),tc_set(t_a)),c_in(v_x,v_S,t_a),ifeq(c_in(A,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(A,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,A,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(A,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_61,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),c_in(v_x,v_S,t_a),ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_15,c_23]) ).
cnf(c_62,plain,
ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),c_in(v_x,v_S,t_a),ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_19,c_61]) ).
cnf(c_63,plain,
ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),c_in(v_x,v_S,t_a),ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_9,c_62]) ).
cnf(c_64,plain,
ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_5,c_63]) ).
cnf(c_65,plain,
ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_17,c_64]) ).
cnf(c_66,plain,
ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_1,c_65]) ).
cnf(c_67,plain,
ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(v_x,v_S,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_1,c_66]) ).
cnf(c_30,plain,
c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_1,c_67]) ).
cnf(c_68,plain,
ifeq(c_in(v_x,v_S,t_a),c_in(v_x,v_S,t_a),c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_in(v_x,v_S,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_30,c_13]) ).
cnf(c_32,plain,
c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) = c_in(v_x,v_S,t_a),
inference(paramod,[status(thm)],[c_1,c_68]) ).
cnf(c_33,plain,
$false,
inference(resolve,[status(thm)],[c_32,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.54 % Computer : n010.cluster.edu
% 0.11/0.54 % Model : x86_64 x86_64
% 0.11/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.54 % Memory : 8046.5625MB
% 0.11/0.54 % OS : Linux 6.8.0-71-generic
% 0.11/0.54 % CPULimit : 300
% 0.11/0.54 % WCLimit : 300
% 0.11/0.54 % DateTime : Fri Sep 25 20:22:34 UTC 2026
% 0.11/0.54 % CPUTime :
% 0.11/0.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.55 % Process 1581449 was started by sandbox2 on n010,
% 0.11/0.55 % Fri Sep 25 20:22:34 2026
% 0.11/0.55 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.55
% 0.11/0.55 % From the command line: assign(max_seconds, 300).
% 0.14/0.56
% 0.14/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.56
% 0.14/0.56 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.56 % Length of proof is 25.
% 0.14/0.56 % Level of proof is 7.
% 0.14/0.56 % Maximum clause weight is 81.000.
% 0.14/0.56 % Given clauses 14.
% 0.14/0.56
% 0.14/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------