%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT268-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 0.03s 5.95s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 26 unt; 0 def)
% Number of atoms : 49 ( 9 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 40 ( 24 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 27 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
c_in(v_x,v_S,t_a),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
c_in(v_x,v_S,t_a),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
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)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_3,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)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
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_4,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_5,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(copy,[status(thm)],[c_4]) ).
fof(cls_Tarski_OCL_Olub__upper_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(c_Pair(VAR_0,c_Tarski_Olub(VAR_1,VAR_3,VAR_2),VAR_2,VAR_2),c_Tarski_Opotype_Oorder(VAR_3,VAR_2,tc_Product__Type_Ounit),tc_prod(VAR_2,VAR_2))
| ~ c_lessequals(VAR_1,c_Tarski_Opotype_Opset(VAR_3,VAR_2,tc_Product__Type_Ounit),tc_set(VAR_2))
| ~ c_in(VAR_3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(VAR_2,tc_Product__Type_Ounit))
| ~ c_in(VAR_3,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(VAR_2,tc_Product__Type_Ounit))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
cnf(c_6,plain,
( c_in(c_Pair(A,c_Tarski_Olub(B,D,C),C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C))
| ~ c_lessequals(B,c_Tarski_Opotype_Opset(D,C,tc_Product__Type_Ounit),tc_set(C))
| ~ c_in(D,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit))
| ~ c_in(D,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Tarski_OCL_Olub__upper_0]) ).
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] :
( 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))
| ~ 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)) ),
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_7,plain,
( c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C))
| ~ 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)) ),
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]) ).
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)),
file('theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
cnf(c_8,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)),
inference(clausify,[status(thm)],[cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0]) ).
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)),
file('theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
cnf(c_9,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)),
inference(clausify,[status(thm)],[cls_Tarski_Odual_Acl_A_58_APartialOrder_0]) ).
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_10,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_11,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_12,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_20,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)),
inference(paramod,[status(thm)],[c_10,c_3]) ).
cnf(c_13,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)),
inference(paramod,[status(thm)],[c_12,c_20]) ).
cnf(c_16,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)),
inference(resolve,[status(thm)],[c_7,c_13]) ).
cnf(c_21,plain,
( 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_lessequals(v_S,c_Tarski_Opotype_Opset(A,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| ~ c_in(A,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(A,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_22,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_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(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(resolve,[status(thm)],[c_21,c_8]) ).
cnf(c_23,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_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_22,c_9]) ).
cnf(c_24,plain,
~ 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)),
inference(resolve,[status(thm)],[c_23,c_16]) ).
cnf(c_25,plain,
~ c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),
inference(paramod,[status(thm)],[c_11,c_24]) ).
cnf(c_18,plain,
~ c_lessequals(v_S,v_A,tc_set(t_a)),
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_19,plain,
$false,
inference(resolve,[status(thm)],[c_18,c_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT268-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/5.94 % Computer : n012.cluster.edu
% 0.03/5.94 % Model : x86_64 x86_64
% 0.03/5.94 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.94 % Memory : 8046.5625MB
% 0.03/5.94 % OS : Linux 6.8.0-71-generic
% 0.03/5.94 % CPULimit : 300
% 0.03/5.94 % WCLimit : 300
% 0.03/5.94 % DateTime : Fri Sep 25 20:21:58 UTC 2026
% 0.03/5.94 % CPUTime :
% 0.03/5.94 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/5.94 % Process 2907224 was started by sandbox on n012,
% 0.03/5.94 % Fri Sep 25 20:21:58 2026
% 0.03/5.94 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/5.94
% 0.03/5.94 % From the command line: assign(max_seconds, 300).
% 0.03/5.95
% 0.03/5.95 % SZS status Unsatisfiable for theBenchmark
% 0.03/5.95
% 0.03/5.95 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/5.95 % Length of proof is 16.
% 0.03/5.95 % Level of proof is 4.
% 0.03/5.95 % Maximum clause weight is 40.000.
% 0.03/5.95 % Given clauses 13.
% 0.03/5.95
% 0.03/5.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------