%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT281-2 : 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 : n026.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 07:50:00 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.55s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 15 unt; 0 def)
% Number of atoms : 36 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 18 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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; 8 con; 0-4 aty)
% Number of variables : 23 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Tarski_OPartialOrder__iff_2,axiom,
! [VAR_0,VAR_1] :
( c_Relation_Otrans(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_2) ).
cnf(c_1,plain,
( c_Relation_Otrans(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_2]) ).
fof(cls_Relation_Otrans__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( c_in(c_Pair(VAR_4,VAR_3,VAR_1,VAR_1),VAR_0,tc_prod(VAR_1,VAR_1))
| ~ c_in(c_Pair(VAR_4,VAR_2,VAR_1,VAR_1),VAR_0,tc_prod(VAR_1,VAR_1))
| ~ c_in(c_Pair(VAR_2,VAR_3,VAR_1,VAR_1),VAR_0,tc_prod(VAR_1,VAR_1))
| ~ c_Relation_Otrans(VAR_0,VAR_1) ),
file('theBenchmark.p',cls_Relation_Otrans__def_0) ).
cnf(c_2,plain,
( c_in(c_Pair(E,D,B,B),A,tc_prod(B,B))
| ~ c_in(c_Pair(E,C,B,B),A,tc_prod(B,B))
| ~ c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))
| ~ c_Relation_Otrans(A,B) ),
inference(clausify,[status(thm)],[cls_Relation_Otrans__def_0]) ).
cnf(c_3,plain,
( c_in(c_Pair(E,D,B,B),c_Tarski_Opotype_Oorder(A,B,tc_Product__Type_Ounit),tc_prod(B,B))
| ~ c_in(c_Pair(E,C,B,B),c_Tarski_Opotype_Oorder(A,B,tc_Product__Type_Ounit),tc_prod(B,B))
| ~ c_in(c_Pair(C,D,B,B),c_Tarski_Opotype_Oorder(A,B,tc_Product__Type_Ounit),tc_prod(B,B))
| ~ c_in(A,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
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_4,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_5,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_conjecture_2,axiom,
~ c_in(c_Pair(v_a,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_6,plain,
~ c_in(c_Pair(v_a,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_7,plain,
~ c_in(c_Pair(v_a,v_c,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_4,c_6]) ).
fof(cls_conjecture_1,axiom,
c_in(c_Pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_8,plain,
c_in(c_Pair(v_b,v_c,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_9,plain,
c_in(c_Pair(v_b,v_c,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_4,c_8]) ).
fof(cls_conjecture_0,axiom,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_10,plain,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_11,plain,
c_in(c_Pair(v_a,v_b,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_4,c_10]) ).
cnf(c_14,plain,
( c_in(c_Pair(C,B,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(C,A,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,B,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_3,c_5]) ).
cnf(c_15,plain,
( c_in(c_Pair(A,v_c,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(A,v_b,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_14,c_9]) ).
cnf(c_12,plain,
~ c_in(c_Pair(v_a,v_b,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_15,c_7]) ).
cnf(c_13,plain,
$false,
inference(resolve,[status(thm)],[c_12,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT281-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.53 % Computer : n026.cluster.edu
% 0.11/0.53 % Model : x86_64 x86_64
% 0.11/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.53 % Memory : 8046.5625MB
% 0.11/0.53 % OS : Linux 6.8.0-71-generic
% 0.11/0.53 % CPULimit : 300
% 0.11/0.53 % WCLimit : 300
% 0.11/0.53 % DateTime : Fri Sep 25 20:27:26 UTC 2026
% 0.11/0.54 % CPUTime :
% 0.11/0.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.54 % Process 3370013 was started by sandbox on n026,
% 0.11/0.54 % Fri Sep 25 20:27:26 2026
% 0.11/0.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.54
% 0.11/0.54 % From the command line: assign(max_seconds, 300).
% 0.11/0.55
% 0.11/0.55 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.55
% 0.11/0.55 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.55 % Length of proof is 13.
% 0.11/0.55 % Level of proof is 3.
% 0.11/0.55 % Maximum clause weight is 45.000.
% 0.11/0.55 % Given clauses 5.
% 0.11/0.55
% 0.11/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------