%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET830-2 : 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 : n014.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 08:37:03 AM UTC 2026
% Result : Unsatisfiable 0.23s 10.51s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 26 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 68 ( 4 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Set_OIntE_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_2,VAR_3)
| ~ c_in(VAR_0,c_inter(VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_Set_OIntE_0) ).
cnf(c_1,plain,
( c_in(A,C,D)
| ~ c_in(A,c_inter(B,C,D),D) ),
inference(clausify,[status(thm)],[cls_Set_OIntE_0]) ).
fof(cls_Set_OIntE_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_1,VAR_3)
| ~ c_in(VAR_0,c_inter(VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_Set_OIntE_1) ).
cnf(c_2,plain,
( c_in(A,B,D)
| ~ c_in(A,c_inter(B,C,D),D) ),
inference(clausify,[status(thm)],[cls_Set_OIntE_1]) ).
fof(cls_Set_OIntI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_inter(VAR_3,VAR_1,VAR_2),VAR_2)
| ~ c_in(VAR_0,VAR_3,VAR_2)
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OIntI_0) ).
cnf(c_3,plain,
( c_in(A,c_inter(D,B,C),C)
| ~ c_in(A,D,C)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OIntI_0]) ).
fof(cls_Set_OsubsetD_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_3,VAR_2)
| ~ c_lessequals(VAR_1,VAR_3,tc_set(VAR_2))
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(c_4,plain,
( c_in(A,D,C)
| ~ c_lessequals(B,D,tc_set(C))
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetD_0]) ).
fof(cls_Set_OsubsetI_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_0,VAR_1,tc_set(VAR_2))
| c_in(c_Main_OsubsetI__1(VAR_0,VAR_1,VAR_2),VAR_0,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(c_5,plain,
( c_lessequals(A,B,tc_set(C))
| c_in(c_Main_OsubsetI__1(A,B,C),A,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetI_0]) ).
fof(cls_Set_OsubsetI_1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( c_lessequals(VAR_0,VAR_1,tc_set(VAR_2))
| ~ c_in(c_Main_OsubsetI__1(VAR_0,VAR_1,VAR_2),VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(c_6,plain,
( c_lessequals(A,B,tc_set(C))
| ~ c_in(c_Main_OsubsetI__1(A,B,C),B,C) ),
inference(clausify,[status(thm)],[cls_Set_OsubsetI_1]) ).
fof(cls_conjecture_2,axiom,
c_in(v_x,v_Y,t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_7,plain,
c_in(v_x,v_Y,t_a),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
c_in(v_x,v_Z,t_a),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_8,plain,
c_in(v_x,v_Z,t_a),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_4,axiom,
~ c_in(v_x,v_X,t_a),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_9,plain,
~ c_in(v_x,v_X,t_a),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_5,axiom,
! [VAR_0] :
( ~ c_lessequals(VAR_0,v_Y,tc_set(t_a))
| ~ c_lessequals(VAR_0,v_Z,tc_set(t_a))
| c_lessequals(VAR_0,v_X,tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_10,plain,
( ~ c_lessequals(A,v_Y,tc_set(t_a))
| ~ c_lessequals(A,v_Z,tc_set(t_a))
| c_lessequals(A,v_X,tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
cnf(c_14,plain,
( c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),A,C)
| c_lessequals(c_inter(A,B,C),D,tc_set(C)) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_15,plain,
( c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),B,C)
| c_lessequals(c_inter(A,B,C),D,tc_set(C)) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_18,plain,
( c_in(v_x,c_inter(v_Y,A,t_a),t_a)
| ~ c_in(v_x,A,t_a) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_177,plain,
( c_lessequals(c_inter(A,B,C),A,tc_set(C))
| c_lessequals(c_inter(A,B,C),A,tc_set(C)) ),
inference(resolve,[status(thm)],[c_14,c_6]) ).
cnf(c_35,plain,
c_lessequals(c_inter(A,B,C),A,tc_set(C)),
inference(copy,[status(thm)],[c_177]) ).
cnf(c_178,plain,
( c_lessequals(c_inter(A,B,C),B,tc_set(C))
| c_lessequals(c_inter(A,B,C),B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_15,c_6]) ).
cnf(c_78,plain,
c_lessequals(c_inter(A,B,C),B,tc_set(C)),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_93,plain,
c_in(v_x,c_inter(v_Y,v_Z,t_a),t_a),
inference(resolve,[status(thm)],[c_18,c_8]) ).
cnf(c_179,plain,
( c_in(v_x,A,t_a)
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),A,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_4,c_93]) ).
cnf(c_121,plain,
~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a)),
inference(resolve,[status(thm)],[c_179,c_9]) ).
cnf(c_180,plain,
( ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_Y,tc_set(t_a))
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_Z,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_10,c_121]) ).
cnf(c_181,plain,
~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_Z,tc_set(t_a)),
inference(resolve,[status(thm)],[c_180,c_35]) ).
cnf(c_176,plain,
$false,
inference(resolve,[status(thm)],[c_78,c_181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET830-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/10.46 % Computer : n014.cluster.edu
% 0.18/10.46 % Model : x86_64 x86_64
% 0.18/10.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.46 % Memory : 8046.5625MB
% 0.18/10.46 % OS : Linux 6.8.0-71-generic
% 0.18/10.46 % CPULimit : 300
% 0.18/10.46 % WCLimit : 300
% 0.18/10.46 % DateTime : Sat Sep 26 08:19:27 UTC 2026
% 0.18/10.46 % CPUTime :
% 0.18/10.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/10.47 % Process 2627299 was started by sandbox2 on n014,
% 0.18/10.47 % Sat Sep 26 08:19:27 2026
% 0.18/10.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/10.47
% 0.18/10.47 % From the command line: assign(max_seconds, 300).
% 0.23/10.51
% 0.23/10.51 % SZS status Unsatisfiable for theBenchmark
% 0.23/10.51
% 0.23/10.51 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.23/10.51 % Length of proof is 18.
% 0.23/10.51 % Level of proof is 4.
% 0.23/10.51 % Maximum clause weight is 33.000.
% 0.23/10.51 % Given clauses 50.
% 0.23/10.51
% 0.23/10.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------