%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET834-2 : 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 : n001.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 08:37:04 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% 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 : 54 ( 27 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 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 ( 6 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Set_OUnCI_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_union(VAR_3,VAR_1,VAR_2),VAR_2)
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OUnCI_0) ).
cnf(c_1,plain,
( c_in(A,c_union(D,B,C),C)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OUnCI_0]) ).
fof(cls_Set_OUnCI_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,c_union(VAR_1,VAR_3,VAR_2),VAR_2)
| ~ c_in(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_Set_OUnCI_1) ).
cnf(c_2,plain,
( c_in(A,c_union(B,D,C),C)
| ~ c_in(A,B,C) ),
inference(clausify,[status(thm)],[cls_Set_OUnCI_1]) ).
fof(cls_Set_OUnE_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_in(VAR_0,VAR_1,VAR_3)
| c_in(VAR_0,VAR_2,VAR_3)
| ~ c_in(VAR_0,c_union(VAR_1,VAR_2,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_Set_OUnE_0) ).
cnf(c_3,plain,
( c_in(A,B,D)
| c_in(A,C,D)
| ~ c_in(A,c_union(B,C,D),D) ),
inference(clausify,[status(thm)],[cls_Set_OUnE_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_X,t_a),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_7,plain,
c_in(v_x,v_X,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_Y,t_a),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_9,plain,
~ c_in(v_x,v_Y,t_a),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_5,axiom,
! [VAR_0] :
( ~ c_lessequals(v_Y,VAR_0,tc_set(t_a))
| ~ c_lessequals(v_Z,VAR_0,tc_set(t_a))
| c_lessequals(v_X,VAR_0,tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_10,plain,
( ~ c_lessequals(v_Y,A,tc_set(t_a))
| ~ c_lessequals(v_Z,A,tc_set(t_a))
| c_lessequals(v_X,A,tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
cnf(c_13,plain,
( c_in(c_Main_OsubsetI__1(A,B,C),c_union(A,D,C),C)
| c_lessequals(A,B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_14,plain,
( c_in(c_Main_OsubsetI__1(A,B,C),c_union(D,A,C),C)
| c_lessequals(A,B,tc_set(C)) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_264,plain,
( c_in(v_x,A,t_a)
| ~ c_in(v_x,c_union(A,v_Z,t_a),t_a) ),
inference(resolve,[status(thm)],[c_3,c_8]) ).
cnf(c_24,plain,
~ c_in(v_x,c_union(v_Y,v_Z,t_a),t_a),
inference(resolve,[status(thm)],[c_264,c_9]) ).
cnf(c_265,plain,
( c_lessequals(A,c_union(A,B,C),tc_set(C))
| c_lessequals(A,c_union(A,B,C),tc_set(C)) ),
inference(resolve,[status(thm)],[c_13,c_6]) ).
cnf(c_51,plain,
c_lessequals(A,c_union(A,B,C),tc_set(C)),
inference(copy,[status(thm)],[c_265]) ).
cnf(c_266,plain,
( c_lessequals(A,c_union(B,A,C),tc_set(C))
| c_lessequals(A,c_union(B,A,C),tc_set(C)) ),
inference(resolve,[status(thm)],[c_14,c_6]) ).
cnf(c_100,plain,
c_lessequals(A,c_union(B,A,C),tc_set(C)),
inference(copy,[status(thm)],[c_266]) ).
cnf(c_267,plain,
( c_in(v_x,A,t_a)
| ~ c_lessequals(v_X,A,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_117,plain,
~ c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a)),
inference(resolve,[status(thm)],[c_267,c_24]) ).
cnf(c_268,plain,
( ~ c_lessequals(v_Y,c_union(v_Y,v_Z,t_a),tc_set(t_a))
| ~ c_lessequals(v_Z,c_union(v_Y,v_Z,t_a),tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_10,c_117]) ).
cnf(c_269,plain,
~ c_lessequals(v_Z,c_union(v_Y,v_Z,t_a),tc_set(t_a)),
inference(resolve,[status(thm)],[c_268,c_51]) ).
cnf(c_263,plain,
$false,
inference(resolve,[status(thm)],[c_100,c_269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET834-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n001.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 08:25:28 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.39 % Process 1362511 was started by sandbox2 on n001,
% 0.13/0.39 % Sat Sep 26 08:25:28 2026
% 0.13/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.40
% 0.13/0.40 % From the command line: assign(max_seconds, 300).
% 0.13/0.44
% 0.13/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.44
% 0.13/0.44 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.13/0.44 % Length of proof is 17.
% 0.13/0.44 % Level of proof is 3.
% 0.13/0.44 % Maximum clause weight is 25.000.
% 0.13/0.44 % Given clauses 50.
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------