%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET837-2 : 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 : n009.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 08:37:05 AM UTC 2026
% Result : Unsatisfiable 7.57s 1.70s
% Output : CNFRefutation 7.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 86 ( 18 unt; 0 def)
% Number of atoms : 210 ( 45 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 214 ( 90 ~; 124 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 115 ( 9 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
( c_lessequals(v_Y,v_X,tc_set(t_a))
| v_X = c_union(v_Y,v_Z,t_a) ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
( c_lessequals(v_Y,v_X,tc_set(t_a))
| v_X = c_union(v_Y,v_Z,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_2,plain,
( c_lessequals(v_Y,v_X,tc_set(t_a))
| c_union(v_Y,v_Z,t_a) = v_X ),
inference(copy,[status(thm)],[c_1]) ).
fof(cls_conjecture_1,axiom,
( c_lessequals(v_Z,v_X,tc_set(t_a))
| v_X = c_union(v_Y,v_Z,t_a) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_3,plain,
( c_lessequals(v_Z,v_X,tc_set(t_a))
| v_X = c_union(v_Y,v_Z,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_4,plain,
( c_lessequals(v_Z,v_X,tc_set(t_a))
| c_union(v_Y,v_Z,t_a) = v_X ),
inference(copy,[status(thm)],[c_3]) ).
fof(cls_conjecture_2,axiom,
( v_X != c_union(v_Y,v_Z,t_a)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_5,plain,
( v_X != c_union(v_Y,v_Z,t_a)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_6,plain,
( c_union(v_Y,v_Z,t_a) != v_X
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
inference(copy,[status(thm)],[c_5]) ).
fof(cls_conjecture_3,axiom,
( v_X != c_union(v_Y,v_Z,t_a)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_x,tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_7,plain,
( v_X != c_union(v_Y,v_Z,t_a)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_x,tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_8,plain,
( c_union(v_Y,v_Z,t_a) != v_X
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_x,tc_set(t_a)) ),
inference(copy,[status(thm)],[c_7]) ).
fof(cls_conjecture_4,axiom,
( v_X != c_union(v_Y,v_Z,t_a)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_9,plain,
( v_X != c_union(v_Y,v_Z,t_a)
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_10,plain,
( c_union(v_Y,v_Z,t_a) != v_X
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(copy,[status(thm)],[c_9]) ).
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))
| v_X = c_union(v_Y,v_Z,t_a) ),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_11,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))
| v_X = c_union(v_Y,v_Z,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
cnf(c_12,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))
| c_union(v_Y,v_Z,t_a) = v_X ),
inference(copy,[status(thm)],[c_11]) ).
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_13,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_14,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_15,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_16,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_17,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_18,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_Set_Osubset__antisym_0,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_0
| ~ c_lessequals(VAR_1,VAR_0,tc_set(VAR_2))
| ~ c_lessequals(VAR_0,VAR_1,tc_set(VAR_2)) ),
file('theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(c_19,plain,
( B = A
| ~ c_lessequals(B,A,tc_set(C))
| ~ c_lessequals(A,B,tc_set(C)) ),
inference(clausify,[status(thm)],[cls_Set_Osubset__antisym_0]) ).
cnf(c_23,plain,
( c_union(v_Y,v_Z,t_a) = v_X
| c_in(A,v_X,t_a)
| ~ c_in(A,v_Z,t_a) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_24,plain,
( c_union(v_Y,v_Z,t_a) = v_X
| c_in(A,v_X,t_a)
| ~ c_in(A,v_Y,t_a) ),
inference(resolve,[status(thm)],[c_16,c_2]) ).
cnf(c_26,plain,
( c_in(c_Main_OsubsetI__1(c_union(A,B,C),D,C),A,C)
| c_in(c_Main_OsubsetI__1(c_union(A,B,C),D,C),B,C)
| c_lessequals(c_union(A,B,C),D,tc_set(C)) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_27,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_17,c_14]) ).
cnf(c_28,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_17,c_13]) ).
cnf(c_2774,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_27,c_18]) ).
cnf(c_37,plain,
c_lessequals(A,c_union(A,B,C),tc_set(C)),
inference(copy,[status(thm)],[c_2774]) ).
cnf(c_42,plain,
( ~ c_lessequals(v_Z,c_union(v_Y,A,t_a),tc_set(t_a))
| c_lessequals(v_X,c_union(v_Y,A,t_a),tc_set(t_a))
| c_union(v_Y,v_Z,t_a) = v_X ),
inference(resolve,[status(thm)],[c_37,c_12]) ).
cnf(c_2775,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_28,c_18]) ).
cnf(c_44,plain,
c_lessequals(A,c_union(B,A,C),tc_set(C)),
inference(copy,[status(thm)],[c_2775]) ).
cnf(c_52,plain,
( c_union(v_Y,v_Z,t_a) = v_X
| c_in(c_Main_OsubsetI__1(c_union(A,v_Z,t_a),B,t_a),v_X,t_a)
| c_in(c_Main_OsubsetI__1(c_union(A,v_Z,t_a),B,t_a),A,t_a)
| c_lessequals(c_union(A,v_Z,t_a),B,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_26,c_23]) ).
cnf(c_57,plain,
( c_in(c_Main_OsubsetI__1(c_union(A,B,C),D,C),c_union(B,E,C),C)
| c_in(c_Main_OsubsetI__1(c_union(A,B,C),D,C),A,C)
| c_lessequals(c_union(A,B,C),D,tc_set(C)) ),
inference(resolve,[status(thm)],[c_26,c_14]) ).
cnf(c_173,plain,
( c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a))
| c_union(v_Y,v_Z,t_a) = v_X ),
inference(resolve,[status(thm)],[c_42,c_44]) ).
cnf(c_2776,plain,
( v_X = c_union(v_Y,v_Z,t_a)
| ~ c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a))
| c_union(v_Y,v_Z,t_a) = v_X ),
inference(resolve,[status(thm)],[c_173,c_19]) ).
cnf(c_2777,plain,
( c_union(v_Y,v_Z,t_a) = v_X
| ~ c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a))
| c_union(v_Y,v_Z,t_a) = v_X ),
inference(copy,[status(thm)],[c_2776]) ).
cnf(c_175,plain,
( ~ c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a))
| c_union(v_Y,v_Z,t_a) = v_X ),
inference(copy,[status(thm)],[c_2777]) ).
cnf(c_2778,plain,
( c_union(v_Y,v_Z,t_a) = v_X
| c_in(c_Main_OsubsetI__1(c_union(v_Y,v_Z,t_a),A,t_a),v_X,t_a)
| c_union(v_Y,v_Z,t_a) = v_X
| c_in(c_Main_OsubsetI__1(c_union(v_Y,v_Z,t_a),A,t_a),v_X,t_a)
| c_lessequals(c_union(v_Y,v_Z,t_a),A,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_52,c_24]) ).
cnf(c_2779,plain,
( c_union(v_Y,v_Z,t_a) = v_X
| c_union(v_Y,v_Z,t_a) = v_X
| c_in(c_Main_OsubsetI__1(c_union(v_Y,v_Z,t_a),A,t_a),v_X,t_a)
| c_lessequals(c_union(v_Y,v_Z,t_a),A,tc_set(t_a)) ),
inference(copy,[status(thm)],[c_2778]) ).
cnf(c_344,plain,
( c_union(v_Y,v_Z,t_a) = v_X
| c_in(c_Main_OsubsetI__1(c_union(v_Y,v_Z,t_a),A,t_a),v_X,t_a)
| c_lessequals(c_union(v_Y,v_Z,t_a),A,tc_set(t_a)) ),
inference(copy,[status(thm)],[c_2779]) ).
cnf(c_769,plain,
( c_in(c_Main_OsubsetI__1(c_union(A,B,C),D,C),c_union(F,A,C),C)
| c_in(c_Main_OsubsetI__1(c_union(A,B,C),D,C),c_union(B,E,C),C)
| c_lessequals(c_union(A,B,C),D,tc_set(C)) ),
inference(resolve,[status(thm)],[c_57,c_13]) ).
cnf(c_797,plain,
( c_in(c_Main_OsubsetI__1(c_union(A,B,C),D,C),c_union(B,A,C),C)
| c_lessequals(c_union(A,B,C),D,tc_set(C)) ),
inference(factor,[status(thm)],[c_769]) ).
cnf(c_2780,plain,
( c_lessequals(c_union(A,B,C),c_union(B,A,C),tc_set(C))
| c_lessequals(c_union(A,B,C),c_union(B,A,C),tc_set(C)) ),
inference(resolve,[status(thm)],[c_797,c_18]) ).
cnf(c_907,plain,
c_lessequals(c_union(A,B,C),c_union(B,A,C),tc_set(C)),
inference(copy,[status(thm)],[c_2780]) ).
cnf(c_2781,plain,
( c_union(B,A,C) = c_union(A,B,C)
| ~ c_lessequals(c_union(A,B,C),c_union(B,A,C),tc_set(C)) ),
inference(resolve,[status(thm)],[c_907,c_19]) ).
cnf(c_929,plain,
c_union(A,B,C) = c_union(B,A,C),
inference(resolve,[status(thm)],[c_907,c_2781]) ).
cnf(c_2782,plain,
( c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a))
| c_union(v_Y,v_Z,t_a) = v_X
| c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_344,c_18]) ).
cnf(c_2567,plain,
( c_union(v_Y,v_Z,t_a) = v_X
| c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(copy,[status(thm)],[c_2782]) ).
cnf(c_2783,plain,
( c_union(v_Y,v_Z,t_a) = v_X
| c_union(v_Y,v_Z,t_a) = v_X ),
inference(resolve,[status(thm)],[c_2567,c_175]) ).
cnf(c_2571,plain,
c_union(v_Y,v_Z,t_a) = v_X,
inference(copy,[status(thm)],[c_2783]) ).
cnf(c_2784,plain,
( v_X != v_X
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_2571,c_10]) ).
cnf(c_2572,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(copy,[status(thm)],[c_2784]) ).
cnf(c_2785,plain,
( v_X != v_X
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_x,tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_2571,c_8]) ).
cnf(c_2573,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_x,tc_set(t_a)) ),
inference(copy,[status(thm)],[c_2785]) ).
cnf(c_2786,plain,
( v_X != v_X
| ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
inference(paramod,[status(thm)],[c_2571,c_6]) ).
cnf(c_2574,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_Z,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
inference(copy,[status(thm)],[c_2786]) ).
cnf(c_2575,plain,
c_lessequals(v_Y,v_X,tc_set(t_a)),
inference(paramod,[status(thm)],[c_2571,c_37]) ).
cnf(c_2576,plain,
c_lessequals(v_Z,v_X,tc_set(t_a)),
inference(paramod,[status(thm)],[c_2571,c_44]) ).
cnf(c_2787,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| c_lessequals(v_Y,v_x,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_2576,c_2574]) ).
cnf(c_2591,plain,
c_lessequals(v_Y,v_x,tc_set(t_a)),
inference(resolve,[status(thm)],[c_2575,c_2787]) ).
cnf(c_2788,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| c_lessequals(v_Z,v_x,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_2576,c_2573]) ).
cnf(c_2592,plain,
c_lessequals(v_Z,v_x,tc_set(t_a)),
inference(resolve,[status(thm)],[c_2575,c_2788]) ).
cnf(c_2789,plain,
( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
inference(resolve,[status(thm)],[c_2576,c_2572]) ).
cnf(c_2593,plain,
~ c_lessequals(v_X,v_x,tc_set(t_a)),
inference(resolve,[status(thm)],[c_2575,c_2789]) ).
cnf(c_2624,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_x,t_a),
inference(resolve,[status(thm)],[c_18,c_2593]) ).
cnf(c_2790,plain,
( c_in(A,v_x,t_a)
| ~ c_in(A,v_Y,t_a) ),
inference(resolve,[status(thm)],[c_16,c_2591]) ).
cnf(c_2661,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_Y,t_a),
inference(resolve,[status(thm)],[c_2790,c_2624]) ).
cnf(c_2791,plain,
( c_in(A,v_x,t_a)
| ~ c_in(A,v_Z,t_a) ),
inference(resolve,[status(thm)],[c_16,c_2592]) ).
cnf(c_2685,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_Z,t_a),
inference(resolve,[status(thm)],[c_2791,c_2624]) ).
cnf(c_2792,plain,
( c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),A,t_a)
| ~ c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),c_union(A,v_Y,t_a),t_a) ),
inference(resolve,[status(thm)],[c_15,c_2661]) ).
cnf(c_2793,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),c_union(v_Z,v_Y,t_a),t_a),
inference(resolve,[status(thm)],[c_2792,c_2685]) ).
cnf(c_2794,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),c_union(v_Y,v_Z,t_a),t_a),
inference(paramod,[status(thm)],[c_929,c_2793]) ).
cnf(c_2756,plain,
~ c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_X,t_a),
inference(paramod,[status(thm)],[c_2571,c_2794]) ).
cnf(c_2795,plain,
c_lessequals(v_X,v_x,tc_set(t_a)),
inference(resolve,[status(thm)],[c_2756,c_17]) ).
cnf(c_2773,plain,
$false,
inference(resolve,[status(thm)],[c_2593,c_2795]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET837-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n009.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 08:20:14 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3821443 was started by sandbox2 on n009,
% 0.13/0.36 % Sat Sep 26 08:20:14 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 7.57/1.70
% 7.57/1.70 % Assigning unary symbol tc_set kb_weight 0 and highest precedence (11).
% 7.57/1.70
% 7.57/1.70 % SZS status Unsatisfiable for theBenchmark
% 7.57/1.70
% 7.57/1.70 % Proof 1 at 1.17 (+ 0.13) seconds.
% 7.57/1.70 % Length of proof is 51.
% 7.57/1.70 % Level of proof is 12.
% 7.57/1.70 % Maximum clause weight is 49.000.
% 7.57/1.70 % Given clauses 288.
% 7.57/1.70
% 7.57/1.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------