%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET831-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 : Fri Sep 25 02:44:03 PM UTC 2026
% Result : Unsatisfiable 16.52s 2.60s
% Output : Proof 16.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of formulae : 111 ( 13 unt; 0 def)
% Number of atoms : 271 ( 50 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 272 ( 112 ~; 160 |; 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 : 149 ( 7 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f10_nnf,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f7,axiom,
( c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
fof(f7_nnf,plain,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( c_in(X0,X1,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p20,plain,
( c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X0,X2)
| c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2)) ),
inference(resolution,[status(thm)],[c10,c7]) ).
cnf(f11,axiom,
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f11_nnf,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p76,plain,
( c_lessequals(c_inter(X0,X1,X2),X0,tc_set(X2))
| c_lessequals(c_inter(X0,X1,X2),X0,tc_set(X2)) ),
inference(resolution,[status(thm)],[p20,c11]) ).
cnf(p270,plain,
c_lessequals(c_inter(X0,X1,X2),X0,tc_set(X2)),
inference(factoring,[status(thm)],[p76]) ).
cnf(f6,axiom,
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
fof(f6_nnf,plain,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( c_in(X0,X2,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p17,plain,
( c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X1,X2)
| c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2)) ),
inference(resolution,[status(thm)],[c10,c6]) ).
cnf(p64,plain,
( c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2))
| c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[p17,c11]) ).
cnf(p184,plain,
c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2)),
inference(factoring,[status(thm)],[p64]) ).
cnf(f5,negated_conjecture,
( ~ c_lessequals(V_U,v_Y,tc_set(t_a))
| ~ c_lessequals(V_U,v_Z,tc_set(t_a))
| c_lessequals(V_U,v_X,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f5_nnf,plain,
! [V_U] :
( ~ c_lessequals(V_U,v_Y,tc_set(t_a))
| ~ c_lessequals(V_U,v_Z,tc_set(t_a))
| c_lessequals(V_U,v_X,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_U] :
( ~ c_lessequals(V_U,v_Y,tc_set(t_a))
| ~ c_lessequals(V_U,v_Z,tc_set(t_a))
| c_lessequals(V_U,v_X,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ c_lessequals(X0,v_Y,tc_set(t_a))
| ~ c_lessequals(X0,v_Z,tc_set(t_a))
| c_lessequals(X0,v_X,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p852,plain,
( ~ c_lessequals(c_inter(X0,v_Z,t_a),v_Y,tc_set(t_a))
| c_lessequals(c_inter(X0,v_Z,t_a),v_X,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(resolution,[status(thm)],[p184,c5]) ).
cnf(p2136,plain,
( c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(resolution,[status(thm)],[p270,p852]) ).
cnf(f9,axiom,
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f9_nnf,plain,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p33,plain,
( c_lessequals(X0,X3,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X3,X2),X1,X2)
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[c9,c10]) ).
cnf(f1,negated_conjecture,
( c_lessequals(v_X,v_Z,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
( c_lessequals(v_X,v_Z,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
( c_lessequals(v_X,v_Z,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_lessequals(v_X,v_Z,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p14,plain,
( c_in(X0,v_Z,t_a)
| ~ c_in(X0,v_X,t_a)
| c_lessequals(v_X,v_Z,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c1,c6]) ).
cnf(p19,plain,
( c_in(c_Main_OsubsetI__1(v_X,X0,t_a),v_Z,t_a)
| c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_X,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c10,p14]) ).
cnf(p28,plain,
( c_in(c_Main_OsubsetI__1(v_X,v_Z,t_a),v_Z,t_a)
| c_lessequals(v_X,v_Z,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p19]) ).
cnf(p49,plain,
( c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_X,v_Z,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c11,p28]) ).
cnf(p52,plain,
c_lessequals(v_X,v_Z,tc_set(t_a)),
inference(factoring,[status(thm)],[p49]) ).
cnf(p113,plain,
( c_lessequals(v_X,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_X,X0,t_a),v_Z,t_a) ),
inference(resolution,[status(thm)],[p33,p52]) ).
cnf(f8,axiom,
( c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
fof(f8_nnf,plain,
! [V_c,V_B,T_a,V_A] :
( c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V_c,V_B,T_a,V_A] :
( c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( c_in(X0,c_inter(X3,X1,X2),X2)
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p117,plain,
( c_in(c_Main_OsubsetI__1(v_X,X0,t_a),c_inter(X1,v_Z,t_a),t_a)
| ~ c_in(c_Main_OsubsetI__1(v_X,X0,t_a),X1,t_a)
| c_lessequals(v_X,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p113,c8]) ).
cnf(f0,negated_conjecture,
( c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
( c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
( c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p15,plain,
( c_in(X0,v_Y,t_a)
| ~ c_in(X0,v_X,t_a)
| c_lessequals(v_X,v_Y,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c0,c7]) ).
cnf(p21,plain,
( c_in(c_Main_OsubsetI__1(v_X,X0,t_a),v_Y,t_a)
| c_lessequals(v_X,v_Y,tc_set(t_a))
| c_lessequals(v_X,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c10,p15]) ).
cnf(p31,plain,
( c_in(c_Main_OsubsetI__1(v_X,v_Y,t_a),v_Y,t_a)
| c_lessequals(v_X,v_Y,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p21]) ).
cnf(p51,plain,
( c_lessequals(v_X,v_Y,tc_set(t_a))
| c_lessequals(v_X,v_Y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c11,p31]) ).
cnf(p56,plain,
c_lessequals(v_X,v_Y,tc_set(t_a)),
inference(factoring,[status(thm)],[p51]) ).
cnf(p114,plain,
( c_lessequals(v_X,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_X,X0,t_a),v_Y,t_a) ),
inference(resolution,[status(thm)],[p33,p56]) ).
cnf(p368,plain,
( c_lessequals(v_X,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_X,X0,t_a),c_inter(v_Y,v_Z,t_a),t_a)
| c_lessequals(v_X,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p117,p114]) ).
cnf(p397,plain,
( c_in(c_Main_OsubsetI__1(v_X,X0,t_a),c_inter(v_Y,v_Z,t_a),t_a)
| c_lessequals(v_X,X0,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p368]) ).
cnf(p400,plain,
( c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a))
| c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)) ),
inference(resolution,[status(thm)],[p397,c11]) ).
cnf(p405,plain,
c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)),
inference(factoring,[status(thm)],[p400]) ).
cnf(f12,axiom,
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f12_nnf,plain,
! [V_B,V_A,T_a] :
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [V_B,V_A,T_a] :
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p417,plain,
( c_inter(v_Y,v_Z,t_a) = v_X
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p405,c12]) ).
cnf(p2166,plain,
( c_inter(v_Y,v_Z,t_a) = v_X
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(resolution,[status(thm)],[p2136,p417]) ).
cnf(f3,negated_conjecture,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Z,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3_nnf,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Z,tc_set(t_a)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Z,tc_set(t_a)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Z,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p54,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| c_lessequals(v_x,v_Z,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p52,c3]) ).
cnf(p65,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| c_lessequals(v_x,v_Z,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p54,p56]) ).
cnf(p2173,plain,
( v_X != v_X
| c_lessequals(v_x,v_Z,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(superposition,[status(thm)],[p2166,p65]) ).
cnf(p2312,plain,
( c_lessequals(v_x,v_Z,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(equality_resolution,[status(thm)],[p2173]) ).
cnf(p2314,plain,
( c_lessequals(v_x,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Z,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p2312,p65]) ).
cnf(p2366,plain,
c_lessequals(v_x,v_Z,tc_set(t_a)),
inference(factoring,[status(thm)],[p2314]) ).
cnf(p2369,plain,
( c_lessequals(v_x,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x,X0,t_a),v_Z,t_a) ),
inference(resolution,[status(thm)],[p2366,p33]) ).
cnf(p2376,plain,
( c_in(c_Main_OsubsetI__1(v_x,X0,t_a),c_inter(X1,v_Z,t_a),t_a)
| ~ c_in(c_Main_OsubsetI__1(v_x,X0,t_a),X1,t_a)
| c_lessequals(v_x,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p2369,c8]) ).
cnf(f2,negated_conjecture,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p53,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p52,c2]) ).
cnf(p59,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p53,p56]) ).
cnf(p2171,plain,
( v_X != v_X
| c_lessequals(v_x,v_Y,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(superposition,[status(thm)],[p2166,p59]) ).
cnf(p2260,plain,
( c_lessequals(v_x,v_Y,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(equality_resolution,[status(thm)],[p2171]) ).
cnf(p2261,plain,
( c_lessequals(v_x,v_Y,tc_set(t_a))
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p2260,p59]) ).
cnf(p2297,plain,
c_lessequals(v_x,v_Y,tc_set(t_a)),
inference(factoring,[status(thm)],[p2261]) ).
cnf(p2299,plain,
( c_lessequals(v_x,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x,X0,t_a),v_Y,t_a) ),
inference(resolution,[status(thm)],[p2297,p33]) ).
cnf(p3421,plain,
( c_lessequals(v_x,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_x,X0,t_a),v_X,t_a)
| c_lessequals(v_x,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p2376,p2299]) ).
cnf(p3429,plain,
( c_in(c_Main_OsubsetI__1(v_x,X0,t_a),v_X,t_a)
| c_lessequals(v_x,X0,tc_set(t_a)) ),
inference(factoring,[status(thm)],[p3421]) ).
cnf(p3432,plain,
( c_lessequals(v_x,v_X,tc_set(t_a))
| c_lessequals(v_x,v_X,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p3429,c11]) ).
cnf(p3435,plain,
c_lessequals(v_x,v_X,tc_set(t_a)),
inference(factoring,[status(thm)],[p3432]) ).
cnf(p2162,plain,
( v_X = c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(resolution,[status(thm)],[p2136,c12]) ).
cnf(p2787,plain,
( ~ c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(factoring,[status(thm)],[p2162]) ).
cnf(p2788,plain,
v_X = c_inter(v_Y,v_Z,t_a),
inference(resolution,[status(thm)],[p2787,p405]) ).
cnf(p2799,plain,
( c_inter(v_Y,v_Z,t_a) = v_X
| ~ c_lessequals(v_X,v_X,tc_set(t_a)) ),
inference(superposition,[status(thm)],[p2788,p417]) ).
cnf(p46,plain,
( c_lessequals(X0,X0,tc_set(X1))
| c_lessequals(X0,X0,tc_set(X1)) ),
inference(resolution,[status(thm)],[c11,c10]) ).
cnf(p135,plain,
c_lessequals(X0,X0,tc_set(X1)),
inference(factoring,[status(thm)],[p46]) ).
cnf(p2824,plain,
c_inter(v_Y,v_Z,t_a) = v_X,
inference(resolution,[status(thm)],[p2799,p135]) ).
cnf(f4,negated_conjecture,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f4_nnf,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p2825,plain,
( v_X != v_X
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
inference(demodulation,[status(thm)],[p2824,c4]) ).
cnf(p2960,plain,
( ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
inference(equality_resolution,[status(thm)],[p2825]) ).
cnf(p3444,plain,
( ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p3435,p2960]) ).
cnf(p3445,plain,
~ c_lessequals(v_X,v_Y,tc_set(t_a)),
inference(resolution,[status(thm)],[p3444,p52]) ).
cnf(p3446,plain,
$false,
inference(resolution,[status(thm)],[p3445,p56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET831-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.01/0.36 % CPULimit : 300
% 0.01/0.36 % WCLimit : 300
% 0.01/0.36 % DateTime : Thu Sep 24 12:10:25 UTC 2026
% 0.01/0.36 % CPUTime :
% 0.01/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.52/2.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.52/2.60 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------