%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET831-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 02:48:42 PM UTC 2026
% Result : Unsatisfiable 2.62s 1.29s
% Output : CNFRefutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 85 ( 10 unt; 2 def)
% Number of atoms : 357 ( 44 equ)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 226 ( 93 ~; 133 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 88 ( 0 sgn 88 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,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(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_Y,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(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_Z,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,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(f6,negated_conjecture,
! [X0] :
( ~ 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X2,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X1,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_inter(X3,X1,X2),X2)
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f11,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f12,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f13,axiom,
! [X2,X0,X1] :
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f14,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(reorient_equations,[],[f13]) ).
tcf(c_62,negated_conjecture,
( c_lessequals(v_X,v_Y,tc_set(t_a))
| ( c_inter(v_Y,v_Z,t_a) = v_X ) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_63,negated_conjecture,
( c_lessequals(v_X,v_Z,tc_set(t_a))
| ( c_inter(v_Y,v_Z,t_a) = v_X ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_64,negated_conjecture,
( 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))
| ( c_inter(v_Y,v_Z,t_a) != v_X ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_65,negated_conjecture,
( c_lessequals(v_x,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ( c_inter(v_Y,v_Z,t_a) != v_X ) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_66,negated_conjecture,
( ~ c_lessequals(v_x,v_X,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ( c_inter(v_Y,v_Z,t_a) != v_X ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_67,negated_conjecture,
! [X0: $i] :
( c_lessequals(X0,v_X,tc_set(t_a))
| ( c_inter(v_Y,v_Z,t_a) = v_X )
| ~ c_lessequals(X0,v_Z,tc_set(t_a))
| ~ c_lessequals(X0,v_Y,tc_set(t_a)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X2,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X1,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,c_inter(X3,X1,X2),X2)
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X3,X1,X2)
| ~ c_in(X3,X0,X2)
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_234,definition,
iPr_def_10 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_235,definition,
iPr_def_11 = c_inter(v_Y,v_Z,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_236,negated_conjecture,
! [X0: $i] :
( c_lessequals(X0,v_X,iPr_def_10)
| ( iPr_def_11 = v_X )
| ~ c_lessequals(X0,v_Z,iPr_def_10)
| ~ c_lessequals(X0,v_Y,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_67,c_235,c_234]) ).
tcf(c_237,negated_conjecture,
( ~ c_lessequals(v_x,v_X,iPr_def_10)
| ~ c_lessequals(v_X,v_Z,iPr_def_10)
| ~ c_lessequals(v_X,v_Y,iPr_def_10)
| ( iPr_def_11 != v_X ) ),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_238,negated_conjecture,
( c_lessequals(v_x,v_Z,iPr_def_10)
| ~ c_lessequals(v_X,v_Z,iPr_def_10)
| ~ c_lessequals(v_X,v_Y,iPr_def_10)
| ( iPr_def_11 != v_X ) ),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_239,negated_conjecture,
( c_lessequals(v_x,v_Y,iPr_def_10)
| ~ c_lessequals(v_X,v_Z,iPr_def_10)
| ~ c_lessequals(v_X,v_Y,iPr_def_10)
| ( iPr_def_11 != v_X ) ),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_240,negated_conjecture,
( c_lessequals(v_X,v_Z,iPr_def_10)
| ( iPr_def_11 = v_X ) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_241,negated_conjecture,
( c_lessequals(v_X,v_Y,iPr_def_10)
| ( iPr_def_11 = v_X ) ),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_549,plain,
! [X0: $i] :
( c_in(X0,v_Z,t_a)
| ~ c_in(X0,iPr_def_11,t_a) ),
inference(superposition,[status(thm)],[c_235,c_68]) ).
tcf(c_557,plain,
! [X0: $i] :
( c_in(X0,v_Y,t_a)
| ~ c_in(X0,iPr_def_11,t_a) ),
inference(superposition,[status(thm)],[c_235,c_69]) ).
tcf(c_576,plain,
! [X0: $i] :
( c_lessequals(iPr_def_11,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(iPr_def_11,X0,t_a),v_Z,t_a) ),
inference(superposition,[status(thm)],[c_72,c_549]) ).
tcf(c_577,plain,
! [X0: $i] :
( c_lessequals(iPr_def_11,X0,iPr_def_10)
| c_in(c_Main_OsubsetI__1(iPr_def_11,X0,t_a),v_Z,t_a) ),
inference(light_normalisation,[status(thm)],[c_576,c_234]) ).
tcf(c_585,plain,
! [X0: $i] :
( c_lessequals(iPr_def_11,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(iPr_def_11,X0,t_a),v_Y,t_a) ),
inference(superposition,[status(thm)],[c_72,c_557]) ).
tcf(c_586,plain,
! [X0: $i] :
( c_lessequals(iPr_def_11,X0,iPr_def_10)
| c_in(c_Main_OsubsetI__1(iPr_def_11,X0,t_a),v_Y,t_a) ),
inference(light_normalisation,[status(thm)],[c_585,c_234]) ).
tcf(c_603,plain,
( c_lessequals(iPr_def_11,v_Z,iPr_def_10)
| c_lessequals(iPr_def_11,v_Z,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_577,c_73]) ).
tcf(c_604,plain,
( c_lessequals(iPr_def_11,v_Y,iPr_def_10)
| c_lessequals(iPr_def_11,v_Y,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_586,c_73]) ).
tcf(c_605,plain,
c_lessequals(iPr_def_11,v_Y,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_604,c_234]) ).
tcf(c_606,plain,
c_lessequals(iPr_def_11,v_Z,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_603,c_234]) ).
tcf(c_608,plain,
( c_lessequals(iPr_def_11,v_X,iPr_def_10)
| ( v_X = iPr_def_11 )
| ~ c_lessequals(iPr_def_11,v_Z,iPr_def_10) ),
inference(superposition,[status(thm)],[c_605,c_236]) ).
tcf(c_612,plain,
( c_lessequals(iPr_def_11,v_X,iPr_def_10)
| ( v_X = iPr_def_11 ) ),
inference(global_subsumption_just,[status(thm)],[c_608,c_606,c_608]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X2,X1,t_a)
| ~ c_in(X2,X0,t_a)
| ~ c_lessequals(X0,X1,iPr_def_10) ),
inference(superposition,[status(thm)],[c_234,c_71]) ).
tcf(c_648,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,iPr_def_10)
| ~ c_lessequals(X0,X1,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_234,c_74]) ).
tcf(c_649,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,iPr_def_10)
| ~ c_lessequals(X0,X1,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_648,c_234]) ).
tcf(c_659,plain,
! [X0: $i] :
( c_in(X0,iPr_def_11,t_a)
| ~ c_in(X0,v_Z,t_a)
| ~ c_in(X0,v_Y,t_a) ),
inference(superposition,[status(thm)],[c_235,c_70]) ).
tcf(c_677,plain,
! [X0: $i] :
( c_in(X0,v_Y,t_a)
| ( v_X = iPr_def_11 )
| ~ c_in(X0,v_X,t_a) ),
inference(superposition,[status(thm)],[c_241,c_637]) ).
tcf(c_678,plain,
! [X0: $i] :
( c_in(X0,v_Z,t_a)
| ( v_X = iPr_def_11 )
| ~ c_in(X0,v_X,t_a) ),
inference(superposition,[status(thm)],[c_240,c_637]) ).
tcf(c_681,plain,
! [X0: $i] :
( c_in(X0,v_X,t_a)
| ( v_X = iPr_def_11 )
| ~ c_in(X0,iPr_def_11,t_a) ),
inference(superposition,[status(thm)],[c_612,c_637]) ).
tcf(c_701,plain,
! [X0: $i] :
( c_lessequals(v_X,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_X,X0,t_a),v_Y,t_a)
| ( v_X = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_72,c_677]) ).
tcf(c_702,plain,
! [X0: $i] :
( c_lessequals(v_X,X0,iPr_def_10)
| c_in(c_Main_OsubsetI__1(v_X,X0,t_a),v_Y,t_a)
| ( v_X = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_701,c_234]) ).
tcf(c_715,plain,
! [X0: $i] :
( c_lessequals(v_X,X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(v_X,X0,t_a),v_Z,t_a)
| ( v_X = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_72,c_678]) ).
tcf(c_716,plain,
! [X0: $i] :
( c_lessequals(v_X,X0,iPr_def_10)
| c_in(c_Main_OsubsetI__1(v_X,X0,t_a),v_Z,t_a)
| ( v_X = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_715,c_234]) ).
tcf(c_752,plain,
( ( v_X = iPr_def_11 )
| ~ c_lessequals(v_X,iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_612,c_649]) ).
tcf(c_925,plain,
! [X0: $i] :
( c_lessequals(v_X,X0,iPr_def_10)
| c_in(c_Main_OsubsetI__1(v_X,X0,t_a),iPr_def_11,t_a)
| ( v_X = iPr_def_11 )
| ~ c_in(c_Main_OsubsetI__1(v_X,X0,t_a),v_Y,t_a) ),
inference(superposition,[status(thm)],[c_716,c_659]) ).
tcf(c_1098,plain,
! [X0: $i] :
( c_lessequals(v_X,X0,iPr_def_10)
| c_in(c_Main_OsubsetI__1(v_X,X0,t_a),iPr_def_11,t_a)
| ( v_X = iPr_def_11 ) ),
inference(global_subsumption_just,[status(thm)],[c_925,c_702,c_925]) ).
tcf(c_1107,plain,
( c_lessequals(v_X,iPr_def_11,iPr_def_10)
| c_lessequals(v_X,iPr_def_11,tc_set(t_a))
| ( v_X = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_1098,c_73]) ).
tcf(c_1108,plain,
! [X0: $i] :
( c_lessequals(v_X,X0,iPr_def_10)
| c_in(c_Main_OsubsetI__1(v_X,X0,t_a),v_X,t_a)
| ( v_X = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_1098,c_681]) ).
tcf(c_1111,plain,
( c_lessequals(v_X,iPr_def_11,iPr_def_10)
| ( v_X = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_1107,c_234]) ).
tcf(c_1132,plain,
v_X = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_1108,c_752,c_1111]) ).
tcf(c_1142,plain,
( ~ c_lessequals(iPr_def_11,v_Z,iPr_def_10)
| ~ c_lessequals(iPr_def_11,v_Y,iPr_def_10)
| ~ c_lessequals(v_x,iPr_def_11,iPr_def_10)
| ( iPr_def_11 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_237,c_1132]) ).
tcf(c_1143,plain,
( c_lessequals(v_x,v_Y,iPr_def_10)
| ~ c_lessequals(iPr_def_11,v_Z,iPr_def_10)
| ~ c_lessequals(iPr_def_11,v_Y,iPr_def_10)
| ( iPr_def_11 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_239,c_1132]) ).
tcf(c_1144,plain,
( c_lessequals(v_x,v_Z,iPr_def_10)
| ~ c_lessequals(iPr_def_11,v_Z,iPr_def_10)
| ~ c_lessequals(iPr_def_11,v_Y,iPr_def_10)
| ( iPr_def_11 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_238,c_1132]) ).
tcf(c_1148,plain,
( c_lessequals(v_x,v_Z,iPr_def_10)
| ~ c_lessequals(iPr_def_11,v_Z,iPr_def_10)
| ~ c_lessequals(iPr_def_11,v_Y,iPr_def_10) ),
inference(equality_resolution_simp,[status(thm)],[c_1144]) ).
tcf(c_1149,plain,
c_lessequals(v_x,v_Z,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1148,c_606,c_605]) ).
tcf(c_1150,plain,
( c_lessequals(v_x,v_Y,iPr_def_10)
| ~ c_lessequals(iPr_def_11,v_Z,iPr_def_10)
| ~ c_lessequals(iPr_def_11,v_Y,iPr_def_10) ),
inference(equality_resolution_simp,[status(thm)],[c_1143]) ).
tcf(c_1151,plain,
c_lessequals(v_x,v_Y,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1150,c_606,c_605]) ).
tcf(c_1152,plain,
( ~ c_lessequals(iPr_def_11,v_Z,iPr_def_10)
| ~ c_lessequals(iPr_def_11,v_Y,iPr_def_10)
| ~ c_lessequals(v_x,iPr_def_11,iPr_def_10) ),
inference(equality_resolution_simp,[status(thm)],[c_1142]) ).
tcf(c_1153,plain,
~ c_lessequals(v_x,iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1152,c_606,c_605]) ).
tcf(c_1155,plain,
! [X0: $i] :
( c_in(X0,v_Z,t_a)
| ~ c_in(X0,v_x,t_a) ),
inference(superposition,[status(thm)],[c_1149,c_637]) ).
tcf(c_1162,plain,
! [X0: $i] :
( c_in(X0,v_Y,t_a)
| ~ c_in(X0,v_x,t_a) ),
inference(superposition,[status(thm)],[c_1151,c_637]) ).
tcf(c_1180,plain,
! [X0: $i] :
( 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(superposition,[status(thm)],[c_72,c_1155]) ).
tcf(c_1182,plain,
! [X0: $i] :
( c_lessequals(v_x,X0,iPr_def_10)
| c_in(c_Main_OsubsetI__1(v_x,X0,t_a),v_Z,t_a) ),
inference(light_normalisation,[status(thm)],[c_1180,c_234]) ).
tcf(c_1198,plain,
! [X0: $i] :
( 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(superposition,[status(thm)],[c_72,c_1162]) ).
tcf(c_1200,plain,
! [X0: $i] :
( c_lessequals(v_x,X0,iPr_def_10)
| c_in(c_Main_OsubsetI__1(v_x,X0,t_a),v_Y,t_a) ),
inference(light_normalisation,[status(thm)],[c_1198,c_234]) ).
tcf(c_1215,plain,
! [X0: $i] :
( c_lessequals(v_x,X0,iPr_def_10)
| c_in(c_Main_OsubsetI__1(v_x,X0,t_a),iPr_def_11,t_a)
| ~ c_in(c_Main_OsubsetI__1(v_x,X0,t_a),v_Y,t_a) ),
inference(superposition,[status(thm)],[c_1182,c_659]) ).
tcf(c_1244,plain,
! [X0: $i] :
( c_lessequals(v_x,X0,iPr_def_10)
| c_in(c_Main_OsubsetI__1(v_x,X0,t_a),iPr_def_11,t_a) ),
inference(global_subsumption_just,[status(thm)],[c_1215,c_1200,c_1215]) ).
tcf(c_1251,plain,
( c_lessequals(v_x,iPr_def_11,iPr_def_10)
| c_lessequals(v_x,iPr_def_11,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_1244,c_73]) ).
tcf(c_1254,plain,
c_lessequals(v_x,iPr_def_11,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_1251,c_234]) ).
tcf(c_1255,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1254,c_1153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET831-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 12:10:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.62/1.29 % SZS status Started for theBenchmark.p
% 2.62/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.62/1.29
% 2.62/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.62/1.29
% 2.62/1.29 % ------ iProver source info
% 2.62/1.29
% 2.62/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.62/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.62/1.29 % git: non_committed_changes: false
% 2.62/1.29
% 2.62/1.29 % ------ Parsing...% successful
% 2.62/1.29
% 2.62/1.29
% 2.62/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.62/1.29
% 2.62/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.62/1.29
% 2.62/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.62/1.29
% 2.62/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.62/1.29 % ------ Proving...
% 2.62/1.29 % ------ Problem Properties
% 2.62/1.29
% 2.62/1.29 %
% 2.62/1.29 % clauses 15
% 2.62/1.29 % conjectures 6
% 2.62/1.29 % EPR 6
% 2.62/1.29 % Horn 11
% 2.62/1.29 % unary 2
% 2.62/1.29 % binary 6
% 2.62/1.29 % lits 39
% 2.62/1.29 % lits eq 9
% 2.62/1.29 % fd_pure 0
% 2.62/1.29 % fd_pseudo 0
% 2.62/1.29 % fd_cond 0
% 2.62/1.29 % fd_pseudo_cond 1
% 2.62/1.29 % AC symbols 0
% 2.62/1.29
% 2.62/1.29 % ------ Schedule dynamic 5 is on
% 2.62/1.29
% 2.62/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.62/1.29
% 2.62/1.29
% 2.62/1.29 % ------
% 2.62/1.29 % Current options:
% 2.62/1.29 % ------
% 2.62/1.29
% 2.62/1.29
% 2.62/1.29 %
% 2.62/1.29
% 2.62/1.29 % ------ Proving...
% 2.62/1.29 %
% 2.62/1.29
% 2.62/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.62/1.29
% 2.62/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.62/1.29
% 2.62/1.29
%------------------------------------------------------------------------------