%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET831-1 : 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 : n007.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 43.00s 7.85s
% Output : CNFRefutation 43.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 120 ( 16 unt; 2 def)
% Number of atoms : 500 ( 51 equ)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 287 ( 113 ~; 174 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 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 : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 140 ( 0 sgn 140 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
fof(f200,axiom,
! [X2,X0,X1] :
( c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax',cls_Set_OComplI_0) ).
fof(f207,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X2,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax',cls_Set_OIntE_0) ).
fof(f208,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X1,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax',cls_Set_OIntE_1) ).
fof(f209,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/Axioms/MSC001-2.ax',cls_Set_OIntI_0) ).
fof(f341,axiom,
! [X2,X3,X0,X1,X4,X5] :
( c_in(X3,c_Relation_OImage(X5,X1,X2,X4),X4)
| ~ c_in(c_Pair(X0,X3,X2,X4),X5,tc_prod(X2,X4))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Relation_OImageI_0) ).
fof(f368,axiom,
! [X0,X1] : c_in(X0,c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OUNIV__I_0) ).
fof(f378,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/Axioms/MSC001-0.ax',cls_Set_OsubsetD_0) ).
fof(f379,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/Axioms/MSC001-0.ax',cls_Set_OsubsetI_0) ).
fof(f380,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/Axioms/MSC001-0.ax',cls_Set_OsubsetI_1) ).
fof(f381,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/Axioms/MSC001-0.ax',cls_Set_Osubset__antisym_0) ).
fof(f382,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(reorient_equations,[],[f381]) ).
fof(f1434,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(f1435,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(f1436,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(f1437,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(f1438,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(f1439,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) ).
tcf(c_1564,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,X1,X2)
| c_in(X0,c_uminus(X1,tc_set(X2)),X2) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_1571,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,[],[f207]) ).
tcf(c_1572,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,[],[f208]) ).
tcf(c_1573,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,[],[f209]) ).
tcf(c_1681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_in(X1,c_Relation_OImage(X4,X5,X2,X3),X3)
| ~ c_in(X0,X5,X2)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[],[f341]) ).
tcf(c_1705,plain,
! [X0: $i,X1: $i] : c_in(X0,c_UNIV,X1),
inference(cnf_transformation,[],[f368]) ).
tcf(c_1715,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,[],[f378]) ).
tcf(c_1716,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,[],[f379]) ).
tcf(c_1717,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,[],[f380]) ).
tcf(c_1718,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,[],[f382]) ).
tcf(c_2003,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,[],[f1434]) ).
tcf(c_2004,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,[],[f1435]) ).
tcf(c_2005,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,[],[f1436]) ).
tcf(c_2006,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,[],[f1437]) ).
tcf(c_2007,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,[],[f1438]) ).
tcf(c_2008,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,[],[f1439]) ).
tcf(c_13564,definition,
iPr_def_10 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_13565,definition,
iPr_def_11 = c_inter(v_Y,v_Z,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_13566,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_2008,c_13565,c_13564]) ).
tcf(c_13567,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_2007]) ).
tcf(c_13568,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_2006]) ).
tcf(c_13569,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_2005]) ).
tcf(c_13570,negated_conjecture,
( c_lessequals(v_X,v_Z,iPr_def_10)
| ( iPr_def_11 = v_X ) ),
inference(demodulation,[status(thm)],[c_2004]) ).
tcf(c_13571,negated_conjecture,
( c_lessequals(v_X,v_Y,iPr_def_10)
| ( iPr_def_11 = v_X ) ),
inference(demodulation,[status(thm)],[c_2003]) ).
tcf(c_19388,plain,
! [X0: $i] :
( c_in(X0,v_Z,t_a)
| ~ c_in(X0,iPr_def_11,t_a) ),
inference(superposition,[status(thm)],[c_13565,c_1571]) ).
tcf(c_19400,plain,
! [X0: $i] :
( c_in(X0,v_Y,t_a)
| ~ c_in(X0,iPr_def_11,t_a) ),
inference(superposition,[status(thm)],[c_13565,c_1572]) ).
tcf(c_19478,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_1716,c_19400]) ).
tcf(c_19479,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_1716,c_19388]) ).
tcf(c_19480,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_19479,c_13564]) ).
tcf(c_19483,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_19478,c_13564]) ).
tcf(c_19704,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_19483,c_1717]) ).
tcf(c_19705,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_19480,c_1717]) ).
tcf(c_19707,plain,
c_lessequals(iPr_def_11,v_Z,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_19705,c_13564]) ).
tcf(c_19708,plain,
c_lessequals(iPr_def_11,v_Y,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_19704,c_13564]) ).
tcf(c_19732,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_19708,c_13566]) ).
tcf(c_19734,plain,
( c_lessequals(iPr_def_11,v_X,iPr_def_10)
| ( v_X = iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19732,c_19707]) ).
tcf(c_20750,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_13564,c_1715]) ).
tcf(c_21061,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_13564,c_1718]) ).
tcf(c_21066,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_21061,c_13564]) ).
tcf(c_21287,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_13571,c_20750]) ).
tcf(c_21289,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_13570,c_20750]) ).
tcf(c_21294,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_19734,c_20750]) ).
tcf(c_21324,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_1716,c_21287]) ).
tcf(c_21325,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_21324,c_13564]) ).
tcf(c_21336,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_1716,c_21289]) ).
tcf(c_21337,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_21336,c_13564]) ).
tcf(c_21497,plain,
( ( v_X = iPr_def_11 )
| ~ c_lessequals(v_X,iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_19734,c_21066]) ).
tcf(c_22007,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_13565,c_1573]) ).
tcf(c_27953,plain,
! [X0: $i,X1: $i] :
( c_in(X0,X1,t_a)
| c_in(X0,c_uminus(X1,iPr_def_10),t_a) ),
inference(superposition,[status(thm)],[c_13564,c_1564]) ).
tcf(c_28273,plain,
! [X0: $i] :
( c_in(X0,v_Z,t_a)
| ~ c_in(X0,iPr_def_11,t_a) ),
inference(superposition,[status(thm)],[c_13565,c_1571]) ).
tcf(c_28454,plain,
! [X0: $i] :
( c_in(X0,v_Y,t_a)
| ~ c_in(X0,iPr_def_11,t_a) ),
inference(superposition,[status(thm)],[c_13565,c_1572]) ).
tcf(c_28531,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_1716,c_28454]) ).
tcf(c_28532,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_1716,c_28273]) ).
tcf(c_28533,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_28532,c_13564]) ).
tcf(c_28536,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_28531,c_13564]) ).
tcf(c_29354,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,c_uminus(X1,iPr_def_10),tc_set(t_a))
| c_in(c_Main_OsubsetI__1(X0,c_uminus(X1,iPr_def_10),t_a),X1,t_a) ),
inference(superposition,[status(thm)],[c_27953,c_1717]) ).
tcf(c_29355,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_28536,c_1717]) ).
tcf(c_29356,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_28533,c_1717]) ).
tcf(c_29358,plain,
c_lessequals(iPr_def_11,v_Z,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_29356,c_13564]) ).
tcf(c_29359,plain,
c_lessequals(iPr_def_11,v_Y,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_29355,c_13564]) ).
tcf(c_29360,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,c_uminus(X1,iPr_def_10),iPr_def_10)
| c_in(c_Main_OsubsetI__1(X0,c_uminus(X1,iPr_def_10),t_a),X1,t_a) ),
inference(light_normalisation,[status(thm)],[c_29354,c_13564]) ).
tcf(c_29740,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_29359,c_13566]) ).
tcf(c_29742,plain,
( c_lessequals(iPr_def_11,v_X,iPr_def_10)
| ( v_X = iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29740,c_29358]) ).
tcf(c_35550,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_13564,c_1715]) ).
tcf(c_37836,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_29742,c_35550]) ).
tcf(c_38898,plain,
! [X0: $i] :
( c_lessequals(X0,c_uminus(iPr_def_11,iPr_def_10),iPr_def_10)
| c_in(c_Main_OsubsetI__1(X0,c_uminus(iPr_def_11,iPr_def_10),t_a),v_X,t_a)
| ( v_X = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_29360,c_37836]) ).
tcf(c_40070,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_13565,c_1573]) ).
tcf(c_54676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(X3,c_Relation_OImage(c_UNIV,X1,X2,X4),X4)
| ~ c_in(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1705,c_1681]) ).
tcf(c_55072,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_21337,c_22007]) ).
tcf(c_56362,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_55072,c_21325,c_55072]) ).
tcf(c_56377,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_56362,c_1717]) ).
tcf(c_56379,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_56362,c_21294]) ).
tcf(c_56382,plain,
( c_lessequals(v_X,iPr_def_11,iPr_def_10)
| ( v_X = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_56377,c_13564]) ).
tcf(c_56389,plain,
v_X = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_56379,c_21497,c_56382]) ).
tcf(c_56438,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_13569,c_56389]) ).
tcf(c_56439,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_13568,c_56389]) ).
tcf(c_56443,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_56439]) ).
tcf(c_56444,plain,
c_lessequals(v_x,v_Z,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_56443,c_19707,c_19708]) ).
tcf(c_56445,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_56438]) ).
tcf(c_56446,plain,
c_lessequals(v_x,v_Y,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_56445,c_19707,c_19708]) ).
tcf(c_56450,plain,
! [X0: $i] :
( c_in(X0,v_Z,t_a)
| ~ c_in(X0,v_x,t_a) ),
inference(superposition,[status(thm)],[c_56444,c_20750]) ).
tcf(c_56461,plain,
! [X0: $i] :
( c_in(X0,v_Y,t_a)
| ~ c_in(X0,v_x,t_a) ),
inference(superposition,[status(thm)],[c_56446,c_20750]) ).
tcf(c_56537,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_1716,c_56450]) ).
tcf(c_56541,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_56537,c_13564]) ).
tcf(c_56582,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_1716,c_56461]) ).
tcf(c_56586,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_56582,c_13564]) ).
tcf(c_56615,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_56541,c_22007]) ).
tcf(c_70557,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,c_uminus(iPr_def_11,iPr_def_10),iPr_def_10)
| c_in(X0,c_Relation_OImage(c_UNIV,v_X,t_a,X1),X1)
| ( v_X = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_38898,c_54676]) ).
tcf(c_71949,plain,
v_X = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_70557,c_56389]) ).
tcf(c_71966,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_13567,c_71949]) ).
tcf(c_71968,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_13568,c_71949]) ).
tcf(c_71972,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_71968]) ).
tcf(c_71973,plain,
c_lessequals(v_x,v_Z,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_71972,c_29358,c_29359]) ).
tcf(c_71976,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_71966]) ).
tcf(c_71977,plain,
~ c_lessequals(v_x,iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_71976,c_29358,c_29359]) ).
tcf(c_71979,plain,
! [X0: $i] :
( c_in(X0,v_Z,t_a)
| ~ c_in(X0,v_x,t_a) ),
inference(superposition,[status(thm)],[c_71973,c_35550]) ).
tcf(c_72724,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_1716,c_71979]) ).
tcf(c_72726,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_72724,c_13564]) ).
tcf(c_104310,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_72726,c_40070]) ).
tcf(c_104442,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_104310,c_56586,c_56615]) ).
tcf(c_104450,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_104442,c_1717]) ).
tcf(c_104454,plain,
c_lessequals(v_x,iPr_def_11,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_104450,c_13564]) ).
tcf(c_104455,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_104454,c_71977]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET831-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:04:22 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 43.00/7.85 % SZS status Started for theBenchmark.p
% 43.00/7.85 % SZS status Unsatisfiable for theBenchmark.p
% 43.00/7.85
% 43.00/7.85 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 43.00/7.85
% 43.00/7.85 % ------ iProver source info
% 43.00/7.85
% 43.00/7.85 % git: date: 2026-07-19 20:42:38 +0200
% 43.00/7.85 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 43.00/7.85 % git: non_committed_changes: false
% 43.00/7.85
% 43.00/7.85 % ------ Parsing...% successful
% 43.00/7.85
% 43.00/7.85
% 43.00/7.85 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 43.00/7.85
% 43.00/7.85 % ------ Preprocessing... sup_sim: 1 sf_s rm: 18 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 0 sf_s rm: 30 0s sf_e pe_s pe_e %
% 43.00/7.85
% 43.00/7.85 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 43.00/7.85
% 43.00/7.85 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 43.00/7.85 % ------ Proving...
% 43.00/7.85 % ------ Problem Properties
% 43.00/7.85
% 43.00/7.85 %
% 43.00/7.85 % clauses 303
% 43.00/7.85 % conjectures 6
% 43.00/7.85 % EPR 32
% 43.00/7.85 % Horn 273
% 43.00/7.85 % unary 77
% 43.00/7.85 % binary 175
% 43.00/7.85 % lits 584
% 43.00/7.85 % lits eq 170
% 43.00/7.85 % fd_pure 0
% 43.00/7.85 % fd_pseudo 0
% 43.00/7.85 % fd_cond 21
% 43.00/7.85 % fd_pseudo_cond 40
% 43.00/7.85 % AC symbols 0
% 43.00/7.85
% 43.00/7.85 % ------ Schedule dynamic 5 is on
% 43.00/7.85
% 43.00/7.85 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 43.00/7.85
% 43.00/7.85
% 43.00/7.85 % ------
% 43.00/7.85 % Current options:
% 43.00/7.85 % ------
% 43.00/7.85
% 43.00/7.85
% 43.00/7.85 %
% 43.00/7.85
% 43.00/7.85 % ------ Proving...
% 43.00/7.85 %
% 43.00/7.85
% 43.00/7.85 % SZS status Unsatisfiable for theBenchmark.p
% 43.00/7.85
% 43.00/7.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 43.00/7.86
% 43.00/7.86
%------------------------------------------------------------------------------