%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET834-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 02:44:04 PM UTC 2026
% Result : Unsatisfiable 7.49s 1.71s
% Output : Proof 7.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 17 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 89 ( 42 ~; 47 |; 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 : 114 ( 8 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,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(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f1,axiom,
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_1) ).
fof(f1_nnf,plain,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_in(X0,c_union(X1,X3,X2),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p60,plain,
( c_in(c_Main_OsubsetI__1(X0,X1,X2),c_union(X0,X3,X2),X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(f5,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(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c5,plain,
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p135,plain,
( c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2))
| c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2)) ),
inference(resolution,[status(thm)],[p60,c5]) ).
cnf(p403,plain,
c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2)),
inference(factoring,[status(thm)],[p135]) ).
cnf(f0,axiom,
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnCI_0) ).
fof(f0_nnf,plain,
! [V_c,V_B,T_a,V_A] :
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_c,V_B,T_a,V_A] :
( c_in(V_c,c_union(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_B,T_a) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( c_in(X0,c_union(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p59,plain,
( c_in(c_Main_OsubsetI__1(X0,X1,X2),c_union(X3,X0,X2),X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(p119,plain,
( c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2))
| c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)) ),
inference(resolution,[status(thm)],[p59,c5]) ).
cnf(p298,plain,
c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)),
inference(factoring,[status(thm)],[p119]) ).
cnf(f9,negated_conjecture,
( ~ c_lessequals(v_Y,V_U,tc_set(t_a))
| ~ c_lessequals(v_Z,V_U,tc_set(t_a))
| c_lessequals(v_X,V_U,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f9_nnf,plain,
! [V_U] :
( ~ c_lessequals(v_Y,V_U,tc_set(t_a))
| ~ c_lessequals(v_Z,V_U,tc_set(t_a))
| c_lessequals(v_X,V_U,tc_set(t_a)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_U] :
( ~ c_lessequals(v_Y,V_U,tc_set(t_a))
| ~ c_lessequals(v_Z,V_U,tc_set(t_a))
| c_lessequals(v_X,V_U,tc_set(t_a)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ c_lessequals(v_Y,X0,tc_set(t_a))
| ~ c_lessequals(v_Z,X0,tc_set(t_a))
| c_lessequals(v_X,X0,tc_set(t_a)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p971,plain,
( ~ c_lessequals(v_Y,c_union(X0,v_Z,t_a),tc_set(t_a))
| c_lessequals(v_X,c_union(X0,v_Z,t_a),tc_set(t_a)) ),
inference(resolution,[status(thm)],[p298,c9]) ).
cnf(p1021,plain,
c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a)),
inference(resolution,[status(thm)],[p403,p971]) ).
cnf(f3,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(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c3,plain,
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f6,negated_conjecture,
c_in(v_x,v_X,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f6_nnf,plain,
c_in(v_x,v_X,t_a),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
c_in(v_x,v_X,t_a),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(p37,plain,
( c_in(v_x,X0,t_a)
| ~ c_lessequals(v_X,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c3,c6]) ).
cnf(p1022,plain,
c_in(v_x,c_union(v_Y,v_Z,t_a),t_a),
inference(resolution,[status(thm)],[p1021,p37]) ).
cnf(f2,axiom,
( c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
fof(f2_nnf,plain,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_A,T_a)
| c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_union(V_A,V_B,T_a),T_a) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_in(X0,X1,X3)
| c_in(X0,X2,X3)
| ~ c_in(X0,c_union(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p1029,plain,
( c_in(v_x,v_Y,t_a)
| c_in(v_x,v_Z,t_a) ),
inference(resolution,[status(thm)],[p1022,c2]) ).
cnf(f8,negated_conjecture,
~ c_in(v_x,v_Y,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f8_nnf,plain,
~ c_in(v_x,v_Y,t_a),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ c_in(v_x,v_Y,t_a),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ c_in(v_x,v_Y,t_a),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p1031,plain,
c_in(v_x,v_Z,t_a),
inference(resolution,[status(thm)],[p1029,c8]) ).
cnf(f7,negated_conjecture,
~ c_in(v_x,v_Z,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f7_nnf,plain,
~ c_in(v_x,v_Z,t_a),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ c_in(v_x,v_Z,t_a),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ c_in(v_x,v_Z,t_a),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p1032,plain,
$false,
inference(resolution,[status(thm)],[p1031,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET834-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 12:12:42 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.49/1.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.49/1.71 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------