%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET842-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:44:06 PM UTC 2026
% Result : Unsatisfiable 4.49s 1.08s
% Output : Proof 4.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 6 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 66 ( 29 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 81 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
( c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a)
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f3_nnf,plain,
! [V_A,V_C,T_a] :
( c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a)
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_A,V_C,T_a] :
( c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a)
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_in(X0,c_Main_OUnionE__1(X0,X1,X2),X2)
| ~ c_in(X0,c_Union(X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
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_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
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_A,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_A,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),X0,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p11,plain,
( c_lessequals(c_Union(X0,X1),X2,tc_set(X1))
| c_in(c_Main_OsubsetI__1(c_Union(X0,X1),X2,X1),c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(X0,X1),X2,X1),X0,X1),X1) ),
inference(resolution,[status(thm)],[c3,c5]) ).
cnf(f4,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(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,plain,
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p19,plain,
( c_in(c_Main_OsubsetI__1(c_Union(X0,X1),X2,X1),X3,X1)
| ~ c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(X0,X1),X2,X1),X0,X1),X3,tc_set(X1))
| c_lessequals(c_Union(X0,X1),X2,tc_set(X1)) ),
inference(resolution,[status(thm)],[p11,c4]) ).
cnf(f2,axiom,
( c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f2_nnf,plain,
! [V_A,V_C,T_a] :
( c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_A,V_C,T_a] :
( c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_in(c_Main_OUnionE__1(X0,X1,X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p8,plain,
( c_lessequals(c_Union(X0,X1),X2,tc_set(X1))
| c_in(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(X0,X1),X2,X1),X0,X1),X0,tc_set(X1)) ),
inference(resolution,[status(thm)],[c2,c5]) ).
cnf(f1,negated_conjecture,
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f1_nnf,plain,
! [V_U] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a))) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_U] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a))) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p15,plain,
( c_lessequals(c_Main_OUnionE__1(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X0,tc_set(t_a)),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p8,c1]) ).
cnf(p35,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X0,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p19,p15]) ).
cnf(p36,plain,
( c_in(c_Main_OsubsetI__1(c_Union(v_Y,tc_set(t_a)),X0,tc_set(t_a)),v_m,tc_set(t_a))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(factoring,[status(thm)],[p35]) ).
cnf(f6,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(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c6,plain,
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p37,plain,
( c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[p36,c6]) ).
cnf(p39,plain,
c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(factoring,[status(thm)],[p37]) ).
cnf(f0,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f0_nnf,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p40,plain,
$false,
inference(resolution,[status(thm)],[p39,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET842-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:10:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.49/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.49/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------