%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET821-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 02:44:01 PM UTC 2026
% Result : Unsatisfiable 22.45s 3.26s
% Output : Proof 22.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 21 unt; 0 def)
% Number of atoms : 69 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 21 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 52 ( 6 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f176,axiom,
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f176_nnf,plain,
! [V_a,V_b,V_A,T_a] :
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(nnf_transformation,[status(thm)],[f176]) ).
fof(f176_sk,plain,
! [V_a,V_b,V_A,T_a] :
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
inference(skolemisation,[status(esa)],[f176_nnf]) ).
cnf(c176,plain,
( X0 = X1
| c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(esa)],[f176_sk]) ).
cnf(f175,axiom,
c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f175_nnf,plain,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
inference(nnf_transformation,[status(thm)],[f175]) ).
fof(f175_sk,plain,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
inference(skolemisation,[status(esa)],[f175_nnf]) ).
cnf(c175,plain,
c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(esa)],[f175_sk]) ).
cnf(f1359,negated_conjecture,
( c_in(v_a,V_U,tc_IntDef_Oint)
| ~ c_in(v_b,V_U,tc_IntDef_Oint)
| c_in(v_c,V_U,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1359_nnf,plain,
! [V_U] :
( c_in(v_a,V_U,tc_IntDef_Oint)
| ~ c_in(v_b,V_U,tc_IntDef_Oint)
| c_in(v_c,V_U,tc_IntDef_Oint) ),
inference(nnf_transformation,[status(thm)],[f1359]) ).
fof(f1359_sk,plain,
! [V_U] :
( c_in(v_a,V_U,tc_IntDef_Oint)
| ~ c_in(v_b,V_U,tc_IntDef_Oint)
| c_in(v_c,V_U,tc_IntDef_Oint) ),
inference(skolemisation,[status(esa)],[f1359_nnf]) ).
cnf(c1359,plain,
( c_in(v_a,X0,tc_IntDef_Oint)
| ~ c_in(v_b,X0,tc_IntDef_Oint)
| c_in(v_c,X0,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(esa)],[f1359_sk]) ).
cnf(p369,plain,
( c_in(v_a,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_c,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[c175,c1359]) ).
cnf(p639,plain,
( c_in(v_a,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| v_c = v_b
| c_in(v_c,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[c176,p369]) ).
cnf(p644,plain,
( v_a = v_b
| c_in(v_a,X0,tc_IntDef_Oint)
| v_c = v_b
| c_in(v_c,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[p639,c176]) ).
cnf(f173,axiom,
~ c_in(V_a,c_emptyset,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f173_nnf,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(nnf_transformation,[status(thm)],[f173]) ).
fof(f173_sk,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(skolemisation,[status(esa)],[f173_nnf]) ).
cnf(c173,plain,
~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(esa)],[f173_sk]) ).
cnf(p645,plain,
( v_a = v_b
| c_in(v_a,c_emptyset,tc_IntDef_Oint)
| v_c = v_b ),
inference(resolution,[status(thm)],[p644,c173]) ).
cnf(p659,plain,
( v_a = v_b
| v_c = v_b ),
inference(resolution,[status(thm)],[p645,c173]) ).
cnf(f1358,negated_conjecture,
c_less(v_b,v_c,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1358_nnf,plain,
c_less(v_b,v_c,tc_IntDef_Oint),
inference(nnf_transformation,[status(thm)],[f1358]) ).
cnf(c1358,plain,
c_less(v_b,v_c,tc_IntDef_Oint),
inference(cnf_transformation,[status(esa)],[f1358_nnf]) ).
cnf(p660,plain,
( c_less(v_b,v_b,tc_IntDef_Oint)
| v_a = v_b ),
inference(superposition,[status(thm)],[p659,c1358]) ).
cnf(f122,axiom,
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
fof(f122_nnf,plain,
! [T_a,V_x] :
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f122]) ).
fof(f122_sk,plain,
! [T_a,V_x] :
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f122_nnf]) ).
cnf(c122,plain,
( ~ c_less(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f122_sk]) ).
cnf(f351,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f351_nnf,plain,
class_Orderings_Oorder(tc_IntDef_Oint),
inference(nnf_transformation,[status(thm)],[f351]) ).
cnf(c351,plain,
class_Orderings_Oorder(tc_IntDef_Oint),
inference(cnf_transformation,[status(esa)],[f351_nnf]) ).
cnf(p367,plain,
~ c_less(X0,X0,tc_IntDef_Oint),
inference(resolution,[status(thm)],[c122,c351]) ).
cnf(p668,plain,
v_a = v_b,
inference(resolution,[status(thm)],[p660,p367]) ).
cnf(f1357,negated_conjecture,
c_less(v_a,v_b,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1357_nnf,plain,
c_less(v_a,v_b,tc_IntDef_Oint),
inference(nnf_transformation,[status(thm)],[f1357]) ).
cnf(c1357,plain,
c_less(v_a,v_b,tc_IntDef_Oint),
inference(cnf_transformation,[status(esa)],[f1357_nnf]) ).
cnf(p669,plain,
c_less(v_a,v_a,tc_IntDef_Oint),
inference(superposition,[status(thm)],[p668,c1357]) ).
cnf(p681,plain,
$false,
inference(resolution,[status(thm)],[p669,p367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET821-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n017.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 11:59:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.45/3.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.45/3.26 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------