%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET821-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 3.14s 0.87s
% Output : Proof 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 18 unt; 0 def)
% Number of atoms : 95 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 31 ~; 47 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 82 ( 10 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
fof(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c5,plain,
( X0 = X1
| c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f4,axiom,
c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,plain,
c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f8,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f8_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)],[f8]) ).
fof(f8_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)],[f8_nnf]) ).
cnf(c8,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)],[f8_sk]) ).
cnf(p11,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)],[c4,c8]) ).
cnf(p28,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)],[c5,p11]) ).
cnf(f3,axiom,
( c_in(V_a,c_insert(V_b,V_B,T_a),T_a)
| ~ c_in(V_a,V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
fof(f3_nnf,plain,
! [V_a,V_B,T_a,V_b] :
( c_in(V_a,c_insert(V_b,V_B,T_a),T_a)
| ~ c_in(V_a,V_B,T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_a,V_B,T_a,V_b] :
( c_in(V_a,c_insert(V_b,V_B,T_a),T_a)
| ~ c_in(V_a,V_B,T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_in(X0,c_insert(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p30,plain,
( c_in(v_a,c_insert(X1,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| v_c = v_b
| c_in(v_c,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[p28,c3]) ).
cnf(f1,axiom,
( ~ c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
fof(f1_nnf,plain,
! [V_c,V_A,T_a] :
( ~ c_in(V_c,c_uminus(V_A,tc_set(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] :
( ~ c_in(V_c,c_uminus(V_A,tc_set(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_uminus(X1,tc_set(X2)),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p40,plain,
( ~ c_in(v_a,c_uminus(c_insert(X1,c_insert(v_b,X0,tc_IntDef_Oint),tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| v_c = v_b
| c_in(v_c,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[p30,c1]) ).
cnf(p31,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)],[p28,c5]) ).
cnf(p12,plain,
~ c_in(X0,c_uminus(c_insert(X0,X1,X2),tc_set(X2)),X2),
inference(resolution,[status(thm)],[c1,c4]) ).
cnf(p33,plain,
( v_a = v_b
| c_in(v_a,c_uminus(c_insert(v_c,X0,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| v_c = v_b ),
inference(resolution,[status(thm)],[p31,p12]) ).
cnf(p58,plain,
( v_a = v_b
| v_c = v_b
| v_c = v_b
| c_in(v_c,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[p40,p33]) ).
cnf(p59,plain,
( v_a = v_b
| v_c = v_b
| c_in(v_c,X0,tc_IntDef_Oint) ),
inference(factoring,[status(thm)],[p58]) ).
cnf(p63,plain,
( v_a = v_b
| v_c = v_b ),
inference(resolution,[status(thm)],[p59,p12]) ).
cnf(f7,negated_conjecture,
c_less(v_b,v_c,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f7_nnf,plain,
c_less(v_b,v_c,tc_IntDef_Oint),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
c_less(v_b,v_c,tc_IntDef_Oint),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p64,plain,
( c_less(v_b,v_b,tc_IntDef_Oint)
| v_a = v_b ),
inference(superposition,[status(thm)],[p63,c7]) ).
cnf(f0,axiom,
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
fof(f0_nnf,plain,
! [T_a,V_x] :
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [T_a,V_x] :
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ c_less(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(f9,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f9_nnf,plain,
class_Orderings_Oorder(tc_IntDef_Oint),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
class_Orderings_Oorder(tc_IntDef_Oint),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(p10,plain,
~ c_less(X0,X0,tc_IntDef_Oint),
inference(resolution,[status(thm)],[c0,c9]) ).
cnf(p70,plain,
v_a = v_b,
inference(resolution,[status(thm)],[p64,p10]) ).
cnf(f6,negated_conjecture,
c_less(v_a,v_b,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f6_nnf,plain,
c_less(v_a,v_b,tc_IntDef_Oint),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
c_less(v_a,v_b,tc_IntDef_Oint),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(p71,plain,
c_less(v_a,v_a,tc_IntDef_Oint),
inference(superposition,[status(thm)],[p70,c6]) ).
cnf(p79,plain,
$false,
inference(resolution,[status(thm)],[p71,p10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET821-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:05:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.14/0.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.14/0.87 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------