%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET822-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 4.03s 1.03s
% Output : Proof 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 50 unt; 0 def)
% Number of atoms : 78 ( 42 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 104 ( 19 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,negated_conjecture,
( ~ v_P(v_x(V_U,V_V))
| ~ c_in(v_f(V_U),V_V,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5_nnf,plain,
! [V_U,V_V] :
( ~ v_P(v_x(V_U,V_V))
| ~ c_in(v_f(V_U),V_V,tc_IntDef_Oint) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_U,V_V] :
( ~ v_P(v_x(V_U,V_V))
| ~ c_in(v_f(V_U),V_V,tc_IntDef_Oint) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ v_P(v_x(X0,X1))
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t15,plain,
or(not(c_in(v_f(X1),X2,tc_IntDef_Oint)),not(v_P(v_x(X1,X2)))) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t31,plain,
or(not(c_in(v_f(X1),X2,tc_IntDef_Oint)),not(v_P(v_x(X1,X2)))) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t12,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t24,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(f4,negated_conjecture,
( c_in(v_x(V_U,V_V),V_V,tc_IntDef_Oint)
| ~ c_in(v_f(V_U),V_V,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4_nnf,plain,
! [V_U,V_V] :
( c_in(v_x(V_U,V_V),V_V,tc_IntDef_Oint)
| ~ c_in(v_f(V_U),V_V,tc_IntDef_Oint) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_U,V_V] :
( c_in(v_x(V_U,V_V),V_V,tc_IntDef_Oint)
| ~ c_in(v_f(V_U),V_V,tc_IntDef_Oint) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_in(v_x(X0,X1),X1,tc_IntDef_Oint)
| ~ c_in(v_f(X0),X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,negated_conjecture,
ifeq(c_in(v_f(X0),X1,tc_IntDef_Oint),true,c_in(v_x(X0,X1),X1,tc_IntDef_Oint),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f1,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(f1_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)],[f1]) ).
fof(f1_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)],[f1_nnf]) ).
cnf(c1,plain,
c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi0,axiom,
c_in(X0,c_insert(X0,X1,X2),X2) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
c_in(v_x(V0,c_insert(v_f(V0),V1,tc_IntDef_Oint)),c_insert(v_f(V0),V1,tc_IntDef_Oint),tc_IntDef_Oint) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi0]) ).
cnf(f2,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(f2_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)],[f2]) ).
fof(f2_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)],[f2_nnf]) ).
cnf(c2,plain,
( X0 = X1
| c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
ifeq(c_in(X0,c_insert(X1,X2,X3),X3),true,or(c_in(X0,X2,X3),eq(X0,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t20,plain,
or(c_in(v_x(X1,c_insert(v_f(X1),X2,tc_IntDef_Oint)),X2,tc_IntDef_Oint),eq(v_x(X1,c_insert(v_f(X1),X2,tc_IntDef_Oint)),v_f(X1))) = true,
inference(hyper_resolution,[status(thm)],[hi1,h0]) ).
cnf(t30,plain,
or(c_in(v_x(X1,c_insert(v_f(X1),X2,tc_IntDef_Oint)),X2,tc_IntDef_Oint),eq(v_x(X1,c_insert(v_f(X1),X2,tc_IntDef_Oint)),v_f(X1))) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(f0,axiom,
~ c_in(V_a,c_emptyset,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
fof(f0_nnf,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_a,T_a] : ~ c_in(V_a,c_emptyset,T_a),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t8,plain,
c_in(X1,c_emptyset,X2) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t43,plain,
c_in(X1,c_emptyset,X2) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t48,plain,
true = or(false,eq(v_x(X1,c_insert(v_f(X1),c_emptyset,tc_IntDef_Oint)),v_f(X1))),
inference(cp,[status(thm)],[t30,t43]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t22,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t75,plain,
true = eq(v_x(X1,c_insert(v_f(X1),c_emptyset,tc_IntDef_Oint)),v_f(X1)),
inference(step,[status(thm)],[t48,t22]) ).
cnf(t55,plain,
eq(v_x(X1,c_insert(v_f(X1),c_emptyset,tc_IntDef_Oint)),v_f(X1)) = true,
inference(orient,[status(thm)],[t75]) ).
cnf(t56,plain,
v_f(X1) = ifeq(true,true,v_x(X1,c_insert(v_f(X1),c_emptyset,tc_IntDef_Oint)),v_f(X1)),
inference(cp,[status(thm)],[t24,t55]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t23,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t76,plain,
v_f(X1) = v_x(X1,c_insert(v_f(X1),c_emptyset,tc_IntDef_Oint)),
inference(step,[status(thm)],[t56,t23]) ).
cnf(t58,plain,
v_x(X1,c_insert(v_f(X1),c_emptyset,tc_IntDef_Oint)) = v_f(X1),
inference(orient,[status(thm)],[t76]) ).
cnf(t60,plain,
true = or(not(c_in(v_f(X1),c_insert(v_f(X1),c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint)),not(v_P(v_f(X1)))),
inference(cp,[status(thm)],[t31,t58]) ).
cnf(t11,plain,
c_in(X1,c_insert(X1,X2,X3),X3) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t25,plain,
c_in(X1,c_insert(X1,X2,X3),X3) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t77,plain,
true = or(not(true),not(v_P(v_f(X1)))),
inference(step,[status(thm)],[t60,t25]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t51,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t78,plain,
true = or(false,not(v_P(v_f(X1)))),
inference(step,[status(thm)],[t77,t51]) ).
cnf(t79,plain,
true = not(v_P(v_f(X1))),
inference(step,[status(thm)],[t78,t22]) ).
cnf(t61,plain,
not(v_P(v_f(X1))) = true,
inference(orient,[status(thm)],[t79]) ).
cnf(f3,negated_conjecture,
v_P(v_f(v_b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3_nnf,plain,
v_P(v_f(v_b)),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
v_P(v_f(v_b)),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(t7,plain,
v_P(v_f(v_b)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t42,plain,
v_P(v_f(v_b)) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t62,plain,
true = not(true),
inference(cp,[status(thm)],[t61,t42]) ).
cnf(t80,plain,
true = false,
inference(step,[status(thm)],[t62,t51]) ).
cnf(t64,plain,
false = true,
inference(orient,[status(thm)],[t80]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c5]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t64]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET822-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n004.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 12:03:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.03/1.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.03/1.03 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------