%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT276-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 01:56:35 PM UTC 2026
% Result : Unsatisfiable 4.62s 21.51s
% Output : Proof 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 80 ( 19 unt; 0 def)
% Number of atoms : 185 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 185 ( 80 ~; 105 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 53 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f11,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
fof(f11_nnf,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(f8,axiom,
( c_in(v_sko__4mP(V_L,V_S,v_r),V_S,t_a)
| c_in(c_Pair(c_Tarski_Olub(V_S,v_cl,t_a),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(V_L,v_A,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL_haf29b7e1c35a7201) ).
fof(f8_nnf,plain,
! [V_L,V_S] :
( c_in(v_sko__4mP(V_L,V_S,v_r),V_S,t_a)
| c_in(c_Pair(c_Tarski_Olub(V_S,v_cl,t_a),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(V_L,v_A,t_a) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V_L,V_S] :
( c_in(v_sko__4mP(V_L,V_S,v_r),V_S,t_a)
| c_in(c_Pair(c_Tarski_Olub(V_S,v_cl,t_a),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(V_L,v_A,t_a) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( c_in(v_sko__4mP(X0,X1,v_r),X1,t_a)
| c_in(c_Pair(c_Tarski_Olub(X1,v_cl,t_a),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,v_A,tc_set(t_a))
| ~ c_in(X0,v_A,t_a) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f7,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
fof(f7_nnf,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(f2,negated_conjecture,
( c_in(v_xa,v_S,t_a)
| c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f2_nnf,plain,
( c_in(v_xa,v_S,t_a)
| c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( c_in(v_xa,v_S,t_a)
| c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_in(v_xa,v_S,t_a)
| c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p12,plain,
( c_in(v_xa,v_S,t_a)
| c_in(v_xa,v_A,t_a) ),
inference(superposition,[status(thm)],[c7,c2]) ).
cnf(p19,plain,
( c_in(v_xa,v_S,t_a)
| c_in(v_sko__4mP(v_xa,X0,v_r),X0,t_a)
| c_in(c_Pair(c_Tarski_Olub(X0,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X0,v_A,tc_set(t_a)) ),
inference(resolution,[status(thm)],[c8,p12]) ).
cnf(f0,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p20,plain,
( c_in(v_xa,v_S,t_a)
| c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[p19,c0]) ).
cnf(f3,negated_conjecture,
( c_in(v_xa,v_S,t_a)
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f3_nnf,plain,
( c_in(v_xa,v_S,t_a)
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
( c_in(v_xa,v_S,t_a)
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_in(v_xa,v_S,t_a)
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p13,plain,
( c_in(v_xa,v_S,t_a)
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c11,c3]) ).
cnf(p22,plain,
( c_in(v_xa,v_S,t_a)
| c_in(v_xa,v_S,t_a)
| c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p20,p13]) ).
cnf(p25,plain,
( c_in(v_xa,v_S,t_a)
| c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
inference(factoring,[status(thm)],[p22]) ).
cnf(f5,negated_conjecture,
( c_in(v_xa,v_S,t_a)
| ~ c_in(V_U,v_S,t_a)
| c_in(c_Pair(V_U,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_9) ).
fof(f5_nnf,plain,
! [V_U] :
( c_in(v_xa,v_S,t_a)
| ~ c_in(V_U,v_S,t_a)
| c_in(c_Pair(V_U,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_U] :
( c_in(v_xa,v_S,t_a)
| ~ c_in(V_U,v_S,t_a)
| c_in(c_Pair(V_U,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_in(v_xa,v_S,t_a)
| ~ c_in(X0,v_S,t_a)
| c_in(c_Pair(X0,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p26,plain,
( c_in(v_xa,v_S,t_a)
| c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ),
inference(resolution,[status(thm)],[p25,c5]) ).
cnf(p37,plain,
( c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ),
inference(factoring,[status(thm)],[p26]) ).
cnf(p38,plain,
( c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ),
inference(superposition,[status(thm)],[c11,p37]) ).
cnf(f9,axiom,
( c_in(c_Pair(c_Tarski_Olub(V_S,v_cl,t_a),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mP(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_L,v_A,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL_haf29b6e1c35a704e) ).
fof(f9_nnf,plain,
! [V_L,V_S] :
( c_in(c_Pair(c_Tarski_Olub(V_S,v_cl,t_a),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mP(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_L,v_A,t_a) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_L,V_S] :
( c_in(c_Pair(c_Tarski_Olub(V_S,v_cl,t_a),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mP(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_L,v_A,t_a) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( c_in(c_Pair(c_Tarski_Olub(X1,v_cl,t_a),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,v_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mP(X0,X1,v_r),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X0,v_A,t_a) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p24,plain,
( c_in(v_xa,v_S,t_a)
| c_in(c_Pair(c_Tarski_Olub(X0,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X0,v_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mP(v_xa,X0,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[c9,p12]) ).
cnf(p41,plain,
( c_in(v_xa,v_S,t_a)
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| c_in(v_xa,v_S,t_a) ),
inference(resolution,[status(thm)],[p38,p24]) ).
cnf(p45,plain,
( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| c_in(v_xa,v_S,t_a) ),
inference(factoring,[status(thm)],[p41]) ).
cnf(p46,plain,
( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ),
inference(resolution,[status(thm)],[p45,c0]) ).
cnf(p48,plain,
( c_in(v_xa,v_S,t_a)
| c_in(v_xa,v_S,t_a) ),
inference(resolution,[status(thm)],[p46,p13]) ).
cnf(p50,plain,
c_in(v_xa,v_S,t_a),
inference(factoring,[status(thm)],[p48]) ).
cnf(f6,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c6,plain,
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p52,plain,
( c_in(v_xa,X0,t_a)
| ~ c_lessequals(v_S,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p50,c6]) ).
cnf(p54,plain,
c_in(v_xa,v_A,t_a),
inference(resolution,[status(thm)],[p52,c0]) ).
cnf(p57,plain,
( c_in(v_sko__4mP(v_xa,X0,v_r),X0,t_a)
| c_in(c_Pair(c_Tarski_Olub(X0,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X0,v_A,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p54,c8]) ).
cnf(p66,plain,
( c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[p57,c0]) ).
cnf(f4,negated_conjecture,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f4_nnf,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p14,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c11,c4]) ).
cnf(p68,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[p66,p14]) ).
cnf(p69,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
inference(superposition,[status(thm)],[c11,p68]) ).
cnf(f10,axiom,
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(V_x,V_S,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax_hfa5c3afdd2c155f8) ).
fof(f10_nnf,plain,
! [V_x,V_S] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(V_x,V_S,t_a) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [V_x,V_S] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(V_x,V_S,t_a) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( c_in(c_Pair(X0,c_Tarski_Olub(X1,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,v_A,tc_set(t_a))
| ~ c_in(X0,X1,t_a) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p53,plain,
( c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,v_A,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p50,c10]) ).
cnf(p60,plain,
c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[p53,c0]) ).
cnf(p70,plain,
c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a),
inference(resolution,[status(thm)],[p69,p60]) ).
cnf(f1,negated_conjecture,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(V_V,v_S,t_a)
| c_in(c_Pair(V_V,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_10) ).
fof(f1_nnf,plain,
! [V_V] :
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(V_V,v_S,t_a)
| c_in(c_Pair(V_V,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_V] :
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(V_V,v_S,t_a)
| c_in(c_Pair(V_V,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(X0,v_S,t_a)
| c_in(c_Pair(X0,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p71,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[p70,c1]) ).
cnf(p79,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c11,p71]) ).
cnf(p84,plain,
c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[p79,p60]) ).
cnf(p85,plain,
c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(superposition,[status(thm)],[c11,p84]) ).
cnf(p58,plain,
( c_in(c_Pair(c_Tarski_Olub(X0,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X0,v_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mP(v_xa,X0,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[p54,c9]) ).
cnf(p88,plain,
( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,v_A,tc_set(t_a)) ),
inference(resolution,[status(thm)],[p85,p58]) ).
cnf(p89,plain,
c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[p88,c0]) ).
cnf(p91,plain,
~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(resolution,[status(thm)],[p89,p14]) ).
cnf(p92,plain,
~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(superposition,[status(thm)],[c11,p91]) ).
cnf(p93,plain,
$false,
inference(resolution,[status(thm)],[p92,p60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT276-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/20.61 % Computer : n010.cluster.edu
% 0.08/20.61 % Model : x86_64 x86_64
% 0.08/20.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/20.61 % Memory : 8046.5625MB
% 0.08/20.61 % OS : Linux 6.8.0-71-generic
% 0.08/20.61 % CPULimit : 300
% 0.08/20.61 % WCLimit : 300
% 0.08/20.61 % DateTime : Wed Sep 23 20:47:34 UTC 2026
% 0.08/20.61 % CPUTime :
% 0.08/20.61 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.62/21.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.62/21.51 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------