%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT268-2 : 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 01:56:32 PM UTC 2026
% Result : Unsatisfiable 4.15s 0.94s
% Output : Proof 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 71 unt; 0 def)
% Number of atoms : 91 ( 54 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 42 ( 26 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-4 aty)
% Number of variables : 64 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( c_in(c_Pair(V_x,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_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_x,V_S,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
fof(f4_nnf,plain,
! [V_x,V_S,T_a,V_cl] :
( c_in(c_Pair(V_x,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_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_x,V_S,T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_x,V_S,T_a,V_cl] :
( c_in(c_Pair(V_x,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_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_x,V_S,T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_in(c_Pair(X0,c_Tarski_Olub(X1,X3,X2),X2,X2),c_Tarski_Opotype_Oorder(X3,X2,tc_Product__Type_Ounit),tc_prod(X2,X2))
| ~ c_lessequals(X1,c_Tarski_Opotype_Opset(X3,X2,tc_Product__Type_Ounit),tc_set(X2))
| ~ c_in(X3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit))
| ~ c_in(X3,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t10,plain,
ifeq(c_in(X1,X2,X3),true,ifeq(c_in(X4,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_in(X4,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_lessequals(X2,c_Tarski_Opotype_Opset(X4,X3,tc_Product__Type_Ounit),tc_set(X3)),true,c_in(c_Pair(X1,c_Tarski_Olub(X2,X4,X3),X3,X3),c_Tarski_Opotype_Oorder(X4,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t19,plain,
ifeq(c_in(X1,X2,X3),true,ifeq(c_in(X4,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_in(X4,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_lessequals(X2,c_Tarski_Opotype_Opset(X4,X3,tc_Product__Type_Ounit),tc_set(X3)),true,c_in(c_Pair(X1,c_Tarski_Olub(X2,X4,X3),X3,X3),c_Tarski_Opotype_Oorder(X4,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true),true),true),true) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(f1,negated_conjecture,
c_in(v_x,v_S,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
c_in(v_x,v_S,t_a),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
c_in(v_x,v_S,t_a),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(t2,plain,
c_in(v_x,v_S,t_a) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t18,plain,
c_in(v_x,v_S,t_a) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t20,plain,
true = ifeq(true,true,ifeq(c_in(X1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X1,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X1,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X1,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),true),
inference(cp,[status(thm)],[t19,t18]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t88,plain,
true = ifeq(c_in(X1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X1,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X1,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X1,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true),true),true),
inference(step,[status(thm)],[t20,t15]) ).
cnf(t13,axiom,
sFlat2 = tc_prod(t_a,t_a),
introduced(definition) ).
cnf(t29,plain,
tc_prod(t_a,t_a) = sFlat2,
inference(orient,[status(thm)],[t13]) ).
cnf(t89,plain,
true = ifeq(c_in(X1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X1,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X1,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X1,t_a,tc_Product__Type_Ounit),sFlat2),true),true),true),
inference(step,[status(thm)],[t88,t29]) ).
cnf(t61,plain,
ifeq(c_in(X1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(X1,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,X1,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(X1,t_a,tc_Product__Type_Ounit),sFlat2),true),true),true) = true,
inference(orient,[status(thm)],[t89]) ).
cnf(f6,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
fof(f6_nnf,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(t5,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t16,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t62,plain,
true = ifeq(true,true,ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),true),true),true),
inference(cp,[status(thm)],[t61,t16]) ).
cnf(t90,plain,
true = ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),true,ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),true),true),
inference(step,[status(thm)],[t62,t15]) ).
cnf(f7,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
fof(f7_nnf,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(t6,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t17,plain,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t91,plain,
true = ifeq(true,true,ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),true),true),
inference(step,[status(thm)],[t90,t17]) ).
cnf(t92,plain,
true = ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),true),
inference(step,[status(thm)],[t91,t15]) ).
cnf(f9,axiom,
c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
fof(f9_nnf,plain,
! [V_cl,T_a] : c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [V_cl,T_a] : c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(X0,X1),X1,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X0,X1,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t8,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(X1,X2),X2,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t41,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(X1,X2),X2,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),
inference(orient,[status(thm)],[t8]) ).
cnf(t93,plain,
true = ifeq(c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),true),
inference(step,[status(thm)],[t92,t41]) ).
cnf(f3,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(f3_nnf,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(t1,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t43,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(orient,[status(thm)],[t1]) ).
cnf(t94,plain,
true = ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),true),
inference(step,[status(thm)],[t93,t43]) ).
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(t3,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t26,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t95,plain,
true = ifeq(true,true,c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),true),
inference(step,[status(thm)],[t94,t26]) ).
cnf(t96,plain,
true = c_in(c_Pair(v_x,c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),
inference(step,[status(thm)],[t95,t15]) ).
cnf(f8,axiom,
c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
fof(f8_nnf,plain,
! [V_S,V_cl,T_a] : c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V_S,V_cl,T_a] : c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
c_Tarski_Oglb(X0,X1,X2) = c_Tarski_Olub(X0,c_Tarski_Odual(X1,X2),X2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t7,plain,
c_Tarski_Olub(X1,c_Tarski_Odual(X2,X3),X3) = c_Tarski_Oglb(X1,X2,X3),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t37,plain,
c_Tarski_Olub(X1,c_Tarski_Odual(X2,X3),X3) = c_Tarski_Oglb(X1,X2,X3),
inference(orient,[status(thm)],[t7]) ).
cnf(t97,plain,
true = c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),
inference(step,[status(thm)],[t96,t37]) ).
cnf(t11,axiom,
sFlat0 = c_Tarski_Oglb(v_S,v_cl,t_a),
introduced(definition) ).
cnf(t39,plain,
c_Tarski_Oglb(v_S,v_cl,t_a) = sFlat0,
inference(orient,[status(thm)],[t11]) ).
cnf(t98,plain,
true = c_in(c_Pair(v_x,sFlat0,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),
inference(step,[status(thm)],[t97,t39]) ).
cnf(t68,plain,
c_in(c_Pair(v_x,sFlat0,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2) = true,
inference(orient,[status(thm)],[t98]) ).
cnf(f2,negated_conjecture,
~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
sFlat3 != true,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
sFlat3 != ifeq(c_in(c_Pair(v_x,sFlat0,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),true,sFlat3,true),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
sFlat3 != ifeq(c_in(c_Pair(v_x,sFlat0,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2),true,sFlat3,c_in(c_Pair(v_x,sFlat0,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2)),
inference(rw,[status(thm)],[g0_1,t68]) ).
cnf(g0_3,plain,
sFlat3 != ifeq(true,true,sFlat3,c_in(c_Pair(v_x,sFlat0,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sFlat2)),
inference(rw,[status(thm)],[g0_2,t68]) ).
cnf(g0_4,plain,
sFlat3 != sFlat3,
inference(rw,[status(thm)],[g0_3,t15]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT268-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 20:45:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.15/0.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.15/0.94 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------