%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Tue Sep 29 11:46:26 AM UTC 2026
% Result : Unsatisfiable 2.29s 1.06s
% Output : Refutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 50 ( 50 unt; 1 def)
% Number of atoms : 50 ( 43 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-4 aty)
% Number of variables : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3,negated_conjecture,
c_in(v_x,v_S,t_a) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4,plain,
true = c_in(v_x,v_S,t_a),
inference(reorient_equations,[],[f3]) ).
fof(f5,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,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f6,plain,
true != 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(reorient_equations,[],[f5]) ).
fof(f7,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] : ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),tc_set(X2)),true,ifeq(c_in(X1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),true,ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),true,ifeq(c_in(X3,X0,X2),true,c_in(c_Pair(X3,c_Tarski_Olub(X0,X1,X2),X2,X2),c_Tarski_Opotype_Oorder(X1,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
fof(f9,plain,
! [X2,X3,X0,X1] : true = ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),tc_set(X2)),true,ifeq(c_in(X1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),true,ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),true,ifeq(c_in(X3,X0,X2),true,c_in(c_Pair(X3,c_Tarski_Olub(X0,X1,X2),X2,X2),c_Tarski_Opotype_Oorder(X1,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),true),true),true),true),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X2,X3,X0,X1] : ifeq(c_in(c_Pair(X0,X1,X2,X2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X3,X2),X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),true,c_in(c_Pair(X1,X0,X2,X2),c_Tarski_Opotype_Oorder(X3,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) ).
fof(f11,plain,
! [X2,X3,X0,X1] : true = ifeq(c_in(c_Pair(X0,X1,X2,X2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X3,X2),X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),true,c_in(c_Pair(X1,X0,X2,X2),c_Tarski_Opotype_Oorder(X3,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),true),
inference(reorient_equations,[],[f10]) ).
fof(f12,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)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
fof(f13,plain,
true = 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(reorient_equations,[],[f12]) ).
fof(f14,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)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
fof(f15,plain,
true = 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(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X2,X0,X1] : c_Tarski_Oglb(X0,X1,X2) = c_Tarski_Olub(X0,c_Tarski_Odual(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
fof(f17,axiom,
! [X0,X1] : c_Tarski_Opotype_Opset(c_Tarski_Odual(X0,X1),X1,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X0,X1,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
fof(f18,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
fof(f19,plain,
true != c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(definition_unfolding,[],[f6,f16]) ).
fof(f20,definition,
~ sP0(c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f21,plain,
sP0(true),
inference(inequality_splitting,[],[f19,f20]) ).
fof(f22,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)) = 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(backward_demodulation,[],[f15,f13]) ).
fof(f23,plain,
! [X2,X3,X0,X1] : c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = ifeq(c_in(c_Pair(X0,X1,X2,X2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X3,X2),X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),c_in(c_Pair(X1,X0,X2,X2),c_Tarski_Opotype_Oorder(X3,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),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(forward_demodulation,[],[f11,f13]) ).
fof(f24,plain,
! [X2,X3,X0,X1] : c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) = ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),tc_set(X2)),c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),ifeq(c_in(X1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),ifeq(c_in(X3,X0,X2),c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),c_in(c_Pair(X3,c_Tarski_Olub(X0,X1,X2),X2,X2),c_Tarski_Opotype_Oorder(X1,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))),c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))),c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))),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(forward_demodulation,[],[f9,f13]) ).
fof(f25,plain,
sP0(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(forward_demodulation,[],[f21,f13]) ).
fof(f26,plain,
c_in(v_x,v_S,t_a) = 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(backward_demodulation,[],[f13,f4]) ).
fof(f27,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = c_in(v_x,v_S,t_a),
inference(backward_demodulation,[],[f4,f2]) ).
fof(f28,plain,
sP0(c_in(v_x,v_S,t_a)),
inference(backward_demodulation,[],[f25,f26]) ).
fof(f29,plain,
! [X2,X3,X0,X1] : c_in(v_x,v_S,t_a) = ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),tc_set(X2)),c_in(v_x,v_S,t_a),ifeq(c_in(X1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),c_in(v_x,v_S,t_a),ifeq(c_in(X3,X0,X2),c_in(v_x,v_S,t_a),c_in(c_Pair(X3,c_Tarski_Olub(X0,X1,X2),X2,X2),c_Tarski_Opotype_Oorder(X1,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),c_in(v_x,v_S,t_a)),
inference(backward_demodulation,[],[f24,f26]) ).
fof(f30,plain,
! [X2,X3,X0,X1] : c_in(v_x,v_S,t_a) = ifeq(c_in(c_Pair(X0,X1,X2,X2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X3,X2),X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),c_in(v_x,v_S,t_a),c_in(c_Pair(X1,X0,X2,X2),c_Tarski_Opotype_Oorder(X3,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),c_in(v_x,v_S,t_a)),
inference(backward_demodulation,[],[f23,f26]) ).
fof(f31,plain,
c_in(v_x,v_S,t_a) = 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(backward_demodulation,[],[f22,f26]) ).
fof(f32,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = 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(backward_demodulation,[],[f26,f27]) ).
fof(f33,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = 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(forward_demodulation,[],[f31,f27]) ).
fof(f34,plain,
! [X2,X3,X0,X1] : c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_in(c_Pair(X0,X1,X2,X2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X3,X2),X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(X1,X0,X2,X2),c_Tarski_Opotype_Oorder(X3,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(forward_demodulation,[],[f30,f27]) ).
fof(f35,plain,
! [X2,X3,X0,X1] : c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),tc_set(X2)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(X1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(X3,X0,X2),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(X3,c_Tarski_Olub(X0,X1,X2),X2,X2),c_Tarski_Opotype_Oorder(X1,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(forward_demodulation,[],[f29,f27]) ).
fof(f36,plain,
sP0(c_lessequals(v_S,v_A,tc_set(t_a))),
inference(forward_demodulation,[],[f28,f27]) ).
fof(f37,plain,
! [X0,X1] : c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_in(c_Pair(X0,X1,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(X1,X0,t_a,t_a),v_r,tc_prod(t_a,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(superposition,[],[f34,f18]) ).
fof(f40,plain,
! [X0,X1] : c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(X1,X0,t_a),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(X1,c_Tarski_Olub(X0,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),tc_prod(t_a,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(superposition,[],[f35,f33]) ).
fof(f49,plain,
! [X0,X1] : c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(X1,X0,t_a),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(X1,c_Tarski_Olub(X0,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),tc_prod(t_a,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(forward_demodulation,[],[f40,f1]) ).
fof(f52,plain,
! [X0,X1] : c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(X1,X0,t_a),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(X1,c_Tarski_Olub(X0,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),tc_prod(t_a,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(forward_demodulation,[],[f49,f32]) ).
fof(f54,plain,
! [X0,X1] : c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(X1,X0,t_a),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(X1,c_Tarski_Olub(X0,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),tc_prod(t_a,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(forward_demodulation,[],[f52,f1]) ).
fof(f56,plain,
! [X0,X1] : c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(X1,X0,t_a),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(X1,c_Tarski_Olub(X0,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),tc_prod(t_a,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(forward_demodulation,[],[f54,f17]) ).
fof(f58,plain,
! [X0,X1] : c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_lessequals(X0,v_A,tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_in(X1,X0,t_a),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(X1,c_Tarski_Olub(X0,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),tc_prod(t_a,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(forward_demodulation,[],[f56,f7]) ).
fof(f60,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),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),tc_prod(t_a,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(superposition,[],[f58,f27]) ).
fof(f63,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),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),tc_prod(t_a,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(forward_demodulation,[],[f60,f1]) ).
fof(f64,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = 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),tc_prod(t_a,t_a)),
inference(forward_demodulation,[],[f63,f1]) ).
fof(f68,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),c_lessequals(v_S,v_A,tc_set(t_a)),c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),c_lessequals(v_S,v_A,tc_set(t_a))),
inference(superposition,[],[f37,f64]) ).
fof(f74,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(forward_demodulation,[],[f68,f1]) ).
fof(f78,plain,
~ sP0(c_lessequals(v_S,v_A,tc_set(t_a))),
inference(backward_demodulation,[],[f20,f74]) ).
fof(f81,plain,
$false,
inference(forward_subsumption_resolution,[],[f78,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n004.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 14:08:51 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.29/1.06 % (3556530)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.29/1.06 % (3556569)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2667242399:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.29/1.06 % (3556564)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1427684134:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.29/1.06 % (3556565)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=622459051:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.29/1.06 % (3556563)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=328296849:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.29/1.06 % (3556567)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=981435027:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.29/1.06 % (3556568)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4076676336:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.29/1.06 % (3556571)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3195948394:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.29/1.06 % (3556567)First to succeed.
% 2.29/1.06 % (3556567)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3556530"
% 2.29/1.06 % (3556569)Also succeeded, but the first one will report.
% 2.29/1.06 % (3556571)Also succeeded, but the first one will report.
% 2.29/1.06 % (3556568)Instruction limit reached!
% 2.29/1.06 % (3556568)------------------------------
% 2.29/1.06 % (3556568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.29/1.06 % (3556568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.29/1.06 % (3556568)CaDiCaL version: 2.1.3
% 2.29/1.06 % (3556568)Termination reason: Instruction limit
% 2.29/1.06 % (3556568)Termination phase: Saturation
% 2.29/1.06 % (3556568)Time elapsed: 0.102 s
% 2.29/1.06 % (3556568)Peak memory usage: 88 MB
% 2.29/1.06 % (3556568)Instructions burned: 181 (million)
% 2.29/1.06 % (3556567)Refutation found. Thanks to Tanya!
% 2.29/1.06 % SZS status Unsatisfiable for theBenchmark
% 2.29/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 3.33/1.25 % (3556567)------------------------------
% 3.33/1.25 % (3556567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.25 % (3556567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.25 % (3556567)CaDiCaL version: 2.1.3
% 3.33/1.25 % (3556567)Termination reason: Refutation
% 3.33/1.25 % (3556567)Time elapsed: 0.008 s
% 3.33/1.25 % (3556567)Peak memory usage: 88 MB
% 3.33/1.25 % (3556567)Instructions burned: 13 (million)
% 3.33/1.25 % (3556567)------------------------------
% 3.33/1.25 % (3556567)------------------------------
% 3.33/1.25 % (3556530)Success in time 0.425 s
% 3.33/1.25 % Vampire exiting
%------------------------------------------------------------------------------