%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT268-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n018.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 01:58:30 PM UTC 2026
% Result : Unsatisfiable 2.30s 1.28s
% Output : CNFRefutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 45 ( 30 unt; 5 def)
% Number of atoms : 125 ( 22 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 86 ( 45 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
c_in(v_x,v_S,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,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(f4,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(f5,axiom,
! [X2,X3,X0,X1] :
( 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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( 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_Pair(X0,X1,X2,X2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X3,X2),X2,tc_Product__Type_Ounit),tc_prod(X2,X2)) ),
file('/export/starexec/sandbox2/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(f7,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(f8,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(f9,axiom,
! [X2,X0,X1] : c_Tarski_Oglb(X0,X1,X2) = c_Tarski_Olub(X0,c_Tarski_Odual(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
fof(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(f12,plain,
~ 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,[],[f3,f9]) ).
tcf(c_60,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_61,negated_conjecture,
c_in(v_x,v_S,t_a),
inference(cnf_transformation,[],[f2]) ).
tcf(c_62,negated_conjecture,
~ 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(cnf_transformation,[],[f12]) ).
tcf(c_63,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(cnf_transformation,[],[f4]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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(X3,X0,X2)
| ~ c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit))
| ~ c_in(X1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit))
| ~ c_lessequals(X0,c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),tc_set(X2)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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_Pair(X0,X1,X2,X2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X3,X2),X2,tc_Product__Type_Ounit),tc_prod(X2,X2)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_66,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,[],[f7]) ).
tcf(c_67,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,[],[f8]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : 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,[],[f10]) ).
tcf(c_69,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(cnf_transformation,[],[f11]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(c_Pair(X3,c_Tarski_Olub(X1,X2,X0),X0,X0),c_Tarski_Opotype_Oorder(X2,X0,tc_Product__Type_Ounit),tc_prod(X0,X0))
| ~ c_in(X3,X1,X0)
| ~ c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X0,tc_Product__Type_Ounit))
| ~ c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X0,tc_Product__Type_Ounit))
| ( X1 != v_S )
| ( tc_set(X0) != tc_set(t_a) )
| ( c_Tarski_Opotype_Opset(X2,X0,tc_Product__Type_Ounit) != v_A ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_64]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X2,c_Tarski_Olub(v_S,X0,X1),X1,X1),c_Tarski_Opotype_Oorder(X0,X1,tc_Product__Type_Ounit),tc_prod(X1,X1))
| ~ c_in(X2,v_S,X1)
| ~ c_in(X0,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X1,tc_Product__Type_Ounit))
| ~ c_in(X0,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X1,tc_Product__Type_Ounit))
| ( tc_set(X1) != tc_set(t_a) )
| ( c_Tarski_Opotype_Opset(X0,X1,tc_Product__Type_Ounit) != v_A ) ),
inference(unflattening,[status(thm)],[c_128]) ).
tcf(c_211,definition,
iPr_def_10 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_212,definition,
iPr_def_11 = c_Tarski_Odual(v_cl,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_213,definition,
iPr_def_12 = c_Tarski_Olub(v_S,iPr_def_11,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_214,definition,
iPr_def_13 = c_Pair(iPr_def_12,v_x,t_a,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_215,definition,
iPr_def_14 = tc_prod(t_a,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Pair(X2,c_Tarski_Olub(v_S,X0,X1),X1,X1),c_Tarski_Opotype_Oorder(X0,X1,tc_Product__Type_Ounit),tc_prod(X1,X1))
| ~ c_in(X2,v_S,X1)
| ~ c_in(X0,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X1,tc_Product__Type_Ounit))
| ~ c_in(X0,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X1,tc_Product__Type_Ounit))
| ( tc_set(X1) != iPr_def_10 )
| ( c_Tarski_Opotype_Opset(X0,X1,tc_Product__Type_Ounit) != v_A ) ),
inference(demodulation,[status(thm)],[c_129,c_211]) ).
tcf(c_217,negated_conjecture,
~ c_in(iPr_def_13,v_r,iPr_def_14),
inference(demodulation,[status(thm)],[c_62,c_215,c_212,c_213,c_214]) ).
tcf(c_218,negated_conjecture,
c_in(v_x,v_S,t_a),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_494,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(iPr_def_11,t_a,tc_Product__Type_Ounit),
inference(superposition,[status(thm)],[c_212,c_68]) ).
tcf(c_496,plain,
c_Tarski_Opotype_Opset(iPr_def_11,t_a,tc_Product__Type_Ounit) = v_A,
inference(light_normalisation,[status(thm)],[c_494,c_63]) ).
tcf(c_504,plain,
c_in(iPr_def_11,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(light_normalisation,[status(thm)],[c_66,c_212]) ).
tcf(c_505,plain,
c_in(iPr_def_11,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(light_normalisation,[status(thm)],[c_67,c_212]) ).
tcf(c_506,plain,
! [X0: $i] :
( c_in(c_Pair(X0,c_Tarski_Olub(v_S,iPr_def_11,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(iPr_def_11,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(X0,v_S,t_a)
| ~ c_in(iPr_def_11,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(iPr_def_11,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ( tc_set(t_a) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_496,c_216]) ).
tcf(c_507,plain,
! [X0: $i] :
( c_in(c_Pair(X0,c_Tarski_Olub(v_S,iPr_def_11,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(iPr_def_11,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(X0,v_S,t_a)
| ~ c_in(iPr_def_11,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(iPr_def_11,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(ground_joinability,[status(thm)],[c_506,c_211]) ).
tcf(c_508,plain,
! [X0: $i] :
( c_in(c_Pair(X0,iPr_def_12,t_a,t_a),c_Tarski_Opotype_Oorder(iPr_def_11,t_a,tc_Product__Type_Ounit),iPr_def_14)
| ~ c_in(X0,v_S,t_a)
| ~ c_in(iPr_def_11,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(iPr_def_11,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(light_normalisation,[status(thm)],[c_507,c_213,c_215]) ).
tcf(c_509,plain,
! [X0: $i] :
( c_in(c_Pair(X0,iPr_def_12,t_a,t_a),c_Tarski_Opotype_Oorder(iPr_def_11,t_a,tc_Product__Type_Ounit),iPr_def_14)
| ~ c_in(X0,v_S,t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_508,c_505,c_504]) ).
tcf(c_522,plain,
! [X0: $i,X1: $i] :
( c_in(c_Pair(X1,X0,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(X0,X1,t_a,t_a),c_Tarski_Opotype_Oorder(iPr_def_11,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(superposition,[status(thm)],[c_212,c_65]) ).
tcf(c_530,plain,
! [X0: $i,X1: $i] :
( c_in(c_Pair(X1,X0,t_a,t_a),v_r,iPr_def_14)
| ~ c_in(c_Pair(X0,X1,t_a,t_a),c_Tarski_Opotype_Oorder(iPr_def_11,t_a,tc_Product__Type_Ounit),iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_522,c_69,c_215]) ).
tcf(c_732,plain,
! [X0: $i] :
( c_in(c_Pair(iPr_def_12,X0,t_a,t_a),v_r,iPr_def_14)
| ~ c_in(X0,v_S,t_a) ),
inference(superposition,[status(thm)],[c_509,c_530]) ).
tcf(c_805,plain,
( c_in(iPr_def_13,v_r,iPr_def_14)
| ~ c_in(v_x,v_S,t_a) ),
inference(superposition,[status(thm)],[c_214,c_732]) ).
tcf(c_806,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_805,c_217,c_218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT268-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n018.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Wed Sep 23 20:47:17 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 2.30/1.28 % SZS status Started for theBenchmark.p
% 2.30/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.30/1.28
% 2.30/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.30/1.28
% 2.30/1.28 % ------ iProver source info
% 2.30/1.28
% 2.30/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.30/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.30/1.28 % git: non_committed_changes: false
% 2.30/1.28
% 2.30/1.28 % ------ Parsing...% successful
% 2.30/1.28
% 2.30/1.28
% 2.30/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.30/1.28
% 2.30/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.30/1.28
% 2.30/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.30/1.28
% 2.30/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.30/1.28 % ------ Proving...
% 2.30/1.28 % ------ Problem Properties
% 2.30/1.28
% 2.30/1.28 %
% 2.30/1.28 % clauses 14
% 2.30/1.28 % conjectures 2
% 2.30/1.28 % EPR 2
% 2.30/1.28 % Horn 14
% 2.30/1.28 % unary 12
% 2.30/1.28 % binary 1
% 2.30/1.28 % lits 20
% 2.30/1.28 % lits eq 10
% 2.30/1.28 % fd_pure 0
% 2.30/1.28 % fd_pseudo 0
% 2.30/1.28 % fd_cond 0
% 2.30/1.28 % fd_pseudo_cond 0
% 2.30/1.28 % AC symbols 0
% 2.30/1.28
% 2.30/1.28 % ------ Schedule dynamic 5 is on
% 2.30/1.28
% 2.30/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.30/1.28
% 2.30/1.28
% 2.30/1.28 % ------
% 2.30/1.28 % Current options:
% 2.30/1.28 % ------
% 2.30/1.28
% 2.30/1.28
% 2.30/1.28 %
% 2.30/1.28
% 2.30/1.28 % ------ Proving...
% 2.30/1.28 %
% 2.30/1.28
% 2.30/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.30/1.28
% 2.30/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.30/1.28
% 2.30/1.28
%------------------------------------------------------------------------------