%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV580-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 03:23:50 PM UTC 2026
% Result : Unsatisfiable 8.24s 1.74s
% Output : CNFRefutation 8.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 22 ( 16 unt; 0 def)
% Number of atoms : 31 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f232,axiom,
! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(X2,X3,tc_nat),tc_nat,X0) = c_HOL_Oplus__class_Oplus(hAPP(X1,X2),c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X2),X3,tc_nat),tc_nat,X0),X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__head__upt__Suc_0) ).
fof(f594,axiom,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X0),X1,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).
fof(f604,axiom,
( c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_0) ).
fof(f654,axiom,
! [X2,X0,X1] : c_Set_Oinsert(X0,X1,X2) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X1,tc_fun(X2,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
fof(f661,axiom,
c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f662,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f663,negated_conjecture,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tcf(c_806,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Oplus__class_Oplus(hAPP(X3,X0),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X0),X1,tc_nat),tc_nat,X2),X2) = c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X0,X1,tc_nat),tc_nat,X2) )
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_1091,plain,
! [X0: $i,X1: $i] : c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(X0),X1,tc_nat) = c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X1,tc_nat),
inference(cnf_transformation,[],[f594]) ).
tcf(c_1097,plain,
( ( c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) = c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) )
| ~ class_OrderedGroup_Ocomm__monoid__add(t_a) ),
inference(cnf_transformation,[],[f604]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i,X2: $i] : c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X2,tc_fun(X1,tc_bool)) = c_Set_Oinsert(X0,X2,X1),
inference(cnf_transformation,[],[f654]) ).
tcf(c_1141,plain,
c_HOL_Oord__class_Oless(v_m,v_n,tc_nat),
inference(cnf_transformation,[],[f661]) ).
tcf(c_1142,negated_conjecture,
class_OrderedGroup_Ocomm__monoid__add(t_a),
inference(cnf_transformation,[],[f662]) ).
tcf(c_1143,negated_conjecture,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(cnf_transformation,[],[f663]) ).
tcf(c_2141,plain,
c_Finite__Set_Osetsum(v_f,c_Set_Oinsert(v_m,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat),tc_nat,t_a) != c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(demodulation,[status(thm)],[c_1143,c_1137]) ).
tcf(c_2429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_HOL_Oplus__class_Oplus(hAPP(X3,X0),c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OgreaterThanLessThan(X0,X1,tc_nat),tc_nat,X2),X2) = c_Finite__Set_Osetsum(X3,c_SetInterval_Oord__class_OatLeastLessThan(X0,X1,tc_nat),tc_nat,X2) )
| ~ class_OrderedGroup_Ocomm__monoid__add(X2)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
inference(demodulation,[status(thm)],[c_806,c_1091]) ).
tcf(c_2439,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oplus__class_Oplus(hAPP(X1,v_m),c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,X0),X0) = c_Finite__Set_Osetsum(X1,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,X0) )
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(superposition,[status(thm)],[c_1141,c_2429]) ).
tcf(c_2453,plain,
c_Finite__Set_Osetsum(v_f,c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_m,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat,t_a) = c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a),
inference(global_subsumption_just,[status(thm)],[c_1097,c_1142,c_1097]) ).
tcf(c_2455,plain,
c_HOL_Oplus__class_Oplus(hAPP(v_f,v_m),c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(v_f,c_Set_Oinsert(v_m,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat),tc_nat,t_a),
inference(demodulation,[status(thm)],[c_2453,c_1137]) ).
tcf(c_14929,plain,
! [X0: $i] : c_HOL_Oplus__class_Oplus(hAPP(X0,v_m),c_Finite__Set_Osetsum(X0,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat,t_a),t_a) = c_Finite__Set_Osetsum(X0,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(superposition,[status(thm)],[c_1142,c_2439]) ).
tcf(c_14931,plain,
c_Finite__Set_Osetsum(v_f,c_Set_Oinsert(v_m,c_SetInterval_Oord__class_OgreaterThanLessThan(v_m,v_n,tc_nat),tc_nat),tc_nat,t_a) = c_Finite__Set_Osetsum(v_f,c_SetInterval_Oord__class_OatLeastLessThan(v_m,v_n,tc_nat),tc_nat,t_a),
inference(demodulation,[status(thm)],[c_2455,c_14929]) ).
tcf(c_14932,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_2141,c_14931]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV580-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n011.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 20:38:28 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.39 Running first-order theorem proving
% 0.07/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.40
% 0.07/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.40
% 0.07/0.40 % Detected problem language: tptp
% 0.07/0.41 % Proving...
% 8.24/1.74 % SZS status Started for theBenchmark.p
% 8.24/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 8.24/1.74
% 8.24/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.24/1.74
% 8.24/1.74 % ------ iProver source info
% 8.24/1.74
% 8.24/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 8.24/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.24/1.74 % git: non_committed_changes: false
% 8.24/1.74
% 8.24/1.74 % ------ Parsing...% successful
% 8.24/1.74
% 8.24/1.74
% 8.24/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.24/1.74 % ------ Proving...
% 8.24/1.74 % ------ Problem Properties
% 8.24/1.74
% 8.24/1.74 %
% 8.24/1.74 % clauses 541
% 8.24/1.74 % conjectures 2
% 8.24/1.74 % EPR 85
% 8.24/1.74 % Horn 480
% 8.24/1.74 % unary 147
% 8.24/1.74 % binary 185
% 8.24/1.74 % lits 1217
% 8.24/1.74 % lits eq 301
% 8.24/1.74 % fd_pure 0
% 8.24/1.74 % fd_pseudo 0
% 8.24/1.74 % fd_cond 3
% 8.24/1.74 % fd_pseudo_cond 50
% 8.24/1.74 % AC symbols 0
% 8.24/1.74
% 8.24/1.74 % ------ Input Options Time Limit: Unbounded
% 8.24/1.74
% 8.24/1.74
% 8.24/1.74 % ------
% 8.24/1.74 % Current options:
% 8.24/1.74 % ------
% 8.24/1.74
% 8.24/1.74
% 8.24/1.74 %
% 8.24/1.74
% 8.24/1.74 % ------ Proving...
% 8.24/1.74 %
% 8.24/1.74
% 8.24/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 8.24/1.74
% 8.24/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.24/1.74
% 8.24/1.74
%------------------------------------------------------------------------------