%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV488+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 03:22:23 PM UTC 2026
% Result : Theorem 3.39s 6.11s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 16 unt; 0 def)
% Number of atoms : 197 ( 53 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 239 ( 91 ~; 85 |; 45 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 67 !; 4 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( int_leq(X0,X1)
<=> ( X0 = X1
| int_less(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_leq) ).
fof(f10,axiom,
! [X0] :
( int_less(int_zero,X0)
<=> int_leq(int_one,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_successor_of_zero) ).
fof(f11,axiom,
real_zero != real_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_constants) ).
fof(f12,axiom,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X2] :
( ( X1 = plus(X0,X2)
& int_less(int_zero,X2) )
=> ! [X3] :
( ( int_leq(X3,X0)
& int_leq(int_one,X3) )
=> a(X3,plus(X3,X2)) = real_zero ) )
& ! [X3] :
( ( int_leq(X3,X1)
& int_leq(int_one,X3) )
=> a(X3,X3) = real_one )
& ! [X2] :
( ( X0 = plus(X1,X2)
& int_less(int_zero,X2) )
=> ! [X3] :
( ( int_leq(X3,X1)
& int_leq(int_one,X3) )
=> a(plus(X3,X2),X3) = lu(plus(X3,X2),X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qil) ).
fof(f13,conjecture,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(X0,X1)
& int_leq(int_one,X0) )
=> ( X0 = X1
=> a(X0,X1) != real_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lti) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(X0,X1)
& int_leq(int_one,X0) )
=> ( X0 = X1
=> a(X0,X1) != real_zero ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( int_leq(X1,n)
& int_leq(int_one,X1)
& int_leq(X0,n)
& int_leq(int_one,X0) )
=> ( ! [X5] :
( ( plus(X0,X5) = X1
& int_less(int_zero,X5) )
=> ! [X6] :
( ( int_leq(X6,X0)
& int_leq(int_one,X6) )
=> real_zero = a(X6,plus(X6,X5)) ) )
& ! [X4] :
( ( int_leq(X4,X1)
& int_leq(int_one,X4) )
=> real_one = a(X4,X4) )
& ! [X2] :
( ( X0 = plus(X1,X2)
& int_less(int_zero,X2) )
=> ! [X3] :
( ( int_leq(X3,X1)
& int_leq(int_one,X3) )
=> a(plus(X3,X2),X3) = lu(plus(X3,X2),X3) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f21,plain,
! [X0,X1] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ( ! [X5] :
( plus(X0,X5) != X1
| ~ int_less(int_zero,X5)
| ! [X6] :
( ~ int_leq(X6,X0)
| ~ int_leq(int_one,X6)
| real_zero = a(X6,plus(X6,X5)) ) )
& ! [X4] :
( ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4)
| real_one = a(X4,X4) )
& ! [X2] :
( plus(X1,X2) != X0
| ~ int_less(int_zero,X2)
| ! [X3] :
( ~ int_leq(X3,X1)
| ~ int_leq(int_one,X3)
| a(plus(X3,X2),X3) = lu(plus(X3,X2),X3) ) ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ( ! [X5] :
( plus(X0,X5) != X1
| ~ int_less(int_zero,X5)
| ! [X6] :
( ~ int_leq(X6,X0)
| ~ int_leq(int_one,X6)
| real_zero = a(X6,plus(X6,X5)) ) )
& ! [X4] :
( ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4)
| real_one = a(X4,X4) )
& ! [X2] :
( plus(X1,X2) != X0
| ~ int_less(int_zero,X2)
| ! [X3] :
( ~ int_leq(X3,X1)
| ~ int_leq(int_one,X3)
| a(plus(X3,X2),X3) = lu(plus(X3,X2),X3) ) ) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
? [X0,X1] :
( int_leq(X1,n)
& int_leq(X0,X1)
& int_leq(int_one,X0)
& X0 = X1
& real_zero = a(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f24,plain,
? [X0,X1] :
( int_leq(X1,n)
& int_leq(X0,X1)
& int_leq(int_one,X0)
& X0 = X1
& real_zero = a(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( ~ int_leq(X0,X1)
| X0 = X1
| int_less(X0,X1) )
& ( ( X0 != X1
& ~ int_less(X0,X1) )
| int_leq(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0,X1] :
( ( ~ int_leq(X0,X1)
| X0 = X1
| int_less(X0,X1) )
& ( ( X0 != X1
& ~ int_less(X0,X1) )
| int_leq(X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f30,plain,
! [X0] :
( ( ~ int_less(int_zero,X0)
| int_leq(int_one,X0) )
& ( ~ int_leq(int_one,X0)
| int_less(int_zero,X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f31,plain,
( int_leq(sK2,n)
& int_leq(sK1,sK2)
& int_leq(int_one,sK1)
& sK1 = sK2
& real_zero = a(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f24]) ).
fof(f33,plain,
! [X0,X1] :
( X0 != X1
| int_leq(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
! [X0] :
( ~ int_less(int_zero,X0)
| int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f46,plain,
! [X0] :
( ~ int_leq(int_one,X0)
| int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f47,plain,
real_zero != real_one,
inference(cnf_transformation,[],[f11]) ).
fof(f49,plain,
! [X0,X1,X4] :
( ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0)
| ~ int_leq(X4,X1)
| ~ int_leq(int_one,X4)
| real_one = a(X4,X4) ),
inference(cnf_transformation,[],[f22]) ).
fof(f51,plain,
int_leq(sK2,n),
inference(cnf_transformation,[],[f31]) ).
fof(f53,plain,
int_leq(int_one,sK1),
inference(cnf_transformation,[],[f31]) ).
fof(f54,plain,
sK1 = sK2,
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
real_zero = a(sK1,sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f56,plain,
real_zero = a(sK2,sK2),
inference(definition_unfolding,[],[f55,f54]) ).
fof(f57,plain,
int_leq(int_one,sK2),
inference(definition_unfolding,[],[f53,f54]) ).
fof(f59,plain,
! [X1] : int_leq(X1,X1),
inference(equality_resolution,[],[f33]) ).
tcf(c_50,plain,
! [X0: $i] : int_leq(X0,X0),
inference(cnf_transformation,[],[f59]) ).
tcf(c_62,plain,
! [X0: $i] :
( int_less(int_zero,X0)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_63,plain,
! [X0: $i] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_64,plain,
real_zero != real_one,
inference(cnf_transformation,[],[f47]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( a(X0,X0) = real_one )
| ~ int_leq(int_one,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(int_one,X0)
| ~ int_leq(X2,n)
| ~ int_leq(X1,n)
| ~ int_leq(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_68,negated_conjecture,
a(sK2,sK2) = real_zero,
inference(cnf_transformation,[],[f56]) ).
tcf(c_69,negated_conjecture,
int_leq(int_one,sK2),
inference(cnf_transformation,[],[f57]) ).
tcf(c_71,negated_conjecture,
int_leq(sK2,n),
inference(cnf_transformation,[],[f51]) ).
tcf(c_83,plain,
! [X0: $i] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( a(X0,X0) = real_one )
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X2)
| ~ int_leq(int_one,X1)
| ~ int_leq(X2,n)
| ~ int_leq(X1,n)
| ~ int_leq(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_66,c_83]) ).
tcf(c_110,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_108]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_11
| ( a(X0,X0) = real_one )
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(X0,X1)
| ~ int_less(int_zero,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_108]) ).
tcf(c_112,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_108]) ).
tcf(c_198,plain,
int_less(int_zero,sK2),
inference(superposition,[status(thm)],[c_69,c_62]) ).
tcf(c_255,plain,
( ~ iPr_def_10
| ~ int_leq(sK2,n) ),
inference(superposition,[status(thm)],[c_69,c_110]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i] :
( ~ int_less(int_zero,X0)
| ~ int_leq(X0,X1)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ( a(X0,X0) = real_one ) ),
inference(global_subsumption_just,[status(thm)],[c_111,c_71,c_111,c_112,c_255]) ).
tcf(c_396,plain,
! [X0: $i,X1: $i] :
( ( a(X0,X0) = real_one )
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X1,n)
| ~ int_leq(X0,X1) ),
inference(renaming,[status(thm)],[c_395]) ).
tcf(c_403,plain,
! [X0: $i] :
( ( a(X0,X0) = real_one )
| ~ int_less(int_zero,X0)
| ~ int_leq(int_one,X0)
| ~ int_leq(X0,n) ),
inference(superposition,[status(thm)],[c_50,c_396]) ).
tcf(c_436,plain,
! [X0: $i] :
( ( a(X0,X0) = real_one )
| ~ int_less(int_zero,X0)
| ~ int_leq(X0,n) ),
inference(forward_subsumption_resolution,[status(thm)],[c_403,c_63]) ).
tcf(c_1876,plain,
( ( a(sK2,sK2) = real_one )
| ~ int_less(int_zero,sK2) ),
inference(superposition,[status(thm)],[c_71,c_436]) ).
tcf(c_1882,plain,
( ( real_zero = real_one )
| ~ int_less(int_zero,sK2) ),
inference(demodulation,[status(thm)],[c_1876,c_68]) ).
tcf(c_1903,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1882,c_198,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV488+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.39 % Computer : n011.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Thu Sep 24 19:54:04 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.43 Running first-order theorem proving
% 0.14/5.43 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
% 0.14/5.44
% 0.14/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.44
% 0.14/5.44 % Detected problem language: tptp
% 0.14/5.45 % Proving...
% 3.39/6.11 % SZS status Started for theBenchmark.p
% 3.39/6.11 % SZS status Theorem for theBenchmark.p
% 3.39/6.11
% 3.39/6.11 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.39/6.11
% 3.39/6.11 % ------ iProver source info
% 3.39/6.11
% 3.39/6.11 % git: date: 2026-07-19 20:42:38 +0200
% 3.39/6.11 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.39/6.11 % git: non_committed_changes: false
% 3.39/6.11
% 3.39/6.11 % ------ Parsing...
% 3.39/6.11 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.39/6.11
% 3.39/6.11 % ------ Preprocessing... sup_sim: 0 pe_s pe_e %
% 3.39/6.11
% 3.39/6.11 % ------ Preprocessing... gs_s sp: 2 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 3.39/6.11
% 3.39/6.11 % ------ Preprocessing...
% 3.39/6.11 % ------ Proving...
% 3.39/6.11 % ------ Problem Properties
% 3.39/6.11
% 3.39/6.11 %
% 3.39/6.11 % clauses 25
% 3.39/6.11 % conjectures 4
% 3.39/6.11 % EPR 15
% 3.39/6.11 % Horn 22
% 3.39/6.11 % unary 10
% 3.39/6.11 % binary 8
% 3.39/6.11 % lits 60
% 3.39/6.11 % lits eq 9
% 3.39/6.11 % fd_pure 0
% 3.39/6.11 % fd_pseudo 0
% 3.39/6.11 % fd_cond 0
% 3.39/6.11 % fd_pseudo_cond 1
% 3.39/6.11 % AC symbols 0
% 3.39/6.11
% 3.39/6.11 % ------ Input Options Time Limit: Unbounded
% 3.39/6.11
% 3.39/6.11
% 3.39/6.11 % ------
% 3.39/6.11 % Current options:
% 3.39/6.11 % ------
% 3.39/6.11
% 3.39/6.11
% 3.39/6.11 %
% 3.39/6.11
% 3.39/6.11 % ------ Proving...
% 3.39/6.11 %
% 3.39/6.11
% 3.39/6.11 % SZS status Theorem for theBenchmark.p
% 3.39/6.11
% 3.39/6.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.39/6.11
% 3.39/6.11
%------------------------------------------------------------------------------