%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEV606+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 03:02:50 PM UTC 2026
% Result : Theorem 0.08s 15.99s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 75 ( 26 ~; 20 |; 15 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 14 !; 4 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1138,axiom,
! [X0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
=> ! [X1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.ZArith.BinInt.Z.square_le_simpl_nonneg') ).
fof(f1728,conjecture,
! [X0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
=> ! [X1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X0)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof(f1729,negated_conjecture,
~ ! [X0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
=> ! [X1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X0))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X0)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1728]) ).
fof(f1730,plain,
? [X0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
& ? [X1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0)))
& ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X0)) ) ),
inference(ennf_transformation,[],[f1729]) ).
fof(f1731,plain,
? [X0] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
& ? [X1] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0)))
& ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X0)) ) ),
inference(flattening,[],[f1730]) ).
fof(f1817,plain,
! [X0] :
( ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
| ! [X1] :
( ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1)))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X1)) ) ),
inference(ennf_transformation,[],[f1138]) ).
fof(f1818,plain,
! [X0] :
( ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
| ! [X1] :
( ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1)))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X1)) ) ),
inference(flattening,[],[f1817]) ).
fof(f1957,plain,
( cCoq_2eNumbers_2eBinNums_2eZ___24t(sK0)
& cCoq_2eNumbers_2eBinNums_2eZ___24t(sK1)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK1))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK1,sK1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK0,sK0)))
& ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK1,sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f1731]) ).
fof(f1986,plain,
cCoq_2eNumbers_2eBinNums_2eZ___24t(sK0),
inference(cnf_transformation,[],[f1957]) ).
fof(f1987,plain,
cCoq_2eNumbers_2eBinNums_2eZ___24t(sK1),
inference(cnf_transformation,[],[f1957]) ).
fof(f1988,plain,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK0)),
inference(cnf_transformation,[],[f1957]) ).
fof(f1990,plain,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK1,sK1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK0,sK0))),
inference(cnf_transformation,[],[f1957]) ).
fof(f1991,plain,
~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK1,sK0)),
inference(cnf_transformation,[],[f1957]) ).
fof(f2039,plain,
! [X0,X1] :
( ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1)))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X1)) ),
inference(cnf_transformation,[],[f1818]) ).
tcf(c_49,negated_conjecture,
~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK1,sK0)),
inference(cnf_transformation,[],[f1991]) ).
tcf(c_50,negated_conjecture,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK1,sK1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK0,sK0))),
inference(cnf_transformation,[],[f1990]) ).
tcf(c_52,negated_conjecture,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK0)),
inference(cnf_transformation,[],[f1988]) ).
tcf(c_53,negated_conjecture,
cCoq_2eNumbers_2eBinNums_2eZ___24t(sK1),
inference(cnf_transformation,[],[f1987]) ).
tcf(c_54,negated_conjecture,
cCoq_2eNumbers_2eBinNums_2eZ___24t(sK0),
inference(cnf_transformation,[],[f1986]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X0,X1))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X0)
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X1))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X0,X0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1))) ),
inference(cnf_transformation,[],[f2039]) ).
tcf(c_6858,plain,
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(sK1,sK0))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK0)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(sK1)
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,sK0))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK1,sK1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(sK0,sK0))) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_6859,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6858,c_50,c_49,c_52,c_53,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV606+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/15.32 % Computer : n012.cluster.edu
% 0.04/15.32 % Model : x86_64 x86_64
% 0.04/15.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/15.32 % Memory : 8046.5625MB
% 0.04/15.32 % OS : Linux 6.8.0-71-generic
% 0.04/15.32 % CPULimit : 300
% 0.04/15.32 % WCLimit : 300
% 0.04/15.32 % DateTime : Thu Sep 24 15:04:52 UTC 2026
% 0.04/15.32 % CPUTime :
% 0.04/15.32 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/15.34 Running first-order theorem proving
% 0.04/15.34 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
% 0.04/15.35
% 0.04/15.35 % ======== iProver multi-core TPTP/SMT =========
% 0.04/15.35
% 0.04/15.35 % Detected problem language: tptp
% 0.04/15.36 % Proving...
% 0.08/15.99 % SZS status Started for theBenchmark.p
% 0.08/15.99 % SZS status Theorem for theBenchmark.p
% 0.08/15.99
% 0.08/15.99 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.08/15.99
% 0.08/15.99 % ------ iProver source info
% 0.08/15.99
% 0.08/15.99 % git: date: 2026-07-19 20:42:38 +0200
% 0.08/15.99 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.08/15.99 % git: non_committed_changes: false
% 0.08/15.99
% 0.08/15.99 % ------ Parsing...
% 0.08/15.99 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.08/15.99
% 0.08/15.99 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.08/15.99
% 0.08/15.99 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.08/15.99
% 0.08/15.99 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.08/15.99 % ------ Proving...
% 0.08/15.99 % ------ Problem Properties
% 0.08/15.99
% 0.08/15.99 %
% 0.08/15.99 % clauses 97
% 0.08/15.99 % conjectures 6
% 0.08/15.99 % EPR 3
% 0.08/15.99 % Horn 75
% 0.08/15.99 % unary 8
% 0.08/15.99 % binary 8
% 0.08/15.99 % lits 458
% 0.08/15.99 % lits eq 22
% 0.08/15.99 % fd_pure 0
% 0.08/15.99 % fd_pseudo 0
% 0.08/15.99 % fd_cond 2
% 0.08/15.99 % fd_pseudo_cond 5
% 0.08/15.99 % AC symbols 0
% 0.08/15.99
% 0.08/15.99 % ------ Schedule dynamic 5 is on
% 0.08/15.99
% 0.08/15.99 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.08/15.99
% 0.08/15.99
% 0.08/15.99 % ------
% 0.08/15.99 % Current options:
% 0.08/15.99 % ------
% 0.08/15.99
% 0.08/15.99
% 0.08/15.99 %
% 0.08/15.99
% 0.08/15.99 % ------ Proving...
% 0.08/15.99 %
% 0.08/15.99
% 0.08/15.99 % SZS status Theorem for theBenchmark.p
% 0.08/15.99
% 0.08/15.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.08/15.99
% 0.08/15.99
%------------------------------------------------------------------------------