%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM837+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p 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 : Fri Sep 25 02:26:50 PM UTC 2026
% Result : Theorem 1.23s 1.28s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 70 ( 38 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 63 ( 28 ~; 22 |; 4 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 58 !; 12 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] : vd269 = vplus(vd268,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(171)') ).
fof(f2,negated_conjecture,
~ ? [X0] : vd269 = vplus(vd268,X0),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
less(vd268,vd269),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(170), 270, 0)') ).
fof(f5,axiom,
! [X0,X1] :
( leq(X0,X1)
=> geq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
fof(f6,axiom,
! [X0,X1] :
( geq(X0,X1)
=> leq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
fof(f7,axiom,
! [X0,X1] :
( leq(X1,X0)
<=> ( X1 = X0
| less(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
fof(f8,axiom,
! [X0,X1] :
( geq(X1,X0)
<=> ( X1 = X0
| greater(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof(f9,axiom,
! [X0,X1] :
( less(X0,X1)
=> greater(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof(f10,axiom,
! [X0,X1] :
( greater(X0,X1)
=> less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof(f11,axiom,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(f12,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof(f13,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof(f14,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof(f15,axiom,
! [X0,X1] :
( less(X1,X0)
<=> ? [X2] : X0 = vplus(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof(f16,axiom,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : X1 = vplus(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f17,axiom,
! [X0,X1] :
( ? [X3] : X1 = vplus(X0,X3)
| ? [X2] : X0 = vplus(X1,X2)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof(f18,axiom,
! [X0,X1] :
( ~ ? [X2] : X1 = vplus(X0,X2)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f19,axiom,
! [X0,X1] :
( ~ ? [X3] : X1 = vplus(X0,X3)
| ~ ? [X2] : X0 = vplus(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof(f20,axiom,
! [X0,X1] :
( ~ ? [X2] : X0 = vplus(X1,X2)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof(f21,axiom,
! [X0,X1] :
( X0 != X1
=> ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof(f22,axiom,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f23,axiom,
! [X0,X1] :
( vplus(X0,v1) = vsucc(X0)
& vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof(f24,plain,
! [X0] : vd269 != vplus(vd268,X0),
inference(ennf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0,X1] :
( ( ~ less(X1,X0)
| ? [X2] : X0 = vplus(X1,X2) )
& ( ! [X2] : vplus(X1,X2) != X0
| less(X1,X0) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f38,plain,
! [X0,X1] :
( ( ~ less(X1,X0)
| ? [X3] : vplus(X1,X3) = X0 )
& ( ! [X2] : vplus(X1,X2) != X0
| less(X1,X0) ) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( ( ~ less(X1,X0)
| vplus(X1,sK0(X0,X1)) = X0 )
& ( ! [X2] : vplus(X1,X2) != X0
| less(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f38]) ).
fof(f44,plain,
! [X0] : vd269 != vplus(vd268,X0),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
less(vd268,vd269),
inference(cnf_transformation,[],[f4]) ).
fof(f61,plain,
! [X0,X1] :
( ~ less(X1,X0)
| vplus(X1,sK0(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] : vplus(vd268,X0) != vd269,
inference(cnf_transformation,[],[f44]) ).
tcf(c_51,plain,
less(vd268,vd269),
inference(cnf_transformation,[],[f46]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( vplus(X0,sK0(X1,X0)) = X1 )
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i] :
( ( vplus(X1,sK0(X0,X1)) = X0 )
| ( X1 != vd268 )
| ( X0 != vd269 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_67]) ).
tcf(c_422,plain,
vplus(vd268,sK0(vd269,vd268)) = vd269,
inference(unflattening,[status(thm)],[c_421]) ).
tcf(c_425,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_422,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM837+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 05:32:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.23/1.28 % SZS status Started for theBenchmark.p
% 1.23/1.28 % SZS status Theorem for theBenchmark.p
% 1.23/1.28
% 1.23/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.23/1.28
% 1.23/1.28 % ------ iProver source info
% 1.23/1.28
% 1.23/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.23/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.23/1.28 % git: non_committed_changes: false
% 1.23/1.28
% 1.23/1.28 % ------ Parsing...
% 1.23/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.23/1.28
% 1.23/1.28 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s%
% 1.23/1.28
% 1.23/1.28 % SZS status Theorem for theBenchmark.p
% 1.23/1.28
% 1.23/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.23/1.28
% 1.23/1.28
%------------------------------------------------------------------------------