%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM850+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 : 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 02:26:54 PM UTC 2026
% Result : Theorem 1.75s 6.16s
% Output : CNFRefutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 51
% Syntax : Number of formulae : 66 ( 25 unt; 0 def)
% Number of atoms : 127 ( 60 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 96 ( 35 ~; 23 |; 13 &)
% ( 4 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 128 !; 12 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] : vd470 = vplus(vd471,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(conseq_conjunct1(conseq(302)))') ).
fof(f2,negated_conjecture,
~ ? [X0] : vd470 = vplus(vd471,X0),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
greater(vd470,vd471),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(302), 472, 0)') ).
fof(f4,axiom,
! [X0,X1,X2] : vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
fof(f5,axiom,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof(f6,axiom,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f7,axiom,
! [X0,X1] : vmul(vsucc(X0),X1) = vplus(vmul(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
fof(f8,axiom,
! [X0] : vmul(v1,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
fof(f9,axiom,
! [X0,X1] :
( vmul(X0,v1) = X0
& vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof(f10,axiom,
! [X0,X1] :
( less(X0,vplus(X1,v1))
=> leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
fof(f11,axiom,
! [X0,X1] :
( greater(X0,X1)
=> geq(X0,vplus(X1,v1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
fof(f12,axiom,
! [X0] : geq(X0,v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
fof(f13,axiom,
! [X0,X1,X2,X3] :
( ( geq(X0,X1)
& geq(X2,X3) )
=> geq(vplus(X0,X2),vplus(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(223, 0), 0)') ).
fof(f14,axiom,
! [X0,X1,X2,X3] :
( ( ( greater(X0,X1)
& geq(X2,X3) )
| ( geq(X0,X1)
& greater(X2,X3) ) )
=> greater(vplus(X0,X2),vplus(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(216), 0), 0)') ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( ( greater(X0,X1)
& greater(X2,X3) )
=> greater(vplus(X0,X2),vplus(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
fof(f16,axiom,
! [X0,X1,X2] :
( less(vplus(X0,X2),vplus(X1,X2))
=> less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
fof(f17,axiom,
! [X0,X1,X2] :
( vplus(X0,X2) = vplus(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
fof(f18,axiom,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
=> greater(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
fof(f19,axiom,
! [X0,X1,X2] :
( less(X0,X1)
=> less(vplus(X0,X2),vplus(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
fof(f20,axiom,
! [X0,X1,X2] :
( X0 = X1
=> vplus(X0,X2) = vplus(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
fof(f21,axiom,
! [X0,X1,X2] :
( greater(X0,X1)
=> greater(vplus(X0,X2),vplus(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
fof(f22,axiom,
! [X0,X1] : greater(vplus(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( leq(X0,X1)
& leq(X1,X2) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).
fof(f24,axiom,
! [X0,X1,X2] :
( ( ( less(X0,X1)
& leq(X1,X2) )
| ( leq(X0,X1)
& less(X1,X2) ) )
=> less(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( less(X0,X1)
& less(X1,X2) )
=> less(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
fof(f26,axiom,
! [X0,X1] :
( leq(X0,X1)
=> geq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
fof(f27,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(f28,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(f29,axiom,
! [X0,X1] :
( less(X0,X1)
=> greater(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof(f30,axiom,
! [X0,X1] :
( greater(X0,X1)
=> less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof(f31,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(f32,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof(f33,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof(f34,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof(f35,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(f36,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(f37,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(f38,axiom,
! [X0,X1] :
( ~ ? [X2] : X1 = vplus(X0,X2)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f39,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(f40,axiom,
! [X0,X1] :
( ~ ? [X2] : X0 = vplus(X1,X2)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof(f41,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(f42,axiom,
! [X0,X1] : X1 != vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof(f43,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f44,axiom,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof(f45,axiom,
! [X0] : vplus(v1,X0) = vsucc(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f46,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(f47,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(f48,axiom,
! [X0] :
( X0 != v1
=> X0 = vsucc(vskolem2(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof(f49,axiom,
! [X0] : vsucc(X0) != X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof(f50,axiom,
! [X0,X1] :
( X0 != X1
=> vsucc(X0) != vsucc(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
fof(f51,axiom,
! [X0,X1] :
( vsucc(X0) = vsucc(X1)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
fof(f52,axiom,
! [X0] : vsucc(X0) != v1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
fof(f53,plain,
! [X0] : vd470 != vplus(vd471,X0),
inference(ennf_transformation,[],[f2]) ).
fof(f89,plain,
! [X0,X1] :
( ( ~ greater(X1,X0)
| ? [X2] : X1 = vplus(X0,X2) )
& ( ! [X2] : vplus(X0,X2) != X1
| greater(X1,X0) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f90,plain,
! [X0,X1] :
( ( ~ greater(X1,X0)
| ? [X3] : vplus(X0,X3) = X1 )
& ( ! [X2] : vplus(X0,X2) != X1
| greater(X1,X0) ) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ( ~ greater(X1,X0)
| vplus(X0,sK1(X0,X1)) = X1 )
& ( ! [X2] : vplus(X0,X2) != X1
| greater(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f90]) ).
fof(f93,plain,
! [X0] : vd470 != vplus(vd471,X0),
inference(cnf_transformation,[],[f53]) ).
fof(f94,plain,
greater(vd470,vd471),
inference(cnf_transformation,[],[f3]) ).
fof(f135,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| vplus(X0,sK1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] : vplus(vd471,X0) != vd470,
inference(cnf_transformation,[],[f93]) ).
tcf(c_50,plain,
greater(vd470,vd471),
inference(cnf_transformation,[],[f94]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( ( vplus(X1,sK1(X1,X0)) = X0 )
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_793,negated_conjecture,
! [X0: $i] : vplus(vd471,X0) != vd470,
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_1596,plain,
( ( vplus(vd471,sK1(vd471,vd470)) = vd470 )
| ~ greater(vd470,vd471) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_2291,plain,
vplus(vd471,sK1(vd471,vd470)) != vd470,
inference(instantiation,[status(thm)],[c_793]) ).
tcf(c_2292,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2291,c_1596,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM850+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.36 % Computer : n012.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Thu Sep 24 05:34:26 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.39 Running first-order theorem proving
% 0.08/5.39 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
% 0.12/5.40
% 0.12/5.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/5.40
% 0.12/5.40 % Detected problem language: tptp
% 0.12/5.41 % Proving...
% 1.75/6.16 % SZS status Started for theBenchmark.p
% 1.75/6.16 % SZS status Theorem for theBenchmark.p
% 1.75/6.16
% 1.75/6.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.75/6.16
% 1.75/6.16 % ------ iProver source info
% 1.75/6.16
% 1.75/6.16 % git: date: 2026-07-19 20:42:38 +0200
% 1.75/6.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.75/6.16 % git: non_committed_changes: false
% 1.75/6.16
% 1.75/6.16 % ------ Parsing...
% 1.75/6.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.75/6.16
% 1.75/6.16 % ------ 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 %
% 1.75/6.16
% 1.75/6.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.75/6.16
% 1.75/6.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.75/6.16 % ------ Proving...
% 1.75/6.16 % ------ Problem Properties
% 1.75/6.16
% 1.75/6.16 %
% 1.75/6.16 % clauses 49
% 1.75/6.16 % conjectures 1
% 1.75/6.16 % EPR 19
% 1.75/6.16 % Horn 44
% 1.75/6.16 % unary 20
% 1.75/6.16 % binary 17
% 1.75/6.16 % lits 90
% 1.75/6.16 % lits eq 26
% 1.75/6.16 % fd_pure 0
% 1.75/6.16 % fd_pseudo 0
% 1.75/6.16 % fd_cond 0
% 1.75/6.16 % fd_pseudo_cond 5
% 1.75/6.16 % AC symbols 2
% 1.75/6.16
% 1.75/6.16 % ------ Schedule dynamic 5 is on
% 1.75/6.16
% 1.75/6.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.75/6.16
% 1.75/6.16
% 1.75/6.16 % ------
% 1.75/6.16 % Current options:
% 1.75/6.16 % ------
% 1.75/6.16
% 1.75/6.16
% 1.75/6.16 %
% 1.75/6.16
% 1.75/6.16 % ------ Proving...
% 1.75/6.16 %
% 1.75/6.16
% 1.75/6.16 % SZS status Theorem for theBenchmark.p
% 1.75/6.16
% 1.75/6.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.75/6.16
% 1.75/6.16
%------------------------------------------------------------------------------