%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM843+2 : 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 : n002.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 02:26:52 PM UTC 2026
% Result : Theorem 1.84s 6.22s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f2ERROR: Could not build tree for root c_1756ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
~ leq(vd390,vd391),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(243), 393, 0)') ).
fof(f4,axiom,
less(vd390,vplus(vd391,v1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(243), 392, 0)') ).
fof(f5,axiom,
! [X0,X1] :
( greater(X0,X1)
=> geq(X0,vplus(X1,v1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
fof(f6,axiom,
! [X0] : geq(X0,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( ( geq(X0,X1)
& geq(X2,X3) )
=> geq(vplus(X0,X2),vplus(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(223, 0), 0)') ).
fof(f8,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/sandbox/benchmark/theBenchmark.p','ass(cond(goal(216), 0), 0)') ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ( greater(X0,X1)
& greater(X2,X3) )
=> greater(vplus(X0,X2),vplus(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(209, 0), 0)') ).
fof(f10,axiom,
! [X0,X1,X2] :
( less(vplus(X0,X2),vplus(X1,X2))
=> less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
fof(f11,axiom,
! [X0,X1,X2] :
( vplus(X0,X2) = vplus(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
fof(f12,axiom,
! [X0,X1,X2] :
( greater(vplus(X0,X2),vplus(X1,X2))
=> greater(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
fof(f13,axiom,
! [X0,X1,X2] :
( less(X0,X1)
=> less(vplus(X0,X2),vplus(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
fof(f14,axiom,
! [X0,X1,X2] :
( X0 = X1
=> vplus(X0,X2) = vplus(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
fof(f15,axiom,
! [X0,X1,X2] :
( greater(X0,X1)
=> greater(vplus(X0,X2),vplus(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
fof(f16,axiom,
! [X0,X1] : greater(vplus(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof(f17,axiom,
! [X0,X1,X2] :
( ( leq(X0,X1)
& leq(X1,X2) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(184, 0), 0)') ).
fof(f18,axiom,
! [X0,X1,X2] :
( ( ( less(X0,X1)
& leq(X1,X2) )
| ( leq(X0,X1)
& less(X1,X2) ) )
=> less(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(177), 0), 0)') ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( less(X0,X1)
& less(X1,X2) )
=> less(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(168, 0), 0)') ).
fof(f20,axiom,
! [X0,X1] :
( leq(X0,X1)
=> geq(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
fof(f21,axiom,
! [X0,X1] :
( geq(X0,X1)
=> leq(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
fof(f22,axiom,
! [X0,X1] :
( leq(X1,X0)
<=> ( X1 = X0
| less(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
fof(f23,axiom,
! [X0,X1] :
( geq(X1,X0)
<=> ( X1 = X0
| greater(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
fof(f24,axiom,
! [X0,X1] :
( less(X0,X1)
=> greater(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof(f25,axiom,
! [X0,X1] :
( greater(X0,X1)
=> less(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof(f26,axiom,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof(f27,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof(f28,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof(f29,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof(f30,axiom,
! [X0,X1] :
( less(X1,X0)
<=> ? [X2] : X0 = vplus(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof(f31,axiom,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : X1 = vplus(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f32,axiom,
! [X0,X1] :
( ? [X3] : X1 = vplus(X0,X3)
| ? [X2] : X0 = vplus(X1,X2)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof(f33,axiom,
! [X0,X1] :
( ~ ? [X2] : X1 = vplus(X0,X2)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f34,axiom,
! [X0,X1] :
( ~ ? [X3] : X1 = vplus(X0,X3)
| ~ ? [X2] : X0 = vplus(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof(f35,axiom,
! [X0,X1] :
( ~ ? [X2] : X0 = vplus(X1,X2)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof(f36,axiom,
! [X0,X1] :
( X0 != X1
=> ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof(f37,axiom,
! [X0,X1] : X1 != vplus(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof(f38,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f39,axiom,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof(f40,axiom,
! [X0] : vplus(v1,X0) = vsucc(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f41,axiom,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f42,axiom,
! [X0,X1] :
( vplus(X0,v1) = vsucc(X0)
& vplus(X0,vsucc(X1)) = vsucc(vplus(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof(f43,axiom,
! [X0] :
( X0 != v1
=> X0 = vsucc(vskolem2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof(f44,axiom,
! [X0] : vsucc(X0) != X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof(f45,axiom,
! [X0,X1] :
( X0 != X1
=> vsucc(X0) != vsucc(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
fof(f46,axiom,
! [X0,X1] :
( vsucc(X0) = vsucc(X1)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
fof(f47,axiom,
! [X0] : vsucc(X0) != v1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
fof(f48,plain,
~ greater(vd390,vd391),
inference(flattening,[],[f2]) ).
fof(f67,plain,
! [X0,X1] :
( ~ geq(X0,X1)
| leq(X1,X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f68,plain,
! [X0,X1] :
( ~ less(X0,X1)
| greater(X1,X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f69,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| less(X1,X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f77,plain,
! [X0,X1] :
( ( ~ leq(X1,X0)
| X1 = X0
| less(X1,X0) )
& ( ( X0 != X1
& ~ less(X1,X0) )
| leq(X1,X0) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f78,plain,
! [X0,X1] :
( ( ~ leq(X1,X0)
| X1 = X0
| less(X1,X0) )
& ( ( X0 != X1
& ~ less(X1,X0) )
| leq(X1,X0) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ( ~ geq(X1,X0)
| X1 = X0
| greater(X1,X0) )
& ( ( X0 != X1
& ~ greater(X1,X0) )
| geq(X1,X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f80,plain,
! [X0,X1] :
( ( ~ geq(X1,X0)
| X1 = X0
| greater(X1,X0) )
& ( ( X0 != X1
& ~ greater(X1,X0) )
| geq(X1,X0) ) ),
inference(flattening,[],[f79]) ).
fof(f88,plain,
~ greater(vd390,vd391),
inference(cnf_transformation,[],[f48]) ).
fof(f89,plain,
~ leq(vd390,vd391),
inference(cnf_transformation,[],[f3]) ).
fof(f109,plain,
! [X0,X1] :
( ~ geq(X0,X1)
| leq(X1,X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f111,plain,
! [X0,X1] :
( X0 != X1
| leq(X1,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f115,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| geq(X1,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f116,plain,
! [X0,X1] :
( ~ less(X0,X1)
| greater(X1,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| less(X1,X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f118,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f152,plain,
! [X1] : leq(X1,X1),
inference(equality_resolution,[],[f111]) ).
tcf(c_49,negated_conjecture,
~ greater(vd390,vd391),
inference(cnf_transformation,[],[f88]) ).
tcf(c_50,plain,
~ leq(vd390,vd391),
inference(cnf_transformation,[],[f89]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( leq(X1,X0)
| ~ geq(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_71,plain,
! [X0: $i] : leq(X0,X0),
inference(cnf_transformation,[],[f152]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( geq(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( less(X0,X1)
| greater(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_753,negated_conjecture,
~ greater(vd390,vd391),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_1343,plain,
! [X0: $i,X1: $i] :
( greater(X1,X0)
| greater(X0,X1)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_78,c_76]) ).
tcf(c_1481,plain,
( greater(vd391,vd390)
| ( vd390 = vd391 ) ),
inference(superposition,[status(thm)],[c_1343,c_753]) ).
tcf(c_1515,plain,
( less(vd390,vd391)
| ( vd390 = vd391 ) ),
inference(superposition,[status(thm)],[c_1481,c_77]) ).
tcf(c_1516,plain,
( geq(vd391,vd390)
| ( vd390 = vd391 ) ),
inference(superposition,[status(thm)],[c_1481,c_73]) ).
tcf(c_1548,plain,
( leq(vd390,vd391)
| ~ geq(vd391,vd390) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_1747,plain,
vd390 = vd391,
inference(global_subsumption_just,[status(thm)],[c_1515,c_50,c_1516,c_1548]) ).
tcf(c_1754,plain,
~ leq(vd390,vd390),
inference(demodulation,[status(thm)],[c_50,c_1747]) ).
tcf(c_1756,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1754,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM843+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.40 % Computer : n002.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.02/5.40 % CPULimit : 300
% 0.02/5.40 % WCLimit : 300
% 0.02/5.40 % DateTime : Thu Sep 24 05:35:56 UTC 2026
% 0.02/5.40 % CPUTime :
% 0.02/5.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/5.44 Running first-order theorem proving
% 0.02/5.44 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
% 0.02/5.45
% 0.02/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.02/5.45
% 0.02/5.45 % Detected problem language: tptp
% 0.02/5.46 % Proving...
% 1.84/6.22 % SZS status Started for theBenchmark.p
% 1.84/6.22 % SZS status Theorem for theBenchmark.p
% 1.84/6.22
% 1.84/6.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.84/6.22
% 1.84/6.22 % ------ iProver source info
% 1.84/6.22
% 1.84/6.22 % git: date: 2026-07-19 20:42:38 +0200
% 1.84/6.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.84/6.22 % git: non_committed_changes: false
% 1.84/6.22
% 1.84/6.22 % ------ Parsing...
% 1.84/6.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.84/6.22
% 1.84/6.22 % ------ 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 %
% 1.84/6.22
% 1.84/6.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.84/6.22
% 1.84/6.22 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.84/6.22 % ------ Proving...
% 1.84/6.22 % ------ Problem Properties
% 1.84/6.22
% 1.84/6.22 %
% 1.84/6.22 % clauses 43
% 1.84/6.22 % conjectures 1
% 1.84/6.22 % EPR 21
% 1.84/6.22 % Horn 38
% 1.84/6.22 % unary 14
% 1.84/6.22 % binary 17
% 1.84/6.22 % lits 84
% 1.84/6.22 % lits eq 18
% 1.84/6.22 % fd_pure 0
% 1.84/6.22 % fd_pseudo 0
% 1.84/6.22 % fd_cond 0
% 1.84/6.22 % fd_pseudo_cond 5
% 1.84/6.22 % AC symbols 1
% 1.84/6.22
% 1.84/6.22 % ------ Schedule dynamic 5 is on
% 1.84/6.22
% 1.84/6.22 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.84/6.22
% 1.84/6.22
% 1.84/6.22 % ------
% 1.84/6.22 % Current options:
% 1.84/6.22 % ------
% 1.84/6.22
% 1.84/6.22
% 1.84/6.22 %
% 1.84/6.22
% 1.84/6.22 % ------ Proving...
% 1.84/6.22 %
% 1.84/6.22
% 1.84/6.22 % SZS status Theorem for theBenchmark.p
% 1.84/6.22
% 1.84/6.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/6.22
% 1.84/6.22
%------------------------------------------------------------------------------