%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM853+1 : 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 : n019.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 02:26:55 PM UTC 2026
% Result : Theorem 4.46s 1.30s
% Output : CNFRefutation 4.46s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f2ERROR: Could not build tree for root c_2513ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(antec(307), 489, 0)') ).
fof(f4,axiom,
! [X0,X1,X2] :
( less(X1,X2)
=> less(vmul(X1,X0),vmul(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 0)') ).
fof(f5,axiom,
! [X0,X1,X2] :
( X1 = X2
=> vmul(X1,X0) = vmul(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 1)') ).
fof(f6,axiom,
! [X0,X1,X2] :
( greater(X1,X2)
=> greater(vmul(X1,X0),vmul(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(299, 0), 2)') ).
fof(f7,axiom,
! [X0,X1,X2] : vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
fof(f8,axiom,
! [X0,X1,X2] : vmul(X0,vplus(X1,X2)) = vplus(vmul(X0,X1),vmul(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
fof(f9,axiom,
! [X0,X1] : vmul(X0,X1) = vmul(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof(f10,axiom,
! [X0,X1] : vmul(vsucc(X0),X1) = vplus(vmul(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
fof(f11,axiom,
! [X0] : vmul(v1,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
fof(f12,axiom,
! [X0,X1] :
( vmul(X0,v1) = X0
& vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof(f13,axiom,
! [X0,X1] :
( less(X0,vplus(X1,v1))
=> leq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
fof(f14,axiom,
! [X0,X1] :
( greater(X0,X1)
=> geq(X0,vplus(X1,v1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
fof(f15,axiom,
! [X0] : geq(X0,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(228, 0), 0)') ).
fof(f16,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(f17,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(f18,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(f19,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(f20,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(f21,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(f22,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(f23,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(f24,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(f25,axiom,
! [X0,X1] : greater(vplus(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof(f26,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(f27,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(f28,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(f29,axiom,
! [X0,X1] :
( leq(X0,X1)
=> geq(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
fof(f30,axiom,
! [X0,X1] :
( geq(X0,X1)
=> leq(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
fof(f31,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(f32,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(f33,axiom,
! [X0,X1] :
( less(X0,X1)
=> greater(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof(f34,axiom,
! [X0,X1] :
( greater(X0,X1)
=> less(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof(f35,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(f36,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof(f37,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof(f38,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof(f39,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(f40,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(f41,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(f42,axiom,
! [X0,X1] :
( ~ ? [X2] : X1 = vplus(X0,X2)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f43,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(f44,axiom,
! [X0,X1] :
( ~ ? [X2] : X0 = vplus(X1,X2)
| X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof(f45,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(f46,axiom,
! [X0,X1] : X1 != vplus(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof(f47,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f48,axiom,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof(f49,axiom,
! [X0] : vplus(v1,X0) = vsucc(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f50,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(f51,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(f52,axiom,
! [X0] :
( X0 != v1
=> X0 = vsucc(vskolem2(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof(f53,axiom,
! [X0] : vsucc(X0) != X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof(f54,axiom,
! [X0,X1] :
( X0 != X1
=> vsucc(X0) != vsucc(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
fof(f55,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(f56,axiom,
! [X0] : vsucc(X0) != v1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
fof(f57,plain,
~ greater(vd486,vd488),
inference(flattening,[],[f2]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ greater(X1,X2)
| greater(vmul(X1,X0),vmul(X2,X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f81,plain,
! [X0,X1] :
( ~ less(X0,X1)
| greater(X1,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f82,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| less(X1,X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f101,plain,
~ greater(vd486,vd488),
inference(cnf_transformation,[],[f57]) ).
fof(f102,plain,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
inference(cnf_transformation,[],[f3]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| greater(vmul(X1,X0),vmul(X2,X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f139,plain,
! [X0,X1] :
( ~ less(X0,X1)
| greater(X1,X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f140,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| less(X1,X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f141,plain,
! [X0,X1] :
( less(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f142,plain,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f143,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f180,plain,
! [X1] : ~ less(X1,X1),
inference(equality_resolution,[],[f142]) ).
tcf(c_49,negated_conjecture,
~ greater(vd486,vd488),
inference(cnf_transformation,[],[f101]) ).
tcf(c_50,plain,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
inference(cnf_transformation,[],[f102]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(vmul(X0,X2),vmul(X1,X2))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( greater(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( less(X1,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( less(X0,X1)
| greater(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_88,plain,
! [X0: $i] : ~ less(X0,X0),
inference(cnf_transformation,[],[f180]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_1351,plain,
less(vmul(vd488,vd487),vmul(vd486,vd487)),
inference(superposition,[status(thm)],[c_50,c_86]) ).
tcf(c_1390,plain,
~ greater(vmul(vd488,vd487),vmul(vd486,vd487)),
inference(superposition,[status(thm)],[c_1351,c_89]) ).
tcf(c_1533,plain,
! [X0: $i,X1: $i] :
( greater(X1,X0)
| greater(X0,X1)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_87,c_85]) ).
tcf(c_1660,plain,
~ greater(vd488,vd486),
inference(superposition,[status(thm)],[c_52,c_1390]) ).
tcf(c_1962,plain,
less(vmul(vd488,vd487),vmul(vd486,vd487)),
inference(superposition,[status(thm)],[c_50,c_86]) ).
tcf(c_2432,plain,
( greater(vd488,vd486)
| ( vd486 = vd488 ) ),
inference(superposition,[status(thm)],[c_1533,c_49]) ).
tcf(c_2437,plain,
( greater(vd486,vd488)
| ( vd486 = vd488 ) ),
inference(superposition,[status(thm)],[c_1533,c_1660]) ).
tcf(c_2470,plain,
vd486 = vd488,
inference(global_subsumption_just,[status(thm)],[c_2432,c_49,c_2437]) ).
tcf(c_2473,plain,
less(vmul(vd486,vd487),vmul(vd486,vd487)),
inference(superposition,[status(thm)],[c_2470,c_1962]) ).
tcf(c_2513,plain,
$false,
inference(superposition,[status(thm)],[c_2473,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM853+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 05:35:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 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...
% 4.46/1.30 % SZS status Started for theBenchmark.p
% 4.46/1.30 % SZS status Theorem for theBenchmark.p
% 4.46/1.30
% 4.46/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.46/1.30
% 4.46/1.30 % ------ iProver source info
% 4.46/1.30
% 4.46/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.46/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.46/1.30 % git: non_committed_changes: false
% 4.46/1.30
% 4.46/1.30 % ------ Parsing...
% 4.46/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.46/1.30
% 4.46/1.30 % ------ 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 %
% 4.46/1.30
% 4.46/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.46/1.30
% 4.46/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.46/1.30 % ------ Proving...
% 4.46/1.30 % ------ Problem Properties
% 4.46/1.30
% 4.46/1.30 %
% 4.46/1.30 % clauses 52
% 4.46/1.30 % conjectures 1
% 4.46/1.30 % EPR 20
% 4.46/1.30 % Horn 47
% 4.46/1.30 % unary 20
% 4.46/1.30 % binary 20
% 4.46/1.30 % lits 96
% 4.46/1.30 % lits eq 25
% 4.46/1.30 % fd_pure 0
% 4.46/1.30 % fd_pseudo 0
% 4.46/1.30 % fd_cond 0
% 4.46/1.30 % fd_pseudo_cond 5
% 4.46/1.30 % AC symbols 2
% 4.46/1.30
% 4.46/1.30 % ------ Input Options Time Limit: Unbounded
% 4.46/1.30
% 4.46/1.30
% 4.46/1.30 % ------
% 4.46/1.30 % Current options:
% 4.46/1.30 % ------
% 4.46/1.30
% 4.46/1.30
% 4.46/1.30 %
% 4.46/1.30
% 4.46/1.30 % ------ Proving...
% 4.46/1.30 %
% 4.46/1.30
% 4.46/1.30 % SZS status Theorem for theBenchmark.p
% 4.46/1.30
% 4.46/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.46/1.30
% 4.46/1.30
%------------------------------------------------------------------------------