%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM838+1 : 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 : n013.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 2.51s 1.15s
% Output : CNFRefutation 2.51s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f2ERROR: Could not build tree for root c_4912ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
greater(vd301,vd302),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(195), 304, 0)') ).
fof(f4,axiom,
! [X0,X1,X2] :
( less(X1,X2)
=> less(vplus(X1,X0),vplus(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 0)') ).
fof(f5,axiom,
! [X0,X1,X2] :
( less(X1,X2)
=> greater(vplus(X2,X0),vplus(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 1)') ).
fof(f6,axiom,
! [X0,X1,X2] :
( less(X1,X2)
=> greater(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 2)') ).
fof(f7,axiom,
! [X0,X1,X2] :
( X1 = X2
=> vplus(X1,X0) = vplus(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 3)') ).
fof(f8,axiom,
! [X0,X1,X2] :
( greater(X1,X2)
=> greater(vplus(X1,X0),vplus(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 4)') ).
fof(f9,axiom,
! [X0,X1,X2] :
( greater(X1,X2)
=> vplus(vskolem7(X1,X2),vplus(X2,X0)) = vplus(vplus(X2,X0),vskolem7(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 5)') ).
fof(f10,axiom,
! [X0,X1,X2] :
( greater(X1,X2)
=> vplus(vplus(vskolem7(X1,X2),X2),X0) = vplus(vskolem7(X1,X2),vplus(X2,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 6)') ).
fof(f11,axiom,
! [X0,X1,X2] :
( greater(X1,X2)
=> vplus(vplus(X2,vskolem7(X1,X2)),X0) = vplus(vplus(vskolem7(X1,X2),X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 7)') ).
fof(f12,axiom,
! [X0,X1,X2] :
( greater(X1,X2)
=> vplus(X1,X0) = vplus(vplus(X2,vskolem7(X1,X2)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 8)') ).
fof(f13,axiom,
! [X0,X1,X2] :
( greater(X1,X2)
=> X1 = vplus(X2,vskolem7(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(proof(196), 0), 9)') ).
fof(f14,axiom,
! [X0,X1] : greater(vplus(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof(f15,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(f16,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(f17,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(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
=> geq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
fof(f19,axiom,
! [X0,X1] :
( geq(X0,X1)
=> leq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
fof(f20,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(f21,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(f22,axiom,
! [X0,X1] :
( less(X0,X1)
=> greater(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof(f23,axiom,
! [X0,X1] :
( greater(X0,X1)
=> less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof(f24,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(f25,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
fof(f26,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof(f27,axiom,
! [X0,X1] :
( ~ greater(X0,X1)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
fof(f28,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(f29,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(f30,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(f31,axiom,
! [X0,X1] :
( ~ ? [X2] : X1 = vplus(X0,X2)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f32,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(f33,axiom,
! [X0,X1] :
( ~ ? [X2] : X0 = vplus(X1,X2)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof(f34,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(f35,axiom,
! [X0,X1] : X1 != vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof(f36,axiom,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f37,axiom,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof(f38,axiom,
! [X0] : vplus(v1,X0) = vsucc(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f39,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(f40,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(f41,axiom,
! [X0] :
( X0 != v1
=> X0 = vsucc(vskolem2(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof(f42,axiom,
! [X0] : vsucc(X0) != X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof(f43,axiom,
! [X0,X1] :
( X0 != X1
=> vsucc(X0) != vsucc(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
fof(f44,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(f45,axiom,
! [X0] : vsucc(X0) != v1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
fof(f46,plain,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(flattening,[],[f2]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ greater(X1,X2)
| greater(vplus(X1,X0),vplus(X2,X0)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f88,plain,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(cnf_transformation,[],[f46]) ).
fof(f89,plain,
greater(vd301,vd302),
inference(cnf_transformation,[],[f3]) ).
fof(f94,plain,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| greater(vplus(X1,X0),vplus(X2,X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f129,plain,
! [X0,X1] : vplus(X1,X0) = vplus(X0,X1),
inference(cnf_transformation,[],[f36]) ).
fof(f132,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_49,negated_conjecture,
~ greater(vplus(vd301,vd303),vplus(vd302,vd303)),
inference(cnf_transformation,[],[f88]) ).
tcf(c_50,plain,
greater(vd301,vd302),
inference(cnf_transformation,[],[f89]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(vplus(X0,X2),vplus(X1,X2))
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f129]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f132]) ).
tcf(c_116,negated_conjecture,
~ greater(vplus(vd301,vd303),vplus(vd303,vd302)),
inference(theory_normalisation,[status(thm)],[c_49,c_91,c_89]) ).
tcf(c_639,definition,
iPr_def_10 = vplus(vd301,vd303),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_640,definition,
iPr_def_11 = vplus(vd303,vd302),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_641,negated_conjecture,
~ greater(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_116,c_640,c_639]) ).
tcf(c_1280,plain,
! [X0: $i] :
( greater(iPr_def_10,vplus(X0,vd303))
| ~ greater(vd301,X0) ),
inference(superposition,[status(thm)],[c_639,c_54]) ).
tcf(c_1559,plain,
! [X0: $i] :
( greater(iPr_def_10,vplus(vd303,X0))
| ~ greater(vd301,X0) ),
inference(superposition,[status(thm)],[c_89,c_1280]) ).
tcf(c_4905,plain,
( greater(iPr_def_10,iPr_def_11)
| ~ greater(vd301,vd302) ),
inference(superposition,[status(thm)],[c_640,c_1559]) ).
tcf(c_4912,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4905,c_641,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM838+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.34 % Computer : n013.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Thu Sep 24 05:32:06 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.40 % Proving...
% 2.51/1.15 % SZS status Started for theBenchmark.p
% 2.51/1.15 % SZS status Theorem for theBenchmark.p
% 2.51/1.15
% 2.51/1.15 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.51/1.15
% 2.51/1.15 % ------ iProver source info
% 2.51/1.15
% 2.51/1.15 % git: date: 2026-07-19 20:42:38 +0200
% 2.51/1.15 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.51/1.15 % git: non_committed_changes: false
% 2.51/1.15
% 2.51/1.15 % ------ Parsing...
% 2.51/1.15 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.51/1.15
% 2.51/1.15 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.51/1.15
% 2.51/1.15 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.51/1.15
% 2.51/1.15 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.51/1.15 % ------ Proving...
% 2.51/1.15 % ------ Problem Properties
% 2.51/1.15
% 2.51/1.15 %
% 2.51/1.15 % clauses 35
% 2.51/1.15 % conjectures 1
% 2.51/1.15 % EPR 17
% 2.51/1.15 % Horn 30
% 2.51/1.15 % unary 13
% 2.51/1.15 % binary 14
% 2.51/1.15 % lits 65
% 2.51/1.15 % lits eq 20
% 2.51/1.15 % fd_pure 0
% 2.51/1.15 % fd_pseudo 0
% 2.51/1.15 % fd_cond 0
% 2.51/1.15 % fd_pseudo_cond 4
% 2.51/1.15 % AC symbols 1
% 2.51/1.15
% 2.51/1.15 % ------ Schedule dynamic 5 is on
% 2.51/1.15
% 2.51/1.15 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.51/1.15
% 2.51/1.15
% 2.51/1.15 % ------
% 2.51/1.15 % Current options:
% 2.51/1.15 % ------
% 2.51/1.15
% 2.51/1.15
% 2.51/1.15 %
% 2.51/1.15
% 2.51/1.15 % ------ Proving...
% 2.51/1.15 %
% 2.51/1.15
% 2.51/1.15 % SZS status Theorem for theBenchmark.p
% 2.51/1.15
% 2.51/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.51/1.15
% 2.51/1.15
%------------------------------------------------------------------------------