TSTP Solution File: NUM855+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM855+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:50:56 EDT 2024
% Result : Theorem 7.83s 1.71s
% Output : CNFRefutation 7.83s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f207)
% Comments :
%------------------------------------------------------------------------------
fof(f166,plain,
! [X0,X1] :
( ? [X3] : vplus(X0,X3) = X1
=> vplus(X0,sK1(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f168,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
=> vplus(X0,sK2(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f169,plain,
! [X0,X1] :
( ? [X3] : vplus(X1,X3) = X0
=> vplus(X1,sK3(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
cnf(c_49,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(cnf_transformation,[],[f171]) ).
cnf(c_51,plain,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
inference(cnf_transformation,[],[f173]) ).
cnf(c_53,plain,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(cnf_transformation,[],[f175]) ).
cnf(c_61,plain,
vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
inference(cnf_transformation,[],[f184]) ).
cnf(c_63,plain,
vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f186]) ).
cnf(c_82,plain,
( ~ less(X0,X1)
| ~ leq(X1,X2)
| less(X0,X2) ),
inference(cnf_transformation,[],[f207]) ).
cnf(c_88,plain,
( ~ less(X0,X1)
| leq(X0,X1) ),
inference(cnf_transformation,[],[f212]) ).
cnf(c_93,plain,
( ~ less(X0,X1)
| greater(X1,X0) ),
inference(cnf_transformation,[],[f217]) ).
cnf(c_94,plain,
( ~ greater(X0,X1)
| less(X1,X0) ),
inference(cnf_transformation,[],[f218]) ).
cnf(c_109,plain,
vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f233]) ).
cnf(c_1121,plain,
( ~ less(vmul(vd509,vd512),vmul(vd511,vd508))
| greater(vmul(vd511,vd508),vmul(vd509,vd512)) ),
inference(instantiation,[status(thm)],[c_93]) ).
cnf(c_1250,plain,
( ~ leq(X0,vmul(vd511,vd508))
| ~ less(X1,X0)
| less(X1,vmul(vd511,vd508)) ),
inference(instantiation,[status(thm)],[c_82]) ).
cnf(c_2356,plain,
( ~ less(vmul(vd509,vd512),vmul(vd509,vd511))
| ~ leq(vmul(vd509,vd511),vmul(vd511,vd508))
| less(vmul(vd509,vd512),vmul(vd511,vd508)) ),
inference(instantiation,[status(thm)],[c_1250]) ).
fof(f48,axiom,
! [X80,X81] :
( greater(X81,X80)
<=> ? [X82] : vplus(X80,X82) = X81 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f261,plain,
! [X2,X0] : greater(vplus(X0,X2),X0),
inference(equality_resolution,[],[f226]) ).
fof(f57,axiom,
! [X96] : vplus(v1,X96) = vsucc(X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f243,plain,
! [X0] : v1 != vsucc(X0),
inference(cnf_transformation,[],[f120]) ).
fof(f104,plain,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : vplus(X0,X2) = X1 ),
inference(rectify,[],[f48]) ).
fof(f113,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(rectify,[],[f57]) ).
fof(f115,plain,
! [X0,X1] :
( vsucc(X0) = vplus(X0,v1)
& vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)) ),
inference(rectify,[],[f59]) ).
fof(f116,plain,
! [X0] :
( v1 != X0
=> vsucc(vskolem2(X0)) = X0 ),
inference(rectify,[],[f60]) ).
fof(f117,plain,
! [X0] : vsucc(X0) != X0,
inference(rectify,[],[f61]) ).
fof(f118,plain,
! [X0,X1] :
( X0 != X1
=> vsucc(X0) != vsucc(X1) ),
inference(rectify,[],[f62]) ).
fof(f119,plain,
! [X0,X1] :
( vsucc(X0) = vsucc(X1)
=> X0 = X1 ),
inference(rectify,[],[f63]) ).
fof(f120,plain,
! [X0] : v1 != vsucc(X0),
inference(rectify,[],[f64]) ).
fof(f153,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(ennf_transformation,[],[f116]) ).
fof(f154,plain,
! [X0,X1] :
( vsucc(X0) != vsucc(X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f118]) ).
fof(f155,plain,
! [X0,X1] :
( X0 = X1
| vsucc(X0) != vsucc(X1) ),
inference(ennf_transformation,[],[f119]) ).
fof(f164,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : vplus(X0,X2) = X1
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f104]) ).
fof(f165,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f164]) ).
fof(f167,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( vplus(X0,sK1(X0,X1)) = X1
| ~ greater(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f165,f166]) ).
fof(f49,axiom,
! [X83,X84] :
( ? [X86] : vplus(X83,X86) = X84
| ? [X85] : vplus(X84,X85) = X83
| X83 = X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof(f225,plain,
! [X0,X1] :
( vplus(X0,sK1(X0,X1)) = X1
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f105,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
| ? [X3] : vplus(X1,X3) = X0
| X0 = X1 ),
inference(rectify,[],[f49]) ).
fof(f170,plain,
! [X0,X1] :
( vplus(X0,sK2(X0,X1)) = X1
| vplus(X1,sK3(X0,X1)) = X0
| X0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f105,f169,f168]) ).
fof(f50,axiom,
! [X83,X84] :
( ~ ? [X86] : vplus(X83,X86) = X84
| X83 != X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f227,plain,
! [X0,X1] :
( vplus(X0,sK2(X0,X1)) = X1
| vplus(X1,sK3(X0,X1)) = X0
| X0 = X1 ),
inference(cnf_transformation,[],[f170]) ).
fof(f106,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| X0 != X1 ),
inference(rectify,[],[f50]) ).
fof(f149,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| X0 != X1 ),
inference(ennf_transformation,[],[f106]) ).
fof(f226,plain,
! [X2,X0,X1] :
( greater(X1,X0)
| vplus(X0,X2) != X1 ),
inference(cnf_transformation,[],[f167]) ).
fof(f228,plain,
! [X2,X0,X1] :
( vplus(X0,X2) != X1
| X0 != X1 ),
inference(cnf_transformation,[],[f149]) ).
fof(f51,axiom,
! [X83,X84] :
( ~ ? [X86] : vplus(X83,X86) = X84
| ~ ? [X85] : vplus(X84,X85) = X83 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof(f262,plain,
! [X2,X0] : vplus(X0,X2) != X0,
inference(equality_resolution,[],[f228]) ).
fof(f107,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| ~ ? [X3] : vplus(X1,X3) = X0 ),
inference(rectify,[],[f51]) ).
fof(f150,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| ! [X3] : vplus(X1,X3) != X0 ),
inference(ennf_transformation,[],[f107]) ).
fof(f229,plain,
! [X2,X3,X0,X1] :
( vplus(X0,X2) != X1
| vplus(X1,X3) != X0 ),
inference(cnf_transformation,[],[f150]) ).
fof(f52,axiom,
! [X83,X84] :
( ~ ? [X85] : vplus(X84,X85) = X83
| X83 != X84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof(f263,plain,
! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
inference(equality_resolution,[],[f229]) ).
fof(f108,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X1,X2) = X0
| X0 != X1 ),
inference(rectify,[],[f52]) ).
fof(f151,plain,
! [X0,X1] :
( ! [X2] : vplus(X1,X2) != X0
| X0 != X1 ),
inference(ennf_transformation,[],[f108]) ).
fof(f230,plain,
! [X2,X0,X1] :
( vplus(X1,X2) != X0
| X0 != X1 ),
inference(cnf_transformation,[],[f151]) ).
fof(f53,axiom,
! [X87,X88] :
( X87 != X88
=> ! [X89] : vplus(X89,X87) != vplus(X89,X88) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof(f264,plain,
! [X2,X1] : vplus(X1,X2) != X1,
inference(equality_resolution,[],[f230]) ).
fof(f109,plain,
! [X0,X1] :
( X0 != X1
=> ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
inference(rectify,[],[f53]) ).
fof(f152,plain,
! [X0,X1] :
( ! [X2] : vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f109]) ).
fof(f54,axiom,
! [X90,X91] : vplus(X90,X91) != X91,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof(f231,plain,
! [X2,X0,X1] :
( vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f152]) ).
fof(f110,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(rectify,[],[f54]) ).
fof(f55,axiom,
! [X92,X93] : vplus(X93,X92) = vplus(X92,X93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f232,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(cnf_transformation,[],[f110]) ).
fof(f111,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(rectify,[],[f55]) ).
fof(f56,axiom,
! [X94,X95] : vplus(vsucc(X94),X95) = vsucc(vplus(X94,X95)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof(f233,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f111]) ).
fof(f112,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
inference(rectify,[],[f56]) ).
fof(f234,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
inference(cnf_transformation,[],[f112]) ).
fof(f235,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(cnf_transformation,[],[f113]) ).
fof(f58,axiom,
! [X97,X98,X99] : vplus(vplus(X97,X98),X99) = vplus(X97,vplus(X98,X99)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f246,plain,
! [X0,X1] : vplus(vplus(v1,X0),X1) = vplus(v1,vplus(X0,X1)),
inference(definition_unfolding,[],[f234,f235,f235]) ).
fof(f114,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(rectify,[],[f58]) ).
fof(f236,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f114]) ).
fof(f237,plain,
! [X0,X1] : vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)),
inference(cnf_transformation,[],[f115]) ).
fof(f60,axiom,
! [X102] :
( v1 != X102
=> vsucc(vskolem2(X102)) = X102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof(f248,plain,
! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1)),
inference(definition_unfolding,[],[f237,f235,f235]) ).
fof(f238,plain,
! [X0] : vsucc(X0) = vplus(X0,v1),
inference(cnf_transformation,[],[f115]) ).
fof(f59,axiom,
! [X100,X101] :
( vplus(X100,v1) = vsucc(X100)
& vplus(X100,vsucc(X101)) = vsucc(vplus(X100,X101)) ),
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(f247,plain,
! [X0] : vplus(v1,X0) = vplus(X0,v1),
inference(definition_unfolding,[],[f238,f235]) ).
fof(f239,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(cnf_transformation,[],[f153]) ).
fof(f61,axiom,
! [X103] : vsucc(X103) != X103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof(f249,plain,
! [X0] :
( vplus(v1,vskolem2(X0)) = X0
| v1 = X0 ),
inference(definition_unfolding,[],[f239,f235]) ).
fof(f240,plain,
! [X0] : vsucc(X0) != X0,
inference(cnf_transformation,[],[f117]) ).
fof(f62,axiom,
! [X104,X105] :
( X104 != X105
=> vsucc(X104) != vsucc(X105) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
fof(f250,plain,
! [X0] : vplus(v1,X0) != X0,
inference(definition_unfolding,[],[f240,f235]) ).
fof(f241,plain,
! [X0,X1] :
( vsucc(X0) != vsucc(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f154]) ).
fof(f63,axiom,
! [X106,X107] :
( vsucc(X106) = vsucc(X107)
=> X106 = X107 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
fof(f251,plain,
! [X0,X1] :
( vplus(v1,X0) != vplus(v1,X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f241,f235,f235]) ).
fof(f242,plain,
! [X0,X1] :
( X0 = X1
| vsucc(X0) != vsucc(X1) ),
inference(cnf_transformation,[],[f155]) ).
fof(f64,axiom,
! [X108] : v1 != vsucc(X108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
fof(f252,plain,
! [X0,X1] :
( X0 = X1
| vplus(v1,X0) != vplus(v1,X1) ),
inference(definition_unfolding,[],[f242,f235,f235]) ).
cnf(c_111,plain,
vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f236]) ).
cnf(c_148,negated_conjecture,
~ greater(vmul(vd511,vd508),vmul(vd509,vd512)),
inference(theory_normalisation,[status(thm)],[c_49,c_111,c_109,c_61,c_63]) ).
cnf(c_149,plain,
greater(vmul(vd509,vd511),vmul(vd509,vd512)),
inference(theory_normalisation,[status(thm)],[c_51,c_111,c_109,c_61,c_63]) ).
cnf(c_150,plain,
greater(vmul(vd511,vd508),vmul(vd509,vd511)),
inference(theory_normalisation,[status(thm)],[c_53,c_111,c_109,c_61,c_63]) ).
cnf(c_1676,plain,
less(vmul(vd509,vd512),vmul(vd509,vd511)),
inference(superposition,[status(thm)],[c_149,c_94]) ).
cnf(c_1730,plain,
less(vmul(vd509,vd511),vmul(vd511,vd508)),
inference(superposition,[status(thm)],[c_150,c_94]) ).
cnf(c_1736,plain,
leq(vmul(vd509,vd511),vmul(vd511,vd508)),
inference(superposition,[status(thm)],[c_1730,c_88]) ).
cnf(c_2358,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2356,c_1736,c_1676,c_1121,c_148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM855+1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 19:11:36 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.83/1.71 % SZS status Started for theBenchmark.p
% 7.83/1.71 % SZS status Theorem for theBenchmark.p
% 7.83/1.71
% 7.83/1.71 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.83/1.71
% 7.83/1.71 ------ iProver source info
% 7.83/1.71
% 7.83/1.71 git: date: 2024-05-02 19:28:25 +0000
% 7.83/1.71 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.83/1.71 git: non_committed_changes: false
% 7.83/1.71
% 7.83/1.71 ------ Parsing...
% 7.83/1.71 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.83/1.71
% 7.83/1.71 ------ 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
% 7.83/1.71
% 7.83/1.71 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.83/1.71
% 7.83/1.71 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.83/1.71 ------ Proving...
% 7.83/1.71 ------ Problem Properties
% 7.83/1.71
% 7.83/1.71
% 7.83/1.71 clauses 58
% 7.83/1.71 conjectures 1
% 7.83/1.71 EPR 21
% 7.83/1.71 Horn 53
% 7.83/1.71 unary 23
% 7.83/1.71 binary 23
% 7.83/1.71 lits 105
% 7.83/1.71 lits eq 27
% 7.83/1.71 fd_pure 0
% 7.83/1.71 fd_pseudo 0
% 7.83/1.71 fd_cond 0
% 7.83/1.71 fd_pseudo_cond 6
% 7.83/1.71 AC symbols 2
% 7.83/1.71
% 7.83/1.71 ------ Input Options Time Limit: Unbounded
% 7.83/1.71
% 7.83/1.71
% 7.83/1.71 ------
% 7.83/1.71 Current options:
% 7.83/1.71 ------
% 7.83/1.71
% 7.83/1.71
% 7.83/1.71
% 7.83/1.71
% 7.83/1.71 ------ Proving...
% 7.83/1.71
% 7.83/1.71
% 7.83/1.71 % SZS status Theorem for theBenchmark.p
% 7.83/1.71
% 7.83/1.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.83/1.71
% 7.83/1.72
%------------------------------------------------------------------------------