TSTP Solution File: NUM852+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM852+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.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 02:50:55 EDT 2024
% Result : Theorem 4.14s 1.20s
% Output : CNFRefutation 4.14s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f164)
% Comments :
%------------------------------------------------------------------------------
fof(f159,plain,
! [X0,X1] :
( ? [X3] : vplus(X0,X3) = X1
=> vplus(X0,sK1(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
=> vplus(X0,sK2(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
! [X0,X1] :
( ? [X3] : vplus(X1,X3) = X0
=> vplus(X1,sK3(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
cnf(c_49,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(cnf_transformation,[],[f164]) ).
cnf(c_50,plain,
greater(vd481,vd480),
inference(cnf_transformation,[],[f165]) ).
cnf(c_54,plain,
( ~ greater(X0,X1)
| vmul(vplus(X1,vskolem9(X0,X1)),vd469) = vmul(X0,vd469) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_56,plain,
vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
inference(cnf_transformation,[],[f172]) ).
cnf(c_57,plain,
vplus(vmul(X0,X1),vmul(X0,X2)) = vmul(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f173]) ).
cnf(c_58,plain,
vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f174]) ).
cnf(c_96,plain,
greater(vplus(X0,X1),X0),
inference(cnf_transformation,[],[f249]) ).
cnf(c_104,plain,
vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f221]) ).
cnf(c_1438,plain,
greater(vmul(X0,vplus(X1,X2)),vmul(X0,X1)),
inference(superposition,[status(thm)],[c_57,c_96]) ).
fof(f43,axiom,
! [X68,X69] :
( greater(X69,X68)
<=> ? [X70] : vplus(X68,X70) = X69 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f249,plain,
! [X2,X0] : greater(vplus(X0,X2),X0),
inference(equality_resolution,[],[f214]) ).
fof(f52,axiom,
! [X84] : vplus(v1,X84) = vsucc(X84),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f231,plain,
! [X0] : v1 != vsucc(X0),
inference(cnf_transformation,[],[f114]) ).
fof(f98,plain,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : vplus(X0,X2) = X1 ),
inference(rectify,[],[f43]) ).
fof(f107,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(rectify,[],[f52]) ).
fof(f109,plain,
! [X0,X1] :
( vsucc(X0) = vplus(X0,v1)
& vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)) ),
inference(rectify,[],[f54]) ).
fof(f110,plain,
! [X0] :
( v1 != X0
=> vsucc(vskolem2(X0)) = X0 ),
inference(rectify,[],[f55]) ).
fof(f111,plain,
! [X0] : vsucc(X0) != X0,
inference(rectify,[],[f56]) ).
fof(f112,plain,
! [X0,X1] :
( X0 != X1
=> vsucc(X0) != vsucc(X1) ),
inference(rectify,[],[f57]) ).
fof(f113,plain,
! [X0,X1] :
( vsucc(X0) = vsucc(X1)
=> X0 = X1 ),
inference(rectify,[],[f58]) ).
fof(f114,plain,
! [X0] : v1 != vsucc(X0),
inference(rectify,[],[f59]) ).
fof(f146,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(ennf_transformation,[],[f110]) ).
fof(f147,plain,
! [X0,X1] :
( vsucc(X0) != vsucc(X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f112]) ).
fof(f148,plain,
! [X0,X1] :
( X0 = X1
| vsucc(X0) != vsucc(X1) ),
inference(ennf_transformation,[],[f113]) ).
fof(f157,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : vplus(X0,X2) = X1
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f158,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f157]) ).
fof(f160,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])],[f158,f159]) ).
fof(f44,axiom,
! [X71,X72] :
( ? [X74] : vplus(X71,X74) = X72
| ? [X73] : vplus(X72,X73) = X71
| X71 = X72 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof(f213,plain,
! [X0,X1] :
( vplus(X0,sK1(X0,X1)) = X1
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f99,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
| ? [X3] : vplus(X1,X3) = X0
| X0 = X1 ),
inference(rectify,[],[f44]) ).
fof(f163,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])],[f99,f162,f161]) ).
fof(f45,axiom,
! [X71,X72] :
( ~ ? [X74] : vplus(X71,X74) = X72
| X71 != X72 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f215,plain,
! [X0,X1] :
( vplus(X0,sK2(X0,X1)) = X1
| vplus(X1,sK3(X0,X1)) = X0
| X0 = X1 ),
inference(cnf_transformation,[],[f163]) ).
fof(f100,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| X0 != X1 ),
inference(rectify,[],[f45]) ).
fof(f142,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| X0 != X1 ),
inference(ennf_transformation,[],[f100]) ).
fof(f214,plain,
! [X2,X0,X1] :
( greater(X1,X0)
| vplus(X0,X2) != X1 ),
inference(cnf_transformation,[],[f160]) ).
fof(f216,plain,
! [X2,X0,X1] :
( vplus(X0,X2) != X1
| X0 != X1 ),
inference(cnf_transformation,[],[f142]) ).
fof(f46,axiom,
! [X71,X72] :
( ~ ? [X74] : vplus(X71,X74) = X72
| ~ ? [X73] : vplus(X72,X73) = X71 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof(f250,plain,
! [X2,X0] : vplus(X0,X2) != X0,
inference(equality_resolution,[],[f216]) ).
fof(f101,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| ~ ? [X3] : vplus(X1,X3) = X0 ),
inference(rectify,[],[f46]) ).
fof(f143,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| ! [X3] : vplus(X1,X3) != X0 ),
inference(ennf_transformation,[],[f101]) ).
fof(f217,plain,
! [X2,X3,X0,X1] :
( vplus(X0,X2) != X1
| vplus(X1,X3) != X0 ),
inference(cnf_transformation,[],[f143]) ).
fof(f47,axiom,
! [X71,X72] :
( ~ ? [X73] : vplus(X72,X73) = X71
| X71 != X72 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof(f251,plain,
! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
inference(equality_resolution,[],[f217]) ).
fof(f102,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X1,X2) = X0
| X0 != X1 ),
inference(rectify,[],[f47]) ).
fof(f144,plain,
! [X0,X1] :
( ! [X2] : vplus(X1,X2) != X0
| X0 != X1 ),
inference(ennf_transformation,[],[f102]) ).
fof(f218,plain,
! [X2,X0,X1] :
( vplus(X1,X2) != X0
| X0 != X1 ),
inference(cnf_transformation,[],[f144]) ).
fof(f48,axiom,
! [X75,X76] :
( X75 != X76
=> ! [X77] : vplus(X77,X75) != vplus(X77,X76) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof(f252,plain,
! [X2,X1] : vplus(X1,X2) != X1,
inference(equality_resolution,[],[f218]) ).
fof(f103,plain,
! [X0,X1] :
( X0 != X1
=> ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
inference(rectify,[],[f48]) ).
fof(f145,plain,
! [X0,X1] :
( ! [X2] : vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f103]) ).
fof(f49,axiom,
! [X78,X79] : vplus(X78,X79) != X79,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof(f219,plain,
! [X2,X0,X1] :
( vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f145]) ).
fof(f104,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(rectify,[],[f49]) ).
fof(f50,axiom,
! [X80,X81] : vplus(X81,X80) = vplus(X80,X81),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f220,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(cnf_transformation,[],[f104]) ).
fof(f105,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(rectify,[],[f50]) ).
fof(f51,axiom,
! [X82,X83] : vplus(vsucc(X82),X83) = vsucc(vplus(X82,X83)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof(f221,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f105]) ).
fof(f106,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
inference(rectify,[],[f51]) ).
fof(f222,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
inference(cnf_transformation,[],[f106]) ).
fof(f223,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(cnf_transformation,[],[f107]) ).
fof(f53,axiom,
! [X85,X86,X87] : vplus(vplus(X85,X86),X87) = vplus(X85,vplus(X86,X87)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f234,plain,
! [X0,X1] : vplus(vplus(v1,X0),X1) = vplus(v1,vplus(X0,X1)),
inference(definition_unfolding,[],[f222,f223,f223]) ).
fof(f108,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(rectify,[],[f53]) ).
fof(f224,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f108]) ).
fof(f225,plain,
! [X0,X1] : vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)),
inference(cnf_transformation,[],[f109]) ).
fof(f55,axiom,
! [X90] :
( v1 != X90
=> vsucc(vskolem2(X90)) = X90 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof(f236,plain,
! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1)),
inference(definition_unfolding,[],[f225,f223,f223]) ).
fof(f226,plain,
! [X0] : vsucc(X0) = vplus(X0,v1),
inference(cnf_transformation,[],[f109]) ).
fof(f54,axiom,
! [X88,X89] :
( vplus(X88,v1) = vsucc(X88)
& vplus(X88,vsucc(X89)) = vsucc(vplus(X88,X89)) ),
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(f235,plain,
! [X0] : vplus(v1,X0) = vplus(X0,v1),
inference(definition_unfolding,[],[f226,f223]) ).
fof(f227,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(cnf_transformation,[],[f146]) ).
fof(f56,axiom,
! [X91] : vsucc(X91) != X91,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof(f237,plain,
! [X0] :
( vplus(v1,vskolem2(X0)) = X0
| v1 = X0 ),
inference(definition_unfolding,[],[f227,f223]) ).
fof(f228,plain,
! [X0] : vsucc(X0) != X0,
inference(cnf_transformation,[],[f111]) ).
fof(f57,axiom,
! [X92,X93] :
( X92 != X93
=> vsucc(X92) != vsucc(X93) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
fof(f238,plain,
! [X0] : vplus(v1,X0) != X0,
inference(definition_unfolding,[],[f228,f223]) ).
fof(f229,plain,
! [X0,X1] :
( vsucc(X0) != vsucc(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f147]) ).
fof(f58,axiom,
! [X94,X95] :
( vsucc(X94) = vsucc(X95)
=> X94 = X95 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
fof(f239,plain,
! [X0,X1] :
( vplus(v1,X0) != vplus(v1,X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f229,f223,f223]) ).
fof(f230,plain,
! [X0,X1] :
( X0 = X1
| vsucc(X0) != vsucc(X1) ),
inference(cnf_transformation,[],[f148]) ).
fof(f59,axiom,
! [X96] : v1 != vsucc(X96),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
fof(f240,plain,
! [X0,X1] :
( X0 = X1
| vplus(v1,X0) != vplus(v1,X1) ),
inference(definition_unfolding,[],[f230,f223,f223]) ).
cnf(c_106,plain,
vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f224]) ).
cnf(c_140,negated_conjecture,
~ greater(vmul(vd481,vd469),vmul(vd469,vd480)),
inference(theory_normalisation,[status(thm)],[c_49,c_106,c_104,c_56,c_58]) ).
cnf(c_143,plain,
( ~ greater(X0,X1)
| vmul(vd469,vplus(X1,vskolem9(X0,X1))) = vmul(X0,vd469) ),
inference(theory_normalisation,[status(thm)],[c_54,c_106,c_104,c_56,c_58]) ).
cnf(c_1502,plain,
vmul(vd469,vplus(vd480,vskolem9(vd481,vd480))) = vmul(vd481,vd469),
inference(superposition,[status(thm)],[c_50,c_143]) ).
cnf(c_2737,plain,
greater(vmul(vd481,vd469),vmul(vd469,vd480)),
inference(superposition,[status(thm)],[c_1502,c_1438]) ).
cnf(c_2751,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_140,c_2737]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM852+1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n018.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 20:01:01 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.14/1.20 % SZS status Started for theBenchmark.p
% 4.14/1.20 % SZS status Theorem for theBenchmark.p
% 4.14/1.20
% 4.14/1.20 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.14/1.20
% 4.14/1.20 ------ iProver source info
% 4.14/1.20
% 4.14/1.20 git: date: 2024-05-02 19:28:25 +0000
% 4.14/1.20 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.14/1.20 git: non_committed_changes: false
% 4.14/1.20
% 4.14/1.20 ------ Parsing...
% 4.14/1.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.14/1.20
% 4.14/1.20 ------ Preprocessing... sup_sim: 1 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
% 4.14/1.20
% 4.14/1.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.14/1.20
% 4.14/1.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.14/1.20 ------ Proving...
% 4.14/1.20 ------ Problem Properties
% 4.14/1.20
% 4.14/1.20
% 4.14/1.20 clauses 53
% 4.14/1.20 conjectures 1
% 4.14/1.20 EPR 21
% 4.14/1.20 Horn 48
% 4.14/1.20 unary 20
% 4.14/1.20 binary 21
% 4.14/1.20 lits 98
% 4.14/1.20 lits eq 27
% 4.14/1.20 fd_pure 0
% 4.14/1.20 fd_pseudo 0
% 4.14/1.20 fd_cond 0
% 4.14/1.20 fd_pseudo_cond 5
% 4.14/1.20 AC symbols 2
% 4.14/1.20
% 4.14/1.20 ------ Input Options Time Limit: Unbounded
% 4.14/1.20
% 4.14/1.20
% 4.14/1.20 ------
% 4.14/1.20 Current options:
% 4.14/1.20 ------
% 4.14/1.20
% 4.14/1.20
% 4.14/1.20
% 4.14/1.20
% 4.14/1.20 ------ Proving...
% 4.14/1.20
% 4.14/1.20
% 4.14/1.20 % SZS status Theorem for theBenchmark.p
% 4.14/1.20
% 4.14/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.14/1.20
% 4.14/1.21
%------------------------------------------------------------------------------