TSTP Solution File: NUM851+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM851+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 : Thu Aug 31 11:33:15 EDT 2023
% Result : Theorem 3.72s 1.14s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f150)
% Comments :
%------------------------------------------------------------------------------
fof(f145,plain,
! [X0,X1] :
( ? [X3] : vplus(X0,X3) = X1
=> vplus(X0,sK1(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f147,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
=> vplus(X0,sK2(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f148,plain,
! [X0,X1] :
( ? [X3] : vplus(X1,X3) = X0
=> vplus(X1,sK3(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
cnf(c_49,negated_conjecture,
vplus(vmul(vd471,vd469),vmul(vd473,vd469)) != vmul(vplus(vd471,vd473),vd469),
inference(cnf_transformation,[],[f150]) ).
cnf(c_51,plain,
vplus(vd471,vd473) = vd470,
inference(cnf_transformation,[],[f152]) ).
cnf(c_53,plain,
vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
inference(cnf_transformation,[],[f154]) ).
cnf(c_54,plain,
vplus(vmul(X0,X1),vmul(X0,X2)) = vmul(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f155]) ).
cnf(c_55,plain,
vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f156]) ).
cnf(c_101,plain,
vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f203]) ).
cnf(c_4346,plain,
vplus(vmul(X0,X1),vmul(X1,X2)) = vmul(X1,vplus(X0,X2)),
inference(superposition,[status(thm)],[c_55,c_54]) ).
fof(f39,axiom,
! [X64,X65] :
( greater(X65,X64)
<=> ? [X66] : vplus(X64,X66) = X65 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f230,plain,
! [X2,X0] : greater(vplus(X0,X2),X0),
inference(equality_resolution,[],[f196]) ).
fof(f48,axiom,
! [X80] : vplus(v1,X80) = vsucc(X80),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f213,plain,
! [X0] : v1 != vsucc(X0),
inference(cnf_transformation,[],[f105]) ).
fof(f89,plain,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : vplus(X0,X2) = X1 ),
inference(rectify,[],[f39]) ).
fof(f98,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(rectify,[],[f48]) ).
fof(f100,plain,
! [X0,X1] :
( vsucc(X0) = vplus(X0,v1)
& vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)) ),
inference(rectify,[],[f50]) ).
fof(f101,plain,
! [X0] :
( v1 != X0
=> vsucc(vskolem2(X0)) = X0 ),
inference(rectify,[],[f51]) ).
fof(f102,plain,
! [X0] : vsucc(X0) != X0,
inference(rectify,[],[f52]) ).
fof(f103,plain,
! [X0,X1] :
( X0 != X1
=> vsucc(X0) != vsucc(X1) ),
inference(rectify,[],[f53]) ).
fof(f104,plain,
! [X0,X1] :
( vsucc(X0) = vsucc(X1)
=> X0 = X1 ),
inference(rectify,[],[f54]) ).
fof(f105,plain,
! [X0] : v1 != vsucc(X0),
inference(rectify,[],[f55]) ).
fof(f132,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(ennf_transformation,[],[f101]) ).
fof(f133,plain,
! [X0,X1] :
( vsucc(X0) != vsucc(X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f103]) ).
fof(f134,plain,
! [X0,X1] :
( X0 = X1
| vsucc(X0) != vsucc(X1) ),
inference(ennf_transformation,[],[f104]) ).
fof(f143,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X2] : vplus(X0,X2) = X1
| ~ greater(X1,X0) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f144,plain,
! [X0,X1] :
( ( greater(X1,X0)
| ! [X2] : vplus(X0,X2) != X1 )
& ( ? [X3] : vplus(X0,X3) = X1
| ~ greater(X1,X0) ) ),
inference(rectify,[],[f143]) ).
fof(f146,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])],[f144,f145]) ).
fof(f40,axiom,
! [X67,X68] :
( ? [X70] : vplus(X67,X70) = X68
| ? [X69] : vplus(X68,X69) = X67
| X67 = X68 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof(f195,plain,
! [X0,X1] :
( vplus(X0,sK1(X0,X1)) = X1
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
| ? [X3] : vplus(X1,X3) = X0
| X0 = X1 ),
inference(rectify,[],[f40]) ).
fof(f149,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])],[f90,f148,f147]) ).
fof(f41,axiom,
! [X67,X68] :
( ~ ? [X70] : vplus(X67,X70) = X68
| X67 != X68 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f197,plain,
! [X0,X1] :
( vplus(X0,sK2(X0,X1)) = X1
| vplus(X1,sK3(X0,X1)) = X0
| X0 = X1 ),
inference(cnf_transformation,[],[f149]) ).
fof(f91,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| X0 != X1 ),
inference(rectify,[],[f41]) ).
fof(f128,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| X0 != X1 ),
inference(ennf_transformation,[],[f91]) ).
fof(f196,plain,
! [X2,X0,X1] :
( greater(X1,X0)
| vplus(X0,X2) != X1 ),
inference(cnf_transformation,[],[f146]) ).
fof(f198,plain,
! [X2,X0,X1] :
( vplus(X0,X2) != X1
| X0 != X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f42,axiom,
! [X67,X68] :
( ~ ? [X70] : vplus(X67,X70) = X68
| ~ ? [X69] : vplus(X68,X69) = X67 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof(f231,plain,
! [X2,X0] : vplus(X0,X2) != X0,
inference(equality_resolution,[],[f198]) ).
fof(f92,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| ~ ? [X3] : vplus(X1,X3) = X0 ),
inference(rectify,[],[f42]) ).
fof(f129,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| ! [X3] : vplus(X1,X3) != X0 ),
inference(ennf_transformation,[],[f92]) ).
fof(f199,plain,
! [X2,X3,X0,X1] :
( vplus(X0,X2) != X1
| vplus(X1,X3) != X0 ),
inference(cnf_transformation,[],[f129]) ).
fof(f43,axiom,
! [X67,X68] :
( ~ ? [X69] : vplus(X68,X69) = X67
| X67 != X68 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof(f232,plain,
! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
inference(equality_resolution,[],[f199]) ).
fof(f93,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X1,X2) = X0
| X0 != X1 ),
inference(rectify,[],[f43]) ).
fof(f130,plain,
! [X0,X1] :
( ! [X2] : vplus(X1,X2) != X0
| X0 != X1 ),
inference(ennf_transformation,[],[f93]) ).
fof(f200,plain,
! [X2,X0,X1] :
( vplus(X1,X2) != X0
| X0 != X1 ),
inference(cnf_transformation,[],[f130]) ).
fof(f44,axiom,
! [X71,X72] :
( X71 != X72
=> ! [X73] : vplus(X73,X71) != vplus(X73,X72) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof(f233,plain,
! [X2,X1] : vplus(X1,X2) != X1,
inference(equality_resolution,[],[f200]) ).
fof(f94,plain,
! [X0,X1] :
( X0 != X1
=> ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
inference(rectify,[],[f44]) ).
fof(f131,plain,
! [X0,X1] :
( ! [X2] : vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f94]) ).
fof(f45,axiom,
! [X74,X75] : vplus(X74,X75) != X75,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof(f201,plain,
! [X2,X0,X1] :
( vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f131]) ).
fof(f95,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(rectify,[],[f45]) ).
fof(f46,axiom,
! [X76,X77] : vplus(X77,X76) = vplus(X76,X77),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f202,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(cnf_transformation,[],[f95]) ).
fof(f96,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(rectify,[],[f46]) ).
fof(f47,axiom,
! [X78,X79] : vplus(vsucc(X78),X79) = vsucc(vplus(X78,X79)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof(f203,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f96]) ).
fof(f97,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
inference(rectify,[],[f47]) ).
fof(f204,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
inference(cnf_transformation,[],[f97]) ).
fof(f205,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(cnf_transformation,[],[f98]) ).
fof(f49,axiom,
! [X81,X82,X83] : vplus(vplus(X81,X82),X83) = vplus(X81,vplus(X82,X83)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f216,plain,
! [X0,X1] : vplus(vplus(v1,X0),X1) = vplus(v1,vplus(X0,X1)),
inference(definition_unfolding,[],[f204,f205,f205]) ).
fof(f99,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(rectify,[],[f49]) ).
fof(f206,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f99]) ).
fof(f207,plain,
! [X0,X1] : vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)),
inference(cnf_transformation,[],[f100]) ).
fof(f51,axiom,
! [X86] :
( v1 != X86
=> vsucc(vskolem2(X86)) = X86 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof(f218,plain,
! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1)),
inference(definition_unfolding,[],[f207,f205,f205]) ).
fof(f208,plain,
! [X0] : vsucc(X0) = vplus(X0,v1),
inference(cnf_transformation,[],[f100]) ).
fof(f50,axiom,
! [X84,X85] :
( vplus(X84,v1) = vsucc(X84)
& vplus(X84,vsucc(X85)) = vsucc(vplus(X84,X85)) ),
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(f217,plain,
! [X0] : vplus(v1,X0) = vplus(X0,v1),
inference(definition_unfolding,[],[f208,f205]) ).
fof(f209,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(cnf_transformation,[],[f132]) ).
fof(f52,axiom,
! [X87] : vsucc(X87) != X87,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof(f219,plain,
! [X0] :
( vplus(v1,vskolem2(X0)) = X0
| v1 = X0 ),
inference(definition_unfolding,[],[f209,f205]) ).
fof(f210,plain,
! [X0] : vsucc(X0) != X0,
inference(cnf_transformation,[],[f102]) ).
fof(f53,axiom,
! [X88,X89] :
( X88 != X89
=> vsucc(X88) != vsucc(X89) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
fof(f220,plain,
! [X0] : vplus(v1,X0) != X0,
inference(definition_unfolding,[],[f210,f205]) ).
fof(f211,plain,
! [X0,X1] :
( vsucc(X0) != vsucc(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f133]) ).
fof(f54,axiom,
! [X90,X91] :
( vsucc(X90) = vsucc(X91)
=> X90 = X91 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).
fof(f221,plain,
! [X0,X1] :
( vplus(v1,X0) != vplus(v1,X1)
| X0 = X1 ),
inference(definition_unfolding,[],[f211,f205,f205]) ).
fof(f212,plain,
! [X0,X1] :
( X0 = X1
| vsucc(X0) != vsucc(X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f55,axiom,
! [X92] : v1 != vsucc(X92),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).
fof(f222,plain,
! [X0,X1] :
( X0 = X1
| vplus(v1,X0) != vplus(v1,X1) ),
inference(definition_unfolding,[],[f212,f205,f205]) ).
cnf(c_103,plain,
vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f206]) ).
cnf(c_137,negated_conjecture,
vplus(vmul(vd471,vd469),vmul(vd469,vd473)) != vmul(vd469,vplus(vd471,vd473)),
inference(theory_normalisation,[status(thm)],[c_49,c_53,c_55,c_103,c_101]) ).
cnf(c_446,plain,
vplus(vmul(vd471,vd469),vmul(vd469,vd473)) != vmul(vd469,vd470),
inference(light_normalisation,[status(thm)],[c_137,c_51]) ).
cnf(c_4442,plain,
vmul(vd469,vplus(vd471,vd473)) != vmul(vd469,vd470),
inference(demodulation,[status(thm)],[c_446,c_4346]) ).
cnf(c_4443,plain,
vmul(vd469,vd470) != vmul(vd469,vd470),
inference(light_normalisation,[status(thm)],[c_4442,c_51]) ).
cnf(c_4444,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_4443]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM851+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n027.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 : Fri Aug 25 17:35:19 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.72/1.14 % SZS status Started for theBenchmark.p
% 3.72/1.14 % SZS status Theorem for theBenchmark.p
% 3.72/1.14
% 3.72/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.72/1.14
% 3.72/1.14 ------ iProver source info
% 3.72/1.14
% 3.72/1.14 git: date: 2023-05-31 18:12:56 +0000
% 3.72/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.72/1.14 git: non_committed_changes: false
% 3.72/1.14 git: last_make_outside_of_git: false
% 3.72/1.14
% 3.72/1.14 ------ Parsing...
% 3.72/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.72/1.14
% 3.72/1.14 ------ Preprocessing... sup_sim: 3 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
% 3.72/1.14
% 3.72/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.72/1.14
% 3.72/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.72/1.14 ------ Proving...
% 3.72/1.14 ------ Problem Properties
% 3.72/1.14
% 3.72/1.14
% 3.72/1.14 clauses 50
% 3.72/1.14 conjectures 0
% 3.72/1.14 EPR 20
% 3.72/1.14 Horn 45
% 3.72/1.14 unary 20
% 3.72/1.14 binary 18
% 3.72/1.14 lits 92
% 3.72/1.14 lits eq 26
% 3.72/1.14 fd_pure 0
% 3.72/1.14 fd_pseudo 0
% 3.72/1.14 fd_cond 0
% 3.72/1.14 fd_pseudo_cond 5
% 3.72/1.14 AC symbols 2
% 3.72/1.14
% 3.72/1.14 ------ Schedule dynamic 5 is on
% 3.72/1.14
% 3.72/1.14 ------ no conjectures: strip conj schedule
% 3.72/1.14
% 3.72/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.72/1.14
% 3.72/1.14
% 3.72/1.14 ------
% 3.72/1.14 Current options:
% 3.72/1.14 ------
% 3.72/1.14
% 3.72/1.14
% 3.72/1.14
% 3.72/1.14
% 3.72/1.14 ------ Proving...
% 3.72/1.14
% 3.72/1.14
% 3.72/1.14 % SZS status Theorem for theBenchmark.p
% 3.72/1.14
% 3.72/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.72/1.15
% 3.72/1.15
%------------------------------------------------------------------------------