TSTP Solution File: NUM851+2 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM851+2 : 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 02:50:55 EDT 2024
% Result : Theorem 0.46s 1.15s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f67)
% Comments :
%------------------------------------------------------------------------------
fof(f62,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
=> vplus(X0,sK0(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
=> vplus(X0,sK1(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X3] : vplus(X1,X3) = X0
=> vplus(X1,sK2(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,[],[f67]) ).
cnf(c_51,plain,
vplus(vd471,vd473) = vd470,
inference(cnf_transformation,[],[f69]) ).
cnf(c_53,plain,
vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
inference(cnf_transformation,[],[f71]) ).
cnf(c_54,plain,
vplus(vmul(X0,X1),vmul(X0,X2)) = vmul(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f72]) ).
cnf(c_55,plain,
vmul(X0,X1) = vmul(X1,X0),
inference(cnf_transformation,[],[f73]) ).
cnf(c_67,plain,
vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f85]) ).
cnf(c_632,plain,
vplus(vmul(X0,X1),vmul(X1,X2)) = vmul(X1,vplus(X0,X2)),
inference(superposition,[status(thm)],[c_55,c_54]) ).
fof(f11,axiom,
! [X11,X12] :
( vmul(X11,v1) = X11
& vmul(X11,vsucc(X12)) = vplus(vmul(X11,X12),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof(f77,plain,
! [X0] : vmul(X0,v1) = X0,
inference(cnf_transformation,[],[f34]) ).
fof(f23,axiom,
! [X33] : vplus(v1,X33) = vsucc(X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof(f93,plain,
! [X0,X1] :
( vsucc(X0) != vsucc(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f61]) ).
fof(f34,plain,
! [X0,X1] :
( vmul(X0,v1) = X0
& vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0) ),
inference(rectify,[],[f11]) ).
fof(f46,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(rectify,[],[f23]) ).
fof(f48,plain,
! [X0,X1] :
( vsucc(X0) = vplus(X0,v1)
& vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)) ),
inference(rectify,[],[f25]) ).
fof(f49,plain,
! [X0] :
( v1 != X0
=> vsucc(vskolem2(X0)) = X0 ),
inference(rectify,[],[f26]) ).
fof(f50,plain,
! [X0] : vsucc(X0) != X0,
inference(rectify,[],[f27]) ).
fof(f51,plain,
! [X0,X1] :
( X0 != X1
=> vsucc(X0) != vsucc(X1) ),
inference(rectify,[],[f28]) ).
fof(f60,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(ennf_transformation,[],[f49]) ).
fof(f61,plain,
! [X0,X1] :
( vsucc(X0) != vsucc(X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f51]) ).
fof(f76,plain,
! [X0,X1] : vmul(X0,vsucc(X1)) = vplus(vmul(X0,X1),X0),
inference(cnf_transformation,[],[f34]) ).
fof(f87,plain,
! [X0] : vsucc(X0) = vplus(v1,X0),
inference(cnf_transformation,[],[f46]) ).
fof(f14,axiom,
! [X17,X18] :
( greater(X18,X17)
<=> ? [X19] : vplus(X17,X19) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof(f95,plain,
! [X0,X1] : vplus(vmul(X0,X1),X0) = vmul(X0,vplus(v1,X1)),
inference(definition_unfolding,[],[f76,f87]) ).
fof(f37,plain,
! [X0,X1] :
( greater(X1,X0)
<=> ? [X2] : vplus(X0,X2) = X1 ),
inference(rectify,[],[f14]) ).
fof(f54,plain,
! [X0,X1] :
( greater(X1,X0)
=> ? [X2] : vplus(X0,X2) = X1 ),
inference(unused_predicate_definition_removal,[],[f37]) ).
fof(f55,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
| ~ greater(X1,X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f63,plain,
! [X0,X1] :
( vplus(X0,sK0(X0,X1)) = X1
| ~ greater(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f55,f62]) ).
fof(f15,axiom,
! [X20,X21] :
( ? [X23] : vplus(X20,X23) = X21
| ? [X22] : vplus(X21,X22) = X20
| X20 = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof(f78,plain,
! [X0,X1] :
( vplus(X0,sK0(X0,X1)) = X1
| ~ greater(X1,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f38,plain,
! [X0,X1] :
( ? [X2] : vplus(X0,X2) = X1
| ? [X3] : vplus(X1,X3) = X0
| X0 = X1 ),
inference(rectify,[],[f15]) ).
fof(f66,plain,
! [X0,X1] :
( vplus(X0,sK1(X0,X1)) = X1
| vplus(X1,sK2(X0,X1)) = X0
| X0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f38,f65,f64]) ).
fof(f16,axiom,
! [X20,X21] :
( ~ ? [X23] : vplus(X20,X23) = X21
| X20 != X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof(f79,plain,
! [X0,X1] :
( vplus(X0,sK1(X0,X1)) = X1
| vplus(X1,sK2(X0,X1)) = X0
| X0 = X1 ),
inference(cnf_transformation,[],[f66]) ).
fof(f39,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| X0 != X1 ),
inference(rectify,[],[f16]) ).
fof(f56,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| X0 != X1 ),
inference(ennf_transformation,[],[f39]) ).
fof(f80,plain,
! [X2,X0,X1] :
( vplus(X0,X2) != X1
| X0 != X1 ),
inference(cnf_transformation,[],[f56]) ).
fof(f17,axiom,
! [X20,X21] :
( ~ ? [X23] : vplus(X20,X23) = X21
| ~ ? [X22] : vplus(X21,X22) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
fof(f102,plain,
! [X2,X0] : vplus(X0,X2) != X0,
inference(equality_resolution,[],[f80]) ).
fof(f40,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X0,X2) = X1
| ~ ? [X3] : vplus(X1,X3) = X0 ),
inference(rectify,[],[f17]) ).
fof(f57,plain,
! [X0,X1] :
( ! [X2] : vplus(X0,X2) != X1
| ! [X3] : vplus(X1,X3) != X0 ),
inference(ennf_transformation,[],[f40]) ).
fof(f81,plain,
! [X2,X3,X0,X1] :
( vplus(X0,X2) != X1
| vplus(X1,X3) != X0 ),
inference(cnf_transformation,[],[f57]) ).
fof(f18,axiom,
! [X20,X21] :
( ~ ? [X22] : vplus(X21,X22) = X20
| X20 != X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
fof(f103,plain,
! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
inference(equality_resolution,[],[f81]) ).
fof(f41,plain,
! [X0,X1] :
( ~ ? [X2] : vplus(X1,X2) = X0
| X0 != X1 ),
inference(rectify,[],[f18]) ).
fof(f58,plain,
! [X0,X1] :
( ! [X2] : vplus(X1,X2) != X0
| X0 != X1 ),
inference(ennf_transformation,[],[f41]) ).
fof(f82,plain,
! [X2,X0,X1] :
( vplus(X1,X2) != X0
| X0 != X1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f19,axiom,
! [X24,X25] :
( X24 != X25
=> ! [X26] : vplus(X26,X24) != vplus(X26,X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof(f104,plain,
! [X2,X1] : vplus(X1,X2) != X1,
inference(equality_resolution,[],[f82]) ).
fof(f42,plain,
! [X0,X1] :
( X0 != X1
=> ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
inference(rectify,[],[f19]) ).
fof(f59,plain,
! [X0,X1] :
( ! [X2] : vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f42]) ).
fof(f20,axiom,
! [X27,X28] : vplus(X27,X28) != X28,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof(f83,plain,
! [X2,X0,X1] :
( vplus(X2,X0) != vplus(X2,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f59]) ).
fof(f43,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(rectify,[],[f20]) ).
fof(f21,axiom,
! [X29,X30] : vplus(X30,X29) = vplus(X29,X30),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof(f84,plain,
! [X0,X1] : vplus(X0,X1) != X1,
inference(cnf_transformation,[],[f43]) ).
fof(f44,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(rectify,[],[f21]) ).
fof(f22,axiom,
! [X31,X32] : vplus(vsucc(X31),X32) = vsucc(vplus(X31,X32)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
fof(f85,plain,
! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
inference(cnf_transformation,[],[f44]) ).
fof(f45,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
inference(rectify,[],[f22]) ).
fof(f86,plain,
! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
inference(cnf_transformation,[],[f45]) ).
fof(f24,axiom,
! [X34,X35,X36] : vplus(vplus(X34,X35),X36) = vplus(X34,vplus(X35,X36)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(f96,plain,
! [X0,X1] : vplus(vplus(v1,X0),X1) = vplus(v1,vplus(X0,X1)),
inference(definition_unfolding,[],[f86,f87,f87]) ).
fof(f47,plain,
! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(rectify,[],[f24]) ).
fof(f88,plain,
! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f47]) ).
fof(f89,plain,
! [X0,X1] : vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)),
inference(cnf_transformation,[],[f48]) ).
fof(f26,axiom,
! [X39] :
( v1 != X39
=> vsucc(vskolem2(X39)) = X39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
fof(f98,plain,
! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1)),
inference(definition_unfolding,[],[f89,f87,f87]) ).
fof(f90,plain,
! [X0] : vsucc(X0) = vplus(X0,v1),
inference(cnf_transformation,[],[f48]) ).
fof(f25,axiom,
! [X37,X38] :
( vplus(X37,v1) = vsucc(X37)
& vplus(X37,vsucc(X38)) = vsucc(vplus(X37,X38)) ),
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(f97,plain,
! [X0] : vplus(v1,X0) = vplus(X0,v1),
inference(definition_unfolding,[],[f90,f87]) ).
fof(f91,plain,
! [X0] :
( vsucc(vskolem2(X0)) = X0
| v1 = X0 ),
inference(cnf_transformation,[],[f60]) ).
fof(f27,axiom,
! [X40] : vsucc(X40) != X40,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
fof(f99,plain,
! [X0] :
( vplus(v1,vskolem2(X0)) = X0
| v1 = X0 ),
inference(definition_unfolding,[],[f91,f87]) ).
fof(f92,plain,
! [X0] : vsucc(X0) != X0,
inference(cnf_transformation,[],[f50]) ).
fof(f28,axiom,
! [X41,X42] :
( X41 != X42
=> vsucc(X41) != vsucc(X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
fof(f100,plain,
! [X0] : vplus(v1,X0) != X0,
inference(definition_unfolding,[],[f92,f87]) ).
cnf(c_69,plain,
vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
inference(cnf_transformation,[],[f88]) ).
cnf(c_90,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_69,c_67]) ).
cnf(c_157,plain,
vplus(vmul(vd471,vd469),vmul(vd469,vd473)) != vmul(vd469,vd470),
inference(light_normalisation,[status(thm)],[c_90,c_51]) ).
cnf(c_667,plain,
vmul(vd469,vplus(vd471,vd473)) != vmul(vd469,vd470),
inference(demodulation,[status(thm)],[c_157,c_632]) ).
cnf(c_668,plain,
vmul(vd469,vd470) != vmul(vd469,vd470),
inference(light_normalisation,[status(thm)],[c_667,c_51]) ).
cnf(c_669,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_668]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM851+2 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 18:55:51 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 0.46/1.15 % SZS status Started for theBenchmark.p
% 0.46/1.15 % SZS status Theorem for theBenchmark.p
% 0.46/1.15
% 0.46/1.15 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.46/1.15
% 0.46/1.15 ------ iProver source info
% 0.46/1.15
% 0.46/1.15 git: date: 2024-05-02 19:28:25 +0000
% 0.46/1.15 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.46/1.15 git: non_committed_changes: false
% 0.46/1.15
% 0.46/1.15 ------ Parsing...
% 0.46/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.46/1.15
% 0.46/1.15 ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 0.46/1.15
% 0.46/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.46/1.15
% 0.46/1.15 ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.46/1.15 ------ Proving...
% 0.46/1.15 ------ Problem Properties
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 clauses 16
% 0.46/1.15 conjectures 0
% 0.46/1.15 EPR 0
% 0.46/1.15 Horn 14
% 0.46/1.15 unary 13
% 0.46/1.15 binary 2
% 0.46/1.15 lits 20
% 0.46/1.15 lits eq 20
% 0.46/1.15 fd_pure 0
% 0.46/1.15 fd_pseudo 0
% 0.46/1.15 fd_cond 0
% 0.46/1.15 fd_pseudo_cond 1
% 0.46/1.15 AC symbols 2
% 0.46/1.15
% 0.46/1.15 ------ Schedule dynamic 5 is on
% 0.46/1.15
% 0.46/1.15 ------ no conjectures: strip conj schedule
% 0.46/1.15
% 0.46/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 ------
% 0.46/1.15 Current options:
% 0.46/1.15 ------
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 ------ Proving...
% 0.46/1.15
% 0.46/1.15
% 0.46/1.15 % SZS status Theorem for theBenchmark.p
% 0.46/1.15
% 0.46/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.15
% 0.46/1.15
%------------------------------------------------------------------------------