%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX217-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 03:32:52 PM UTC 2026
% Result : Unsatisfiable 1.05s 6.20s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 25
% Syntax : Number of formulae : 103 ( 103 unt; 0 def)
% Number of atoms : 103 ( 102 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 70 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : aux(X0,btrue) = cons(o,shw(half(suc(X0)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
fof(f2,axiom,
! [X0] : aux(X0,bfalse) = cons(i,shw(half(suc(X0)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
fof(f3,axiom,
notb(btrue) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
fof(f4,plain,
bfalse = notb(btrue),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
notb(bfalse) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
fof(f6,plain,
btrue = notb(bfalse),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
half(zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
fof(f8,plain,
zero = half(zero),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
half(suc(zero)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(f10,plain,
zero = half(suc(zero)),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0] : half(suc(suc(X0))) = suc(half(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
fof(f12,axiom,
evenNat(zero) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(f13,plain,
btrue = evenNat(zero),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X0] : evenNat(suc(X0)) = notb(evenNat(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
fof(f15,axiom,
shw(zero) = nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
fof(f16,axiom,
! [X0] : shw(suc(X0)) = aux(X0,evenNat(suc(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
fof(f17,axiom,
! [X0] : append(nil,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
fof(f18,axiom,
! [X2,X0,X1] : append(cons(X0,X1),X2) = cons(X0,append(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
fof(f19,axiom,
! [X0] : addNat(zero,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
fof(f20,axiom,
! [X0,X1] : addNat(suc(X0),X1) = suc(addNat(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
fof(f21,axiom,
! [X0] : double(X0) = addNat(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
fof(f22,axiom,
rd(nil) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
fof(f23,plain,
zero = rd(nil),
inference(reorient_equations,[],[f22]) ).
fof(f24,axiom,
! [X0] : rd(cons(i,X0)) = suc(double(rd(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
fof(f25,axiom,
! [X0] : rd(cons(o,X0)) = double(rd(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
fof(f26,plain,
! [X0] : double(rd(X0)) = rd(cons(o,X0)),
inference(reorient_equations,[],[f25]) ).
fof(f27,axiom,
! [X0,X1] : x(X0,X1) = rd(append(shw(X0),shw(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
fof(f28,axiom,
! [X0,X1] : sat_comm(X0,X1) = eq(x(X0,X1),x(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
fof(f37,axiom,
! [X0,X1] : eq(suc(X0),suc(X1)) = eq(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
fof(f40,axiom,
! [X0] : eq(suc(X0),zero) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
fof(f41,plain,
! [X0] : bfalse = eq(suc(X0),zero),
inference(reorient_equations,[],[f40]) ).
fof(f44,axiom,
! [X0] : eq2(X0,X0) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
fof(f45,plain,
! [X0] : btrue = eq2(X0,X0),
inference(reorient_equations,[],[f44]) ).
fof(f48,negated_conjecture,
! [X0,X1] : eq2(sat_comm(X0,X1),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f49,plain,
! [X0,X1] : btrue != eq2(sat_comm(X0,X1),bfalse),
inference(reorient_equations,[],[f48]) ).
fof(f50,plain,
! [X0,X1] : sat_comm(X0,X1) = eq(rd(append(shw(X0),shw(X1))),rd(append(shw(X1),shw(X0)))),
inference(definition_unfolding,[],[f28,f27,f27]) ).
fof(f51,plain,
! [X0] : rd(cons(i,X0)) = suc(addNat(rd(X0),rd(X0))),
inference(definition_unfolding,[],[f24,f21]) ).
fof(f52,plain,
! [X0] : rd(cons(o,X0)) = addNat(rd(X0),rd(X0)),
inference(definition_unfolding,[],[f26,f21]) ).
fof(f53,plain,
! [X0,X1] : btrue != eq2(eq(rd(append(shw(X0),shw(X1))),rd(append(shw(X1),shw(X0)))),bfalse),
inference(definition_unfolding,[],[f49,f50]) ).
tcf(c_81,plain,
! [X0: $i] : cons(o,shw(half(suc(X0)))) = aux(X0,btrue),
inference(cnf_transformation,[],[f1]) ).
tcf(c_82,plain,
! [X0: $i] : cons(i,shw(half(suc(X0)))) = aux(X0,bfalse),
inference(cnf_transformation,[],[f2]) ).
tcf(c_83,plain,
notb(btrue) = bfalse,
inference(cnf_transformation,[],[f4]) ).
tcf(c_84,plain,
notb(bfalse) = btrue,
inference(cnf_transformation,[],[f6]) ).
tcf(c_85,plain,
half(zero) = zero,
inference(cnf_transformation,[],[f8]) ).
tcf(c_86,plain,
half(suc(zero)) = zero,
inference(cnf_transformation,[],[f10]) ).
tcf(c_87,plain,
! [X0: $i] : half(suc(suc(X0))) = suc(half(X0)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_88,plain,
evenNat(zero) = btrue,
inference(cnf_transformation,[],[f13]) ).
tcf(c_89,plain,
! [X0: $i] : notb(evenNat(X0)) = evenNat(suc(X0)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_90,plain,
shw(zero) = nil,
inference(cnf_transformation,[],[f15]) ).
tcf(c_91,plain,
! [X0: $i] : aux(X0,evenNat(suc(X0))) = shw(suc(X0)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,plain,
! [X0: $i] : append(nil,X0) = X0,
inference(cnf_transformation,[],[f17]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] : cons(X0,append(X1,X2)) = append(cons(X0,X1),X2),
inference(cnf_transformation,[],[f18]) ).
tcf(c_94,plain,
! [X0: $i] : addNat(zero,X0) = X0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : suc(addNat(X0,X1)) = addNat(suc(X0),X1),
inference(cnf_transformation,[],[f20]) ).
tcf(c_96,plain,
rd(nil) = zero,
inference(cnf_transformation,[],[f23]) ).
tcf(c_97,plain,
! [X0: $i] : suc(addNat(rd(X0),rd(X0))) = rd(cons(i,X0)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_98,plain,
! [X0: $i] : addNat(rd(X0),rd(X0)) = rd(cons(o,X0)),
inference(cnf_transformation,[],[f52]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] : eq(suc(X0),suc(X1)) = eq(X0,X1),
inference(cnf_transformation,[],[f37]) ).
tcf(c_105,plain,
! [X0: $i] : eq(suc(X0),zero) = bfalse,
inference(cnf_transformation,[],[f41]) ).
tcf(c_107,plain,
! [X0: $i] : eq2(X0,X0) = btrue,
inference(cnf_transformation,[],[f45]) ).
tcf(c_109,negated_conjecture,
! [X0: $i,X1: $i] : eq2(eq(rd(append(shw(X0),shw(X1))),rd(append(shw(X1),shw(X0)))),bfalse) != btrue,
inference(cnf_transformation,[],[f53]) ).
tcf(c_144,plain,
evenNat(suc(zero)) = notb(btrue),
inference(superposition,[status(thm)],[c_88,c_89]) ).
tcf(c_145,plain,
! [X0: $i] : cons(o,shw(suc(half(X0)))) = aux(suc(X0),btrue),
inference(superposition,[status(thm)],[c_87,c_81]) ).
tcf(c_148,plain,
cons(i,shw(zero)) = aux(zero,bfalse),
inference(superposition,[status(thm)],[c_86,c_82]) ).
tcf(c_149,plain,
! [X0: $i] : cons(i,shw(suc(half(X0)))) = aux(suc(X0),bfalse),
inference(superposition,[status(thm)],[c_87,c_82]) ).
tcf(c_150,plain,
rd(cons(o,nil)) = addNat(zero,zero),
inference(superposition,[status(thm)],[c_96,c_98]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] : cons(o,append(shw(half(suc(X0))),X1)) = append(aux(X0,btrue),X1),
inference(superposition,[status(thm)],[c_81,c_93]) ).
tcf(c_155,plain,
suc(addNat(zero,zero)) = rd(cons(i,nil)),
inference(superposition,[status(thm)],[c_96,c_97]) ).
tcf(c_160,plain,
! [X0: $i] : aux(addNat(rd(X0),rd(X0)),evenNat(rd(cons(i,X0)))) = shw(rd(cons(i,X0))),
inference(superposition,[status(thm)],[c_97,c_91]) ).
tcf(c_172,plain,
evenNat(suc(zero)) = bfalse,
inference(light_normalisation,[status(thm)],[c_144,c_83]) ).
tcf(c_173,plain,
rd(cons(o,nil)) = zero,
inference(demodulation,[status(thm)],[c_150,c_94]) ).
tcf(c_174,plain,
aux(zero,bfalse) = cons(i,nil),
inference(light_normalisation,[status(thm)],[c_148,c_90]) ).
tcf(c_176,plain,
rd(cons(i,nil)) = suc(zero),
inference(demodulation,[status(thm)],[c_155,c_94]) ).
tcf(c_185,plain,
! [X0: $i] : aux(rd(cons(o,X0)),evenNat(rd(cons(i,X0)))) = shw(rd(cons(i,X0))),
inference(demodulation,[status(thm)],[c_160,c_98]) ).
tcf(c_246,plain,
evenNat(suc(suc(zero))) = notb(bfalse),
inference(superposition,[status(thm)],[c_172,c_89]) ).
tcf(c_249,plain,
suc(addNat(suc(zero),suc(zero))) = rd(cons(i,cons(i,nil))),
inference(superposition,[status(thm)],[c_176,c_97]) ).
tcf(c_250,plain,
rd(cons(o,cons(i,nil))) = addNat(suc(zero),suc(zero)),
inference(superposition,[status(thm)],[c_176,c_98]) ).
tcf(c_266,plain,
cons(o,shw(suc(zero))) = aux(suc(zero),btrue),
inference(superposition,[status(thm)],[c_85,c_145]) ).
tcf(c_271,plain,
cons(i,shw(suc(zero))) = aux(suc(zero),bfalse),
inference(superposition,[status(thm)],[c_85,c_149]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i] : cons(o,append(shw(suc(half(X0))),X1)) = append(aux(suc(X0),btrue),X1),
inference(superposition,[status(thm)],[c_87,c_152]) ).
tcf(c_361,plain,
aux(rd(cons(o,nil)),evenNat(suc(zero))) = shw(suc(zero)),
inference(superposition,[status(thm)],[c_176,c_185]) ).
tcf(c_366,plain,
evenNat(suc(suc(zero))) = btrue,
inference(light_normalisation,[status(thm)],[c_246,c_84]) ).
tcf(c_373,plain,
shw(suc(zero)) = cons(i,nil),
inference(light_normalisation,[status(thm)],[c_361,c_172,c_173,c_174]) ).
tcf(c_384,plain,
rd(cons(o,cons(i,nil))) = suc(suc(zero)),
inference(demodulation,[status(thm)],[c_250,c_94,c_95]) ).
tcf(c_391,plain,
rd(cons(i,cons(i,nil))) = suc(suc(suc(zero))),
inference(demodulation,[status(thm)],[c_249,c_94,c_95]) ).
tcf(c_484,plain,
aux(suc(zero),btrue) = shw(suc(suc(zero))),
inference(superposition,[status(thm)],[c_366,c_91]) ).
tcf(c_682,plain,
! [X0: $i] : cons(i,append(nil,X0)) = append(shw(suc(zero)),X0),
inference(superposition,[status(thm)],[c_373,c_93]) ).
tcf(c_744,plain,
suc(addNat(suc(suc(zero)),suc(suc(zero)))) = rd(cons(i,cons(o,cons(i,nil)))),
inference(superposition,[status(thm)],[c_384,c_97]) ).
tcf(c_779,plain,
addNat(suc(suc(suc(zero))),suc(suc(suc(zero)))) = rd(cons(o,cons(i,cons(i,nil)))),
inference(superposition,[status(thm)],[c_391,c_98]) ).
tcf(c_863,plain,
! [X0: $i] : cons(o,append(shw(suc(zero)),X0)) = append(aux(suc(zero),btrue),X0),
inference(superposition,[status(thm)],[c_85,c_285]) ).
tcf(c_944,plain,
! [X0: $i] : append(shw(suc(zero)),X0) = cons(i,X0),
inference(demodulation,[status(thm)],[c_682,c_92]) ).
tcf(c_965,plain,
! [X0: $i] : append(aux(suc(zero),btrue),X0) = cons(o,cons(i,X0)),
inference(demodulation,[status(thm)],[c_863,c_944]) ).
tcf(c_1032,plain,
rd(cons(i,cons(o,cons(i,nil)))) = suc(suc(suc(suc(suc(zero))))),
inference(demodulation,[status(thm)],[c_744,c_94,c_95]) ).
tcf(c_1033,plain,
rd(cons(i,aux(suc(zero),btrue))) = suc(suc(suc(suc(suc(zero))))),
inference(light_normalisation,[status(thm)],[c_1032,c_266,c_373]) ).
tcf(c_1051,plain,
rd(cons(o,cons(i,cons(i,nil)))) = suc(suc(suc(suc(suc(suc(zero)))))),
inference(demodulation,[status(thm)],[c_779,c_94,c_95]) ).
tcf(c_1052,plain,
suc(suc(suc(suc(suc(suc(zero)))))) = rd(cons(o,aux(suc(zero),bfalse))),
inference(light_normalisation,[status(thm)],[c_1051,c_271,c_373]) ).
tcf(c_1581,plain,
! [X0: $i] : eq2(eq(rd(append(shw(X0),shw(suc(zero)))),rd(cons(i,shw(X0)))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_944,c_109]) ).
tcf(c_1714,plain,
! [X0: $i] : append(shw(suc(suc(zero))),X0) = cons(o,cons(i,X0)),
inference(superposition,[status(thm)],[c_484,c_965]) ).
tcf(c_1741,plain,
rd(cons(i,shw(suc(suc(zero))))) = suc(suc(suc(suc(suc(zero))))),
inference(superposition,[status(thm)],[c_484,c_1033]) ).
tcf(c_5982,plain,
eq2(eq(rd(append(shw(suc(suc(zero))),shw(suc(zero)))),suc(suc(suc(suc(suc(zero)))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_1741,c_1581]) ).
tcf(c_6040,plain,
eq2(eq(rd(cons(o,cons(i,shw(suc(zero))))),suc(suc(suc(suc(suc(zero)))))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_5982,c_1714]) ).
tcf(c_6041,plain,
eq2(eq(suc(suc(suc(suc(suc(suc(zero)))))),suc(suc(suc(suc(suc(zero)))))),bfalse) != btrue,
inference(light_normalisation,[status(thm)],[c_6040,c_271,c_1052]) ).
tcf(c_6042,plain,
$false,
inference(ground_joinability,[status(thm)],[c_6041,c_103,c_105,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX217-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n017.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 23:37:07 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running UEQ theorem proving
% 0.14/5.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.44
% 0.14/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.44
% 0.14/5.44 % Detected problem language: tptp
% 0.14/5.45 % Proving...
% 1.05/6.20 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 1.05/6.20 % SZS status Started for theBenchmark.p
% 1.05/6.20 % SZS status Unsatisfiable for theBenchmark.p
% 1.05/6.20
% 1.05/6.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.05/6.20
% 1.05/6.20 % ------ iProver source info
% 1.05/6.20
% 1.05/6.20 % git: date: 2026-07-19 20:42:38 +0200
% 1.05/6.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.05/6.20 % git: non_committed_changes: false
% 1.05/6.20
% 1.05/6.20 % ------ Parsing...% successful
% 1.05/6.20
% 1.05/6.20
% 1.05/6.20 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.05/6.20 % ------ Proving...
% 1.05/6.20 % ------ Problem Properties
% 1.05/6.20
% 1.05/6.20 %
% 1.05/6.20 % clauses 29
% 1.05/6.20 % conjectures 1
% 1.05/6.20 % EPR 0
% 1.05/6.20 % Horn 29
% 1.05/6.20 % unary 29
% 1.05/6.20 % binary 0
% 1.05/6.20 % lits 29
% 1.05/6.20 % lits eq 29
% 1.05/6.20 % fd_pure 0
% 1.05/6.20 % fd_pseudo 0
% 1.05/6.20 % fd_cond 0
% 1.05/6.20 % fd_pseudo_cond 0
% 1.05/6.20 % AC symbols 0
% 1.05/6.20
% 1.05/6.20 % ------ Input Options Time Limit: Unbounded
% 1.05/6.20
% 1.05/6.20
% 1.05/6.20 % ------
% 1.05/6.20 % Current options:
% 1.05/6.20 % ------
% 1.05/6.20
% 1.05/6.20
% 1.05/6.20 %
% 1.05/6.20
% 1.05/6.20 % ------ Proving...
% 1.05/6.20 %
% 1.05/6.20
% 1.05/6.20 % SZS status Unsatisfiable for theBenchmark.p
% 1.05/6.20
% 1.05/6.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.05/6.20
% 1.05/6.20
%------------------------------------------------------------------------------