%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX201-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n013.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 03:32:49 PM UTC 2026
% Result : Unsatisfiable 1.98s 16.88s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 28
% Syntax : Number of formulae : 114 ( 114 unt; 0 def)
% Number of atoms : 114 ( 113 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 19 ( 19 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 12 ( 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 : 22 ( 22 usr; 4 con; 0-5 aty)
% Number of variables : 249 ( 0 sgn 249 !; 0 ?; 181 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4] : aux(X0,X1,X2,pair2(X3,X4)) = pair2(cons(X1,X3),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
fof(f2,axiom,
! [X2,X3,X0,X1] : aux2(X0,X1,X2,X3,btrue) = cons(X0,merge(X1,cons(X2,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X4] : aux3(X0,X1,X2,pair2(X3,X4)) = merge(msort(X3),msort(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
fof(f5,axiom,
! [X2,X0,X1] : aux4(X0,X1,X2,btrue) = s(count(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
fof(f6,axiom,
! [X2,X0,X1] : aux4(X0,X1,X2,bfalse) = count(X0,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(f7,plain,
! [X2,X0,X1] : count(X0,X2) = aux4(X0,X1,X2,bfalse),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0] : splitAtNat(z,X0) = pair2(nil,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
fof(f10,axiom,
! [X2,X0,X1] : splitAtNat(s(X0),cons(X1,X2)) = aux(X0,X1,X2,splitAtNat(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(f11,axiom,
! [X0] : leqNat(z,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
fof(f12,plain,
! [X0] : btrue = leqNat(z,X0),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X0] : leqNat(s(X0),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(f14,plain,
! [X0] : bfalse = leqNat(s(X0),z),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X0,X1] : leqNat(s(X0),s(X1)) = leqNat(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(f16,axiom,
! [X0] : merge(nil,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(f19,axiom,
! [X2,X3,X0,X1] : merge(cons(X0,X1),cons(X2,X3)) = aux2(X0,X1,X2,X3,leqNat(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
fof(f20,axiom,
lengthNat(nil) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
fof(f21,plain,
z = lengthNat(nil),
inference(reorient_equations,[],[f20]) ).
fof(f22,axiom,
! [X0,X1] : lengthNat(cons(X0,X1)) = s(lengthNat(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(f23,axiom,
! [X0] : impl(btrue,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
fof(f26,axiom,
div2(z) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
fof(f27,plain,
z = div2(z),
inference(reorient_equations,[],[f26]) ).
fof(f28,axiom,
div2(s(z)) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
fof(f29,plain,
z = div2(s(z)),
inference(reorient_equations,[],[f28]) ).
fof(f30,axiom,
! [X0] : div2(s(s(X0))) = s(div2(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
fof(f33,axiom,
! [X0] : msort(cons(X0,nil)) = cons(X0,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
fof(f34,plain,
! [X0] : cons(X0,nil) = msort(cons(X0,nil)),
inference(reorient_equations,[],[f33]) ).
fof(f35,axiom,
! [X2,X0,X1] : msort(cons(X0,cons(X1,X2))) = aux3(X0,X1,X2,splitAtNat(div2(lengthNat(cons(X0,cons(X1,X2)))),cons(X0,cons(X1,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
fof(f36,axiom,
! [X0] : count(X0,nil) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
fof(f37,plain,
! [X0] : z = count(X0,nil),
inference(reorient_equations,[],[f36]) ).
fof(f38,axiom,
! [X2,X0,X1] : count(X0,cons(X1,X2)) = aux4(X0,X1,X2,eq(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(f39,axiom,
! [X0,X1] : prop_msort_permutation_wrong1(X0,X1) = impl(eq2(leqNat(count(X1,X0),s(s(s(s(s(z)))))),bfalse),eq(count(X1,X0),count(s(X1),msort(X0)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
fof(f45,axiom,
! [X0] : eq(z,s(X0)) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
fof(f46,plain,
! [X0] : bfalse = eq(z,s(X0)),
inference(reorient_equations,[],[f45]) ).
fof(f47,axiom,
! [X0] : eq(s(X0),z) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_032) ).
fof(f48,plain,
! [X0] : bfalse = eq(s(X0),z),
inference(reorient_equations,[],[f47]) ).
fof(f49,axiom,
! [X0] : eq(X0,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_033) ).
fof(f50,plain,
! [X0] : btrue = eq(X0,X0),
inference(reorient_equations,[],[f49]) ).
fof(f51,axiom,
! [X0] : eq2(X0,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_034) ).
fof(f52,plain,
! [X0] : btrue = eq2(X0,X0),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
! [X0,X1] : eq2(prop_msort_permutation_wrong1(X0,X1),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f54,plain,
! [X0,X1] : btrue != eq2(prop_msort_permutation_wrong1(X0,X1),bfalse),
inference(reorient_equations,[],[f53]) ).
fof(f55,plain,
! [X0,X1] : btrue != eq2(impl(eq2(leqNat(count(X1,X0),s(s(s(s(s(z)))))),bfalse),eq(count(X1,X0),count(s(X1),msort(X0)))),bfalse),
inference(definition_unfolding,[],[f54,f39]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : aux(X0,X1,X2,pair2(X3,X4)) = pair2(cons(X1,X3),X4),
inference(cnf_transformation,[],[f1]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : cons(X0,merge(X1,cons(X2,X3))) = aux2(X0,X1,X2,X3,btrue),
inference(cnf_transformation,[],[f2]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : aux3(X0,X1,X2,pair2(X3,X4)) = merge(msort(X3),msort(X4)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] : aux4(X0,X1,X2,btrue) = s(count(X0,X2)),
inference(cnf_transformation,[],[f5]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] : aux4(X0,X1,X2,bfalse) = count(X0,X2),
inference(cnf_transformation,[],[f7]) ).
tcf(c_91,plain,
! [X0: $i] : pair2(nil,X0) = splitAtNat(z,X0),
inference(cnf_transformation,[],[f8]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i] : aux(X0,X1,X2,splitAtNat(X0,X2)) = splitAtNat(s(X0),cons(X1,X2)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_94,plain,
! [X0: $i] : leqNat(z,X0) = btrue,
inference(cnf_transformation,[],[f12]) ).
tcf(c_95,plain,
! [X0: $i] : leqNat(s(X0),z) = bfalse,
inference(cnf_transformation,[],[f14]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] : leqNat(s(X0),s(X1)) = leqNat(X0,X1),
inference(cnf_transformation,[],[f15]) ).
tcf(c_97,plain,
! [X0: $i] : merge(nil,X0) = X0,
inference(cnf_transformation,[],[f16]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : aux2(X0,X1,X2,X3,leqNat(X0,X2)) = merge(cons(X0,X1),cons(X2,X3)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_100,plain,
lengthNat(nil) = z,
inference(cnf_transformation,[],[f21]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] : lengthNat(cons(X0,X1)) = s(lengthNat(X1)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_102,plain,
! [X0: $i] : impl(btrue,X0) = X0,
inference(cnf_transformation,[],[f23]) ).
tcf(c_104,plain,
div2(z) = z,
inference(cnf_transformation,[],[f27]) ).
tcf(c_105,plain,
div2(s(z)) = z,
inference(cnf_transformation,[],[f29]) ).
tcf(c_106,plain,
! [X0: $i] : div2(s(s(X0))) = s(div2(X0)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_108,plain,
! [X0: $i] : msort(cons(X0,nil)) = cons(X0,nil),
inference(cnf_transformation,[],[f34]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] : aux3(X0,X1,X2,splitAtNat(div2(lengthNat(cons(X0,cons(X1,X2)))),cons(X0,cons(X1,X2)))) = msort(cons(X0,cons(X1,X2))),
inference(cnf_transformation,[],[f35]) ).
tcf(c_110,plain,
! [X0: $i] : count(X0,nil) = z,
inference(cnf_transformation,[],[f37]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] : aux4(X0,X1,X2,eq(X1,X0)) = count(X0,cons(X1,X2)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_115,plain,
! [X0: $i] : eq(z,s(X0)) = bfalse,
inference(cnf_transformation,[],[f46]) ).
tcf(c_116,plain,
! [X0: $i] : eq(s(X0),z) = bfalse,
inference(cnf_transformation,[],[f48]) ).
tcf(c_117,plain,
! [X0: $i] : eq(X0,X0) = btrue,
inference(cnf_transformation,[],[f50]) ).
tcf(c_118,plain,
! [X0: $i] : eq2(X0,X0) = btrue,
inference(cnf_transformation,[],[f52]) ).
tcf(c_119,negated_conjecture,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(count(X0,X1),s(s(s(s(s(z)))))),bfalse),eq(count(X0,X1),count(s(X0),msort(X1)))),bfalse) != btrue,
inference(cnf_transformation,[],[f55]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i,X2: $i] : aux3(X0,X1,X2,splitAtNat(s(div2(lengthNat(X2))),cons(X0,cons(X1,X2)))) = msort(cons(X0,cons(X1,X2))),
inference(demodulation,[status(thm)],[c_109,c_101,c_106]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i] : aux(z,X0,X1,pair2(nil,X1)) = splitAtNat(s(z),cons(X0,X1)),
inference(superposition,[status(thm)],[c_91,c_93]) ).
tcf(c_441,plain,
! [X0: $i,X1: $i,X2: $i] : merge(cons(z,X0),cons(X1,X2)) = aux2(z,X0,X1,X2,btrue),
inference(superposition,[status(thm)],[c_94,c_99]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i] : aux4(s(X0),z,X1,bfalse) = count(s(X0),cons(z,X1)),
inference(superposition,[status(thm)],[c_115,c_111]) ).
tcf(c_448,plain,
! [X0: $i,X1: $i] : aux4(X0,X0,X1,btrue) = count(X0,cons(X0,X1)),
inference(superposition,[status(thm)],[c_117,c_111]) ).
tcf(c_455,plain,
! [X0: $i,X1: $i] : aux3(X0,X1,nil,splitAtNat(s(div2(z)),cons(X0,cons(X1,nil)))) = msort(cons(X0,cons(X1,nil))),
inference(superposition,[status(thm)],[c_100,c_437]) ).
tcf(c_456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : aux3(X0,X1,cons(X2,X3),splitAtNat(s(div2(s(lengthNat(X3)))),cons(X0,cons(X1,cons(X2,X3))))) = msort(cons(X0,cons(X1,cons(X2,X3)))),
inference(superposition,[status(thm)],[c_101,c_437]) ).
tcf(c_457,plain,
! [X0: $i,X1: $i] : count(X0,cons(X0,X1)) = s(count(X0,X1)),
inference(demodulation,[status(thm)],[c_448,c_89]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i] : count(s(X0),cons(z,X1)) = count(s(X0),X1),
inference(demodulation,[status(thm)],[c_445,c_90]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i,X2: $i] : cons(z,merge(X0,cons(X1,X2))) = merge(cons(z,X0),cons(X1,X2)),
inference(demodulation,[status(thm)],[c_441,c_86]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i] : splitAtNat(s(z),cons(X0,X1)) = pair2(cons(X0,nil),X1),
inference(demodulation,[status(thm)],[c_439,c_85]) ).
tcf(c_464,plain,
! [X0: $i,X1: $i] : aux3(X0,X1,nil,splitAtNat(s(z),cons(X0,cons(X1,nil)))) = msort(cons(X0,cons(X1,nil))),
inference(light_normalisation,[status(thm)],[c_455,c_104]) ).
tcf(c_484,plain,
! [X0: $i,X1: $i,X2: $i] : aux3(X0,X1,cons(X2,nil),splitAtNat(s(div2(s(z))),cons(X0,cons(X1,cons(X2,nil))))) = msort(cons(X0,cons(X1,cons(X2,nil)))),
inference(superposition,[status(thm)],[c_100,c_456]) ).
tcf(c_485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : aux3(X0,X1,cons(X2,cons(X3,X4)),splitAtNat(s(div2(s(s(lengthNat(X4))))),cons(X0,cons(X1,cons(X2,cons(X3,X4)))))) = msort(cons(X0,cons(X1,cons(X2,cons(X3,X4))))),
inference(superposition,[status(thm)],[c_101,c_456]) ).
tcf(c_487,plain,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(s(count(X0,X1)),s(s(s(s(s(z)))))),bfalse),eq(s(count(X0,X1)),count(s(X0),msort(cons(X0,X1))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_457,c_119]) ).
tcf(c_498,plain,
! [X0: $i,X1: $i,X2: $i] : aux(s(z),X0,cons(X1,X2),pair2(cons(X1,nil),X2)) = splitAtNat(s(s(z)),cons(X0,cons(X1,X2))),
inference(superposition,[status(thm)],[c_461,c_93]) ).
tcf(c_504,plain,
! [X0: $i,X1: $i] : aux3(X0,X1,nil,pair2(cons(X0,nil),cons(X1,nil))) = msort(cons(X0,cons(X1,nil))),
inference(superposition,[status(thm)],[c_461,c_464]) ).
tcf(c_507,plain,
! [X0: $i,X1: $i] : merge(cons(X0,nil),cons(X1,nil)) = msort(cons(X0,cons(X1,nil))),
inference(demodulation,[status(thm)],[c_504,c_88,c_108]) ).
tcf(c_510,plain,
! [X0: $i,X1: $i,X2: $i] : splitAtNat(s(s(z)),cons(X0,cons(X1,X2))) = pair2(cons(X0,cons(X1,nil)),X2),
inference(demodulation,[status(thm)],[c_498,c_85]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i,X2: $i] : aux3(X0,X1,cons(X2,nil),splitAtNat(s(z),cons(X0,cons(X1,cons(X2,nil))))) = msort(cons(X0,cons(X1,cons(X2,nil)))),
inference(light_normalisation,[status(thm)],[c_484,c_105]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i,X2: $i] : merge(cons(X0,nil),msort(cons(X1,cons(X2,nil)))) = msort(cons(X0,cons(X1,cons(X2,nil)))),
inference(demodulation,[status(thm)],[c_512,c_88,c_108,c_461]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(count(X0,X1),s(s(s(s(z))))),bfalse),eq(s(count(X0,X1)),count(s(X0),msort(cons(X0,X1))))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_487,c_96]) ).
tcf(c_529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : aux3(X0,X1,cons(X2,cons(X3,X4)),splitAtNat(s(s(div2(lengthNat(X4)))),cons(X0,cons(X1,cons(X2,cons(X3,X4)))))) = msort(cons(X0,cons(X1,cons(X2,cons(X3,X4))))),
inference(demodulation,[status(thm)],[c_485,c_106]) ).
tcf(c_572,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : aux(s(s(z)),X0,cons(X1,cons(X2,X3)),pair2(cons(X1,cons(X2,nil)),X3)) = splitAtNat(s(s(s(z))),cons(X0,cons(X1,cons(X2,X3)))),
inference(superposition,[status(thm)],[c_510,c_93]) ).
tcf(c_594,plain,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(s(count(X0,X1)),s(s(s(s(z))))),bfalse),eq(s(s(count(X0,X1))),count(s(X0),msort(cons(X0,cons(X0,X1)))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_457,c_527]) ).
tcf(c_607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : aux3(X0,X1,cons(X2,cons(X3,cons(X4,X5))),splitAtNat(s(s(div2(s(lengthNat(X5))))),cons(X0,cons(X1,cons(X2,cons(X3,cons(X4,X5))))))) = msort(cons(X0,cons(X1,cons(X2,cons(X3,cons(X4,X5)))))),
inference(superposition,[status(thm)],[c_101,c_529]) ).
tcf(c_644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : splitAtNat(s(s(s(z))),cons(X0,cons(X1,cons(X2,X3)))) = pair2(cons(X0,cons(X1,cons(X2,nil))),X3),
inference(demodulation,[status(thm)],[c_572,c_85]) ).
tcf(c_648,plain,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(count(X0,X1),s(s(s(z)))),bfalse),eq(s(s(count(X0,X1))),count(s(X0),msort(cons(X0,cons(X0,X1)))))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_594,c_96]) ).
tcf(c_871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : aux3(X0,X1,cons(X2,cons(X3,cons(X4,cons(X5,X6)))),splitAtNat(s(s(div2(s(s(lengthNat(X6)))))),cons(X0,cons(X1,cons(X2,cons(X3,cons(X4,cons(X5,X6)))))))) = msort(cons(X0,cons(X1,cons(X2,cons(X3,cons(X4,cons(X5,X6))))))),
inference(superposition,[status(thm)],[c_101,c_607]) ).
tcf(c_911,plain,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(s(count(X0,X1)),s(s(s(z)))),bfalse),eq(s(s(s(count(X0,X1)))),count(s(X0),msort(cons(X0,cons(X0,cons(X0,X1))))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_457,c_648]) ).
tcf(c_1112,plain,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(count(X0,X1),s(s(z))),bfalse),eq(s(s(s(count(X0,X1)))),count(s(X0),msort(cons(X0,cons(X0,cons(X0,X1))))))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_911,c_96]) ).
tcf(c_1241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : aux3(X0,X1,cons(X2,cons(X3,cons(X4,cons(X5,X6)))),splitAtNat(s(s(s(div2(lengthNat(X6))))),cons(X0,cons(X1,cons(X2,cons(X3,cons(X4,cons(X5,X6)))))))) = msort(cons(X0,cons(X1,cons(X2,cons(X3,cons(X4,cons(X5,X6))))))),
inference(demodulation,[status(thm)],[c_871,c_106]) ).
tcf(c_2169,plain,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(s(count(X0,X1)),s(s(z))),bfalse),eq(s(s(s(s(count(X0,X1))))),count(s(X0),msort(cons(X0,cons(X0,cons(X0,cons(X0,X1)))))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_457,c_1112]) ).
tcf(c_2924,plain,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(count(X0,X1),s(z)),bfalse),eq(s(s(s(s(count(X0,X1))))),count(s(X0),msort(cons(X0,cons(X0,cons(X0,cons(X0,X1)))))))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_2169,c_96]) ).
tcf(c_5112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : aux3(X0,X1,cons(X2,cons(X3,cons(X4,cons(X5,nil)))),splitAtNat(s(s(s(div2(z)))),cons(X0,cons(X1,cons(X2,cons(X3,cons(X4,cons(X5,nil)))))))) = msort(cons(X0,cons(X1,cons(X2,cons(X3,cons(X4,cons(X5,nil))))))),
inference(superposition,[status(thm)],[c_100,c_1241]) ).
tcf(c_5814,plain,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(s(count(X0,X1)),s(z)),bfalse),eq(s(s(s(s(s(count(X0,X1)))))),count(s(X0),msort(cons(X0,cons(X0,cons(X0,cons(X0,cons(X0,X1))))))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_457,c_2924]) ).
tcf(c_6131,plain,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(count(X0,X1),z),bfalse),eq(s(s(s(s(s(count(X0,X1)))))),count(s(X0),msort(cons(X0,cons(X0,cons(X0,cons(X0,cons(X0,X1))))))))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_5814,c_96]) ).
tcf(c_6441,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : aux3(X0,X1,cons(X2,cons(X3,cons(X4,cons(X5,nil)))),splitAtNat(s(s(s(z))),cons(X0,cons(X1,cons(X2,cons(X3,cons(X4,cons(X5,nil)))))))) = msort(cons(X0,cons(X1,cons(X2,cons(X3,cons(X4,cons(X5,nil))))))),
inference(light_normalisation,[status(thm)],[c_5112,c_104]) ).
tcf(c_6442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : merge(merge(cons(X0,nil),merge(cons(X1,nil),cons(X2,nil))),merge(cons(X3,nil),merge(cons(X4,nil),cons(X5,nil)))) = msort(cons(X0,cons(X1,cons(X2,cons(X3,cons(X4,cons(X5,nil))))))),
inference(demodulation,[status(thm)],[c_6441,c_88,c_507,c_513,c_644]) ).
tcf(c_13061,plain,
! [X0: $i,X1: $i] : eq2(impl(eq2(leqNat(s(count(X0,X1)),z),bfalse),eq(s(s(s(s(s(s(count(X0,X1))))))),count(s(X0),msort(cons(X0,cons(X0,cons(X0,cons(X0,cons(X0,cons(X0,X1)))))))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_457,c_6131]) ).
tcf(c_14007,plain,
! [X0: $i,X1: $i] : eq2(eq(s(s(s(s(s(s(count(X0,X1))))))),count(s(X0),msort(cons(X0,cons(X0,cons(X0,cons(X0,cons(X0,cons(X0,X1))))))))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_13061,c_95,c_102,c_118]) ).
tcf(c_15216,plain,
! [X0: $i] : eq2(eq(s(s(s(s(s(s(z)))))),count(s(X0),msort(cons(X0,cons(X0,cons(X0,cons(X0,cons(X0,cons(X0,nil))))))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_110,c_14007]) ).
tcf(c_16005,plain,
! [X0: $i] : eq2(eq(s(s(s(s(s(s(z)))))),count(s(X0),merge(merge(cons(X0,nil),merge(cons(X0,nil),cons(X0,nil))),merge(cons(X0,nil),merge(cons(X0,nil),cons(X0,nil)))))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_15216,c_6442]) ).
tcf(c_24185,plain,
eq2(eq(s(s(s(s(s(s(z)))))),count(s(z),merge(merge(cons(z,nil),cons(z,merge(nil,cons(z,nil)))),merge(cons(z,nil),cons(z,merge(nil,cons(z,nil))))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_460,c_16005]) ).
tcf(c_25066,plain,
$false,
inference(ground_joinability,[status(thm)],[c_24185,c_97,c_110,c_116,c_118,c_459,c_460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX201-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 23:37:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running UEQ theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 1.98/16.88 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 1.98/16.88 % SZS status Started for theBenchmark.p
% 1.98/16.88 % SZS status Unsatisfiable for theBenchmark.p
% 1.98/16.88
% 1.98/16.88 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.98/16.88
% 1.98/16.88 % ------ iProver source info
% 1.98/16.88
% 1.98/16.88 % git: date: 2026-07-19 20:42:38 +0200
% 1.98/16.88 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.98/16.88 % git: non_committed_changes: false
% 1.98/16.88
% 1.98/16.88 % ------ Parsing...% successful
% 1.98/16.88
% 1.98/16.88
% 1.98/16.88 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.98/16.88
% 1.98/16.88 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.98/16.88
% 1.98/16.88 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.98/16.88
% 1.98/16.88 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.98/16.88 % ------ Proving...
% 1.98/16.88 % ------ Problem Properties
% 1.98/16.88
% 1.98/16.88 %
% 1.98/16.88 % clauses 35
% 1.98/16.88 % conjectures 1
% 1.98/16.88 % EPR 0
% 1.98/16.88 % Horn 35
% 1.98/16.88 % unary 35
% 1.98/16.88 % binary 0
% 1.98/16.88 % lits 35
% 1.98/16.88 % lits eq 35
% 1.98/16.88 % fd_pure 0
% 1.98/16.88 % fd_pseudo 0
% 1.98/16.88 % fd_cond 0
% 1.98/16.88 % fd_pseudo_cond 0
% 1.98/16.88 % AC symbols 0
% 1.98/16.88
% 1.98/16.88 % ------ Input Options Time Limit: Unbounded
% 1.98/16.88
% 1.98/16.88
% 1.98/16.88 % ------
% 1.98/16.88 % Current options:
% 1.98/16.88 % ------
% 1.98/16.88
% 1.98/16.88
% 1.98/16.88 %
% 1.98/16.88
% 1.98/16.88 % ------ Proving...
% 1.98/16.88 %
% 1.98/16.88
% 1.98/16.88 % SZS status Unsatisfiable for theBenchmark.p
% 1.98/16.88
% 1.98/16.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.98/16.88
% 1.98/16.88
%------------------------------------------------------------------------------